Monoclinic tridymite (295K) AlPO$_{4}$ Structure: AB4C_mP288_7_24a_96a_24a-001
| Prototype | AlO$_{4}$P |
| AFLOW prototype label | AB4C_mP288_7_24a_96a_24a-001 |
| ICSD | 280308 |
| CCDC | 1721024 |
| Pearson symbol | mP288 |
| Space group number | 7 |
| Space group symbol | $Pc$ |
| AFLOW prototype command |
aflow --proto=AB4C_mP288_7_24a_96a_24a-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak y_{18}, \allowbreak z_{18}, \allowbreak x_{19}, \allowbreak y_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak y_{20}, \allowbreak z_{20}, \allowbreak x_{21}, \allowbreak y_{21}, \allowbreak z_{21}, \allowbreak x_{22}, \allowbreak y_{22}, \allowbreak z_{22}, \allowbreak x_{23}, \allowbreak y_{23}, \allowbreak z_{23}, \allowbreak x_{24}, \allowbreak y_{24}, \allowbreak z_{24}, \allowbreak x_{25}, \allowbreak y_{25}, \allowbreak z_{25}, \allowbreak x_{26}, \allowbreak y_{26}, \allowbreak z_{26}, \allowbreak x_{27}, \allowbreak y_{27}, \allowbreak z_{27}, \allowbreak x_{28}, \allowbreak y_{28}, \allowbreak z_{28}, \allowbreak x_{29}, \allowbreak y_{29}, \allowbreak z_{29}, \allowbreak x_{30}, \allowbreak y_{30}, \allowbreak z_{30}, \allowbreak x_{31}, \allowbreak y_{31}, \allowbreak z_{31}, \allowbreak x_{32}, \allowbreak y_{32}, \allowbreak z_{32}, \allowbreak x_{33}, \allowbreak y_{33}, \allowbreak z_{33}, \allowbreak x_{34}, \allowbreak y_{34}, \allowbreak z_{34}, \allowbreak x_{35}, \allowbreak y_{35}, \allowbreak z_{35}, \allowbreak x_{36}, \allowbreak y_{36}, \allowbreak z_{36}, \allowbreak x_{37}, \allowbreak y_{37}, \allowbreak z_{37}, \allowbreak x_{38}, \allowbreak y_{38}, \allowbreak z_{38}, \allowbreak x_{39}, \allowbreak y_{39}, \allowbreak z_{39}, \allowbreak x_{40}, \allowbreak y_{40}, \allowbreak z_{40}, \allowbreak x_{41}, \allowbreak y_{41}, \allowbreak z_{41}, \allowbreak x_{42}, \allowbreak y_{42}, \allowbreak z_{42}, \allowbreak x_{43}, \allowbreak y_{43}, \allowbreak z_{43}, \allowbreak x_{44}, \allowbreak y_{44}, \allowbreak z_{44}, \allowbreak x_{45}, \allowbreak y_{45}, \allowbreak z_{45}, \allowbreak x_{46}, \allowbreak y_{46}, \allowbreak z_{46}, \allowbreak x_{47}, \allowbreak y_{47}, \allowbreak z_{47}, \allowbreak x_{48}, \allowbreak y_{48}, \allowbreak z_{48}, \allowbreak x_{49}, \allowbreak y_{49}, \allowbreak z_{49}, \allowbreak x_{50}, \allowbreak y_{50}, \allowbreak z_{50}, \allowbreak x_{51}, \allowbreak y_{51}, \allowbreak z_{51}, \allowbreak x_{52}, \allowbreak y_{52}, \allowbreak z_{52}, \allowbreak x_{53}, \allowbreak y_{53}, \allowbreak z_{53}, \allowbreak x_{54}, \allowbreak y_{54}, \allowbreak z_{54}, \allowbreak x_{55}, \allowbreak y_{55}, \allowbreak z_{55}, \allowbreak x_{56}, \allowbreak y_{56}, \allowbreak z_{56}, \allowbreak x_{57}, \allowbreak y_{57}, \allowbreak z_{57}, \allowbreak x_{58}, \allowbreak y_{58}, \allowbreak z_{58}, \allowbreak x_{59}, \allowbreak y_{59}, \allowbreak z_{59}, \allowbreak x_{60}, \allowbreak y_{60}, \allowbreak z_{60}, \allowbreak x_{61}, \allowbreak y_{61}, \allowbreak z_{61}, \allowbreak x_{62}, \allowbreak y_{62}, \allowbreak z_{62}, \allowbreak x_{63}, \allowbreak y_{63}, \allowbreak z_{63}, \allowbreak x_{64}, \allowbreak y_{64}, \allowbreak z_{64}, \allowbreak x_{65}, \allowbreak y_{65}, \allowbreak z_{65}, \allowbreak x_{66}, \allowbreak y_{66}, \allowbreak z_{66}, \allowbreak x_{67}, \allowbreak y_{67}, \allowbreak z_{67}, \allowbreak x_{68}, \allowbreak y_{68}, \allowbreak z_{68}, \allowbreak x_{69}, \allowbreak y_{69}, \allowbreak z_{69}, \allowbreak x_{70}, \allowbreak y_{70}, \allowbreak z_{70}, \allowbreak x_{71}, \allowbreak y_{71}, \allowbreak z_{71}, \allowbreak x_{72}, \allowbreak y_{72}, \allowbreak z_{72}, \allowbreak x_{73}, \allowbreak y_{73}, \allowbreak z_{73}, \allowbreak x_{74}, \allowbreak y_{74}, \allowbreak z_{74}, \allowbreak x_{75}, \allowbreak y_{75}, \allowbreak z_{75}, \allowbreak x_{76}, \allowbreak y_{76}, \allowbreak z_{76}, \allowbreak x_{77}, \allowbreak y_{77}, \allowbreak z_{77}, \allowbreak x_{78}, \allowbreak y_{78}, \allowbreak z_{78}, \allowbreak x_{79}, \allowbreak y_{79}, \allowbreak z_{79}, \allowbreak x_{80}, \allowbreak y_{80}, \allowbreak z_{80}, \allowbreak x_{81}, \allowbreak y_{81}, \allowbreak z_{81}, \allowbreak x_{82}, \allowbreak y_{82}, \allowbreak z_{82}, \allowbreak x_{83}, \allowbreak y_{83}, \allowbreak z_{83}, \allowbreak x_{84}, \allowbreak y_{84}, \allowbreak z_{84}, \allowbreak x_{85}, \allowbreak y_{85}, \allowbreak z_{85}, \allowbreak x_{86}, \allowbreak y_{86}, \allowbreak z_{86}, \allowbreak x_{87}, \allowbreak y_{87}, \allowbreak z_{87}, \allowbreak x_{88}, \allowbreak y_{88}, \allowbreak z_{88}, \allowbreak x_{89}, \allowbreak y_{89}, \allowbreak z_{89}, \allowbreak x_{90}, \allowbreak y_{90}, \allowbreak z_{90}, \allowbreak x_{91}, \allowbreak y_{91}, \allowbreak z_{91}, \allowbreak x_{92}, \allowbreak y_{92}, \allowbreak z_{92}, \allowbreak x_{93}, \allowbreak y_{93}, \allowbreak z_{93}, \allowbreak x_{94}, \allowbreak y_{94}, \allowbreak z_{94}, \allowbreak x_{95}, \allowbreak y_{95}, \allowbreak z_{95}, \allowbreak x_{96}, \allowbreak y_{96}, \allowbreak z_{96}, \allowbreak x_{97}, \allowbreak y_{97}, \allowbreak z_{97}, \allowbreak x_{98}, \allowbreak y_{98}, \allowbreak z_{98}, \allowbreak x_{99}, \allowbreak y_{99}, \allowbreak z_{99}, \allowbreak x_{100}, \allowbreak y_{100}, \allowbreak z_{100}, \allowbreak x_{101}, \allowbreak y_{101}, \allowbreak z_{101}, \allowbreak x_{102}, \allowbreak y_{102}, \allowbreak z_{102}, \allowbreak x_{103}, \allowbreak y_{103}, \allowbreak z_{103}, \allowbreak x_{104}, \allowbreak y_{104}, \allowbreak z_{104}, \allowbreak x_{105}, \allowbreak y_{105}, \allowbreak z_{105}, \allowbreak x_{106}, \allowbreak y_{106}, \allowbreak z_{106}, \allowbreak x_{107}, \allowbreak y_{107}, \allowbreak z_{107}, \allowbreak x_{108}, \allowbreak y_{108}, \allowbreak z_{108}, \allowbreak x_{109}, \allowbreak y_{109}, \allowbreak z_{109}, \allowbreak x_{110}, \allowbreak y_{110}, \allowbreak z_{110}, \allowbreak x_{111}, \allowbreak y_{111}, \allowbreak z_{111}, \allowbreak x_{112}, \allowbreak y_{112}, \allowbreak z_{112}, \allowbreak x_{113}, \allowbreak y_{113}, \allowbreak z_{113}, \allowbreak x_{114}, \allowbreak y_{114}, \allowbreak z_{114}, \allowbreak x_{115}, \allowbreak y_{115}, \allowbreak z_{115}, \allowbreak x_{116}, \allowbreak y_{116}, \allowbreak z_{116}, \allowbreak x_{117}, \allowbreak y_{117}, \allowbreak z_{117}, \allowbreak x_{118}, \allowbreak y_{118}, \allowbreak z_{118}, \allowbreak x_{119}, \allowbreak y_{119}, \allowbreak z_{119}, \allowbreak x_{120}, \allowbreak y_{120}, \allowbreak z_{120}, \allowbreak x_{121}, \allowbreak y_{121}, \allowbreak z_{121}, \allowbreak x_{122}, \allowbreak y_{122}, \allowbreak z_{122}, \allowbreak x_{123}, \allowbreak y_{123}, \allowbreak z_{123}, \allowbreak x_{124}, \allowbreak y_{124}, \allowbreak z_{124}, \allowbreak x_{125}, \allowbreak y_{125}, \allowbreak z_{125}, \allowbreak x_{126}, \allowbreak y_{126}, \allowbreak z_{126}, \allowbreak x_{127}, \allowbreak y_{127}, \allowbreak z_{127}, \allowbreak x_{128}, \allowbreak y_{128}, \allowbreak z_{128}, \allowbreak x_{129}, \allowbreak y_{129}, \allowbreak z_{129}, \allowbreak x_{130}, \allowbreak y_{130}, \allowbreak z_{130}, \allowbreak x_{131}, \allowbreak y_{131}, \allowbreak z_{131}, \allowbreak x_{132}, \allowbreak y_{132}, \allowbreak z_{132}, \allowbreak x_{133}, \allowbreak y_{133}, \allowbreak z_{133}, \allowbreak x_{134}, \allowbreak y_{134}, \allowbreak z_{134}, \allowbreak x_{135}, \allowbreak y_{135}, \allowbreak z_{135}, \allowbreak x_{136}, \allowbreak y_{136}, \allowbreak z_{136}, \allowbreak x_{137}, \allowbreak y_{137}, \allowbreak z_{137}, \allowbreak x_{138}, \allowbreak y_{138}, \allowbreak z_{138}, \allowbreak x_{139}, \allowbreak y_{139}, \allowbreak z_{139}, \allowbreak x_{140}, \allowbreak y_{140}, \allowbreak z_{140}, \allowbreak x_{141}, \allowbreak y_{141}, \allowbreak z_{141}, \allowbreak x_{142}, \allowbreak y_{142}, \allowbreak z_{142}, \allowbreak x_{143}, \allowbreak y_{143}, \allowbreak z_{143}, \allowbreak x_{144}, \allowbreak y_{144}, \allowbreak z_{144}$ |
- The tridymite form of AlPO$_{4}$ is related to the tridymite forms of SiO$_{2}$. Like SiO$_{2}$ it undergoes a series of temperature driven phase transitions (Graetsch, 2002):
- The high temperature form is hexagonal, space group $P6_3mc$ #186 at temperatures above ≈ 590K
- The first intermediate form is monoclinic, space group $P2_{1}$ #4 at temperatures above ≈ 460K
- The second intermediate form, $P2_{1}(\alpha\beta0)$, is incommensurate but averages to a structure similar to the previous one
- This is followed by an orthorhombic form, space group $P2_{1}2_{1}2_{1}$ #19, for which we have no data.
- Near room temperature we find another monoclinic structure, space group $Pc$ #7 (this structure)
- The low temperature structure is triclinic, space group $P1$ #1, also measured at room temperature.
- The astute reader will recognize that we are very vague about these phase transitions, as we have found no definitive phase diagram.
- For more information on realted structures see our silica and aluminum phosphate page.
- Data for this structure was taken at 295K.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}+c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al I |
| $\mathbf{B_{2}}$ | = | $x_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{1} + c \left(z_{1} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al II |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{2} + c \left(z_{2} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al II |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al III |
| $\mathbf{B_{6}}$ | = | $x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c \left(z_{3} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al III |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al IV |
| $\mathbf{B_{8}}$ | = | $x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c \left(z_{4} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al IV |
| $\mathbf{B_{9}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al V |
| $\mathbf{B_{10}}$ | = | $x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c \left(z_{5} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al V |
| $\mathbf{B_{11}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al VI |
| $\mathbf{B_{12}}$ | = | $x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c \left(z_{6} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al VI |
| $\mathbf{B_{13}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}+c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al VII |
| $\mathbf{B_{14}}$ | = | $x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{7} + c \left(z_{7} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al VII |
| $\mathbf{B_{15}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al VIII |
| $\mathbf{B_{16}}$ | = | $x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{8} + c \left(z_{8} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al VIII |
| $\mathbf{B_{17}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al IX |
| $\mathbf{B_{18}}$ | = | $x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{9} + c \left(z_{9} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al IX |
| $\mathbf{B_{19}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al X |
| $\mathbf{B_{20}}$ | = | $x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{10} + c \left(z_{10} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al X |
| $\mathbf{B_{21}}$ | = | $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\left(a x_{11} + c z_{11} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c z_{11} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XI |
| $\mathbf{B_{22}}$ | = | $x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{11} + c \left(z_{11} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XI |
| $\mathbf{B_{23}}$ | = | $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\left(a x_{12} + c z_{12} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}+c z_{12} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XII |
| $\mathbf{B_{24}}$ | = | $x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{12} + c \left(z_{12} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XII |
| $\mathbf{B_{25}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\left(a x_{13} + c z_{13} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}+c z_{13} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XIII |
| $\mathbf{B_{26}}$ | = | $x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{13} + c \left(z_{13} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XIII |
| $\mathbf{B_{27}}$ | = | $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\left(a x_{14} + c z_{14} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}+c z_{14} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XIV |
| $\mathbf{B_{28}}$ | = | $x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{14} + c \left(z_{14} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XIV |
| $\mathbf{B_{29}}$ | = | $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\left(a x_{15} + c z_{15} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{15} \,\mathbf{\hat{y}}+c z_{15} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XV |
| $\mathbf{B_{30}}$ | = | $x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{15} + c \left(z_{15} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XV |
| $\mathbf{B_{31}}$ | = | $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\left(a x_{16} + c z_{16} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{16} \,\mathbf{\hat{y}}+c z_{16} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XVI |
| $\mathbf{B_{32}}$ | = | $x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{16} + c \left(z_{16} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XVI |
| $\mathbf{B_{33}}$ | = | $x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\left(a x_{17} + c z_{17} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{17} \,\mathbf{\hat{y}}+c z_{17} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XVII |
| $\mathbf{B_{34}}$ | = | $x_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{17} + c \left(z_{17} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XVII |
| $\mathbf{B_{35}}$ | = | $x_{18} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $\left(a x_{18} + c z_{18} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{18} \,\mathbf{\hat{y}}+c z_{18} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XVIII |
| $\mathbf{B_{36}}$ | = | $x_{18} \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{18} + c \left(z_{18} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XVIII |
| $\mathbf{B_{37}}$ | = | $x_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $\left(a x_{19} + c z_{19} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{19} \,\mathbf{\hat{y}}+c z_{19} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XIX |
| $\mathbf{B_{38}}$ | = | $x_{19} \, \mathbf{a}_{1}- y_{19} \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{19} + c \left(z_{19} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{19} \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XIX |
| $\mathbf{B_{39}}$ | = | $x_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $\left(a x_{20} + c z_{20} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{20} \,\mathbf{\hat{y}}+c z_{20} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XX |
| $\mathbf{B_{40}}$ | = | $x_{20} \, \mathbf{a}_{1}- y_{20} \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{20} + c \left(z_{20} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{20} \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XX |
| $\mathbf{B_{41}}$ | = | $x_{21} \, \mathbf{a}_{1}+y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $\left(a x_{21} + c z_{21} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{21} \,\mathbf{\hat{y}}+c z_{21} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XXI |
| $\mathbf{B_{42}}$ | = | $x_{21} \, \mathbf{a}_{1}- y_{21} \, \mathbf{a}_{2}+\left(z_{21} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{21} + c \left(z_{21} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{21} \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XXI |
| $\mathbf{B_{43}}$ | = | $x_{22} \, \mathbf{a}_{1}+y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $\left(a x_{22} + c z_{22} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{22} \,\mathbf{\hat{y}}+c z_{22} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XXII |
| $\mathbf{B_{44}}$ | = | $x_{22} \, \mathbf{a}_{1}- y_{22} \, \mathbf{a}_{2}+\left(z_{22} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{22} + c \left(z_{22} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{22} \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XXII |
| $\mathbf{B_{45}}$ | = | $x_{23} \, \mathbf{a}_{1}+y_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $\left(a x_{23} + c z_{23} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{23} \,\mathbf{\hat{y}}+c z_{23} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XXIII |
| $\mathbf{B_{46}}$ | = | $x_{23} \, \mathbf{a}_{1}- y_{23} \, \mathbf{a}_{2}+\left(z_{23} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{23} + c \left(z_{23} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{23} \,\mathbf{\hat{y}}+c \left(z_{23} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XXIII |
| $\mathbf{B_{47}}$ | = | $x_{24} \, \mathbf{a}_{1}+y_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $\left(a x_{24} + c z_{24} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{24} \,\mathbf{\hat{y}}+c z_{24} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XXIV |
| $\mathbf{B_{48}}$ | = | $x_{24} \, \mathbf{a}_{1}- y_{24} \, \mathbf{a}_{2}+\left(z_{24} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{24} + c \left(z_{24} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{24} \,\mathbf{\hat{y}}+c \left(z_{24} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XXIV |
| $\mathbf{B_{49}}$ | = | $x_{25} \, \mathbf{a}_{1}+y_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $\left(a x_{25} + c z_{25} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{25} \,\mathbf{\hat{y}}+c z_{25} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O I |
| $\mathbf{B_{50}}$ | = | $x_{25} \, \mathbf{a}_{1}- y_{25} \, \mathbf{a}_{2}+\left(z_{25} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{25} + c \left(z_{25} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{25} \,\mathbf{\hat{y}}+c \left(z_{25} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O I |
| $\mathbf{B_{51}}$ | = | $x_{26} \, \mathbf{a}_{1}+y_{26} \, \mathbf{a}_{2}+z_{26} \, \mathbf{a}_{3}$ | = | $\left(a x_{26} + c z_{26} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{26} \,\mathbf{\hat{y}}+c z_{26} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O II |
| $\mathbf{B_{52}}$ | = | $x_{26} \, \mathbf{a}_{1}- y_{26} \, \mathbf{a}_{2}+\left(z_{26} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{26} + c \left(z_{26} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{26} \,\mathbf{\hat{y}}+c \left(z_{26} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O II |
| $\mathbf{B_{53}}$ | = | $x_{27} \, \mathbf{a}_{1}+y_{27} \, \mathbf{a}_{2}+z_{27} \, \mathbf{a}_{3}$ | = | $\left(a x_{27} + c z_{27} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{27} \,\mathbf{\hat{y}}+c z_{27} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O III |
| $\mathbf{B_{54}}$ | = | $x_{27} \, \mathbf{a}_{1}- y_{27} \, \mathbf{a}_{2}+\left(z_{27} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{27} + c \left(z_{27} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{27} \,\mathbf{\hat{y}}+c \left(z_{27} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O III |
| $\mathbf{B_{55}}$ | = | $x_{28} \, \mathbf{a}_{1}+y_{28} \, \mathbf{a}_{2}+z_{28} \, \mathbf{a}_{3}$ | = | $\left(a x_{28} + c z_{28} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{28} \,\mathbf{\hat{y}}+c z_{28} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O IV |
| $\mathbf{B_{56}}$ | = | $x_{28} \, \mathbf{a}_{1}- y_{28} \, \mathbf{a}_{2}+\left(z_{28} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{28} + c \left(z_{28} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{28} \,\mathbf{\hat{y}}+c \left(z_{28} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O IV |
| $\mathbf{B_{57}}$ | = | $x_{29} \, \mathbf{a}_{1}+y_{29} \, \mathbf{a}_{2}+z_{29} \, \mathbf{a}_{3}$ | = | $\left(a x_{29} + c z_{29} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{29} \,\mathbf{\hat{y}}+c z_{29} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O V |
| $\mathbf{B_{58}}$ | = | $x_{29} \, \mathbf{a}_{1}- y_{29} \, \mathbf{a}_{2}+\left(z_{29} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{29} + c \left(z_{29} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{29} \,\mathbf{\hat{y}}+c \left(z_{29} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O V |
| $\mathbf{B_{59}}$ | = | $x_{30} \, \mathbf{a}_{1}+y_{30} \, \mathbf{a}_{2}+z_{30} \, \mathbf{a}_{3}$ | = | $\left(a x_{30} + c z_{30} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{30} \,\mathbf{\hat{y}}+c z_{30} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O VI |
| $\mathbf{B_{60}}$ | = | $x_{30} \, \mathbf{a}_{1}- y_{30} \, \mathbf{a}_{2}+\left(z_{30} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{30} + c \left(z_{30} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{30} \,\mathbf{\hat{y}}+c \left(z_{30} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O VI |
| $\mathbf{B_{61}}$ | = | $x_{31} \, \mathbf{a}_{1}+y_{31} \, \mathbf{a}_{2}+z_{31} \, \mathbf{a}_{3}$ | = | $\left(a x_{31} + c z_{31} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{31} \,\mathbf{\hat{y}}+c z_{31} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O VII |
| $\mathbf{B_{62}}$ | = | $x_{31} \, \mathbf{a}_{1}- y_{31} \, \mathbf{a}_{2}+\left(z_{31} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{31} + c \left(z_{31} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{31} \,\mathbf{\hat{y}}+c \left(z_{31} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O VII |
| $\mathbf{B_{63}}$ | = | $x_{32} \, \mathbf{a}_{1}+y_{32} \, \mathbf{a}_{2}+z_{32} \, \mathbf{a}_{3}$ | = | $\left(a x_{32} + c z_{32} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{32} \,\mathbf{\hat{y}}+c z_{32} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O VIII |
| $\mathbf{B_{64}}$ | = | $x_{32} \, \mathbf{a}_{1}- y_{32} \, \mathbf{a}_{2}+\left(z_{32} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{32} + c \left(z_{32} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{32} \,\mathbf{\hat{y}}+c \left(z_{32} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O VIII |
| $\mathbf{B_{65}}$ | = | $x_{33} \, \mathbf{a}_{1}+y_{33} \, \mathbf{a}_{2}+z_{33} \, \mathbf{a}_{3}$ | = | $\left(a x_{33} + c z_{33} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{33} \,\mathbf{\hat{y}}+c z_{33} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O IX |
| $\mathbf{B_{66}}$ | = | $x_{33} \, \mathbf{a}_{1}- y_{33} \, \mathbf{a}_{2}+\left(z_{33} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{33} + c \left(z_{33} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{33} \,\mathbf{\hat{y}}+c \left(z_{33} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O IX |
| $\mathbf{B_{67}}$ | = | $x_{34} \, \mathbf{a}_{1}+y_{34} \, \mathbf{a}_{2}+z_{34} \, \mathbf{a}_{3}$ | = | $\left(a x_{34} + c z_{34} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{34} \,\mathbf{\hat{y}}+c z_{34} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O X |
| $\mathbf{B_{68}}$ | = | $x_{34} \, \mathbf{a}_{1}- y_{34} \, \mathbf{a}_{2}+\left(z_{34} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{34} + c \left(z_{34} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{34} \,\mathbf{\hat{y}}+c \left(z_{34} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O X |
| $\mathbf{B_{69}}$ | = | $x_{35} \, \mathbf{a}_{1}+y_{35} \, \mathbf{a}_{2}+z_{35} \, \mathbf{a}_{3}$ | = | $\left(a x_{35} + c z_{35} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{35} \,\mathbf{\hat{y}}+c z_{35} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XI |
| $\mathbf{B_{70}}$ | = | $x_{35} \, \mathbf{a}_{1}- y_{35} \, \mathbf{a}_{2}+\left(z_{35} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{35} + c \left(z_{35} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{35} \,\mathbf{\hat{y}}+c \left(z_{35} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XI |
| $\mathbf{B_{71}}$ | = | $x_{36} \, \mathbf{a}_{1}+y_{36} \, \mathbf{a}_{2}+z_{36} \, \mathbf{a}_{3}$ | = | $\left(a x_{36} + c z_{36} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{36} \,\mathbf{\hat{y}}+c z_{36} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XII |
| $\mathbf{B_{72}}$ | = | $x_{36} \, \mathbf{a}_{1}- y_{36} \, \mathbf{a}_{2}+\left(z_{36} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{36} + c \left(z_{36} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{36} \,\mathbf{\hat{y}}+c \left(z_{36} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XII |
| $\mathbf{B_{73}}$ | = | $x_{37} \, \mathbf{a}_{1}+y_{37} \, \mathbf{a}_{2}+z_{37} \, \mathbf{a}_{3}$ | = | $\left(a x_{37} + c z_{37} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{37} \,\mathbf{\hat{y}}+c z_{37} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XIII |
| $\mathbf{B_{74}}$ | = | $x_{37} \, \mathbf{a}_{1}- y_{37} \, \mathbf{a}_{2}+\left(z_{37} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{37} + c \left(z_{37} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{37} \,\mathbf{\hat{y}}+c \left(z_{37} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XIII |
| $\mathbf{B_{75}}$ | = | $x_{38} \, \mathbf{a}_{1}+y_{38} \, \mathbf{a}_{2}+z_{38} \, \mathbf{a}_{3}$ | = | $\left(a x_{38} + c z_{38} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{38} \,\mathbf{\hat{y}}+c z_{38} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XIV |
| $\mathbf{B_{76}}$ | = | $x_{38} \, \mathbf{a}_{1}- y_{38} \, \mathbf{a}_{2}+\left(z_{38} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{38} + c \left(z_{38} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{38} \,\mathbf{\hat{y}}+c \left(z_{38} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XIV |
| $\mathbf{B_{77}}$ | = | $x_{39} \, \mathbf{a}_{1}+y_{39} \, \mathbf{a}_{2}+z_{39} \, \mathbf{a}_{3}$ | = | $\left(a x_{39} + c z_{39} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{39} \,\mathbf{\hat{y}}+c z_{39} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XV |
| $\mathbf{B_{78}}$ | = | $x_{39} \, \mathbf{a}_{1}- y_{39} \, \mathbf{a}_{2}+\left(z_{39} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{39} + c \left(z_{39} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{39} \,\mathbf{\hat{y}}+c \left(z_{39} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XV |
| $\mathbf{B_{79}}$ | = | $x_{40} \, \mathbf{a}_{1}+y_{40} \, \mathbf{a}_{2}+z_{40} \, \mathbf{a}_{3}$ | = | $\left(a x_{40} + c z_{40} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{40} \,\mathbf{\hat{y}}+c z_{40} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XVI |
| $\mathbf{B_{80}}$ | = | $x_{40} \, \mathbf{a}_{1}- y_{40} \, \mathbf{a}_{2}+\left(z_{40} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{40} + c \left(z_{40} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{40} \,\mathbf{\hat{y}}+c \left(z_{40} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XVI |
| $\mathbf{B_{81}}$ | = | $x_{41} \, \mathbf{a}_{1}+y_{41} \, \mathbf{a}_{2}+z_{41} \, \mathbf{a}_{3}$ | = | $\left(a x_{41} + c z_{41} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{41} \,\mathbf{\hat{y}}+c z_{41} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XVII |
| $\mathbf{B_{82}}$ | = | $x_{41} \, \mathbf{a}_{1}- y_{41} \, \mathbf{a}_{2}+\left(z_{41} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{41} + c \left(z_{41} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{41} \,\mathbf{\hat{y}}+c \left(z_{41} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XVII |
| $\mathbf{B_{83}}$ | = | $x_{42} \, \mathbf{a}_{1}+y_{42} \, \mathbf{a}_{2}+z_{42} \, \mathbf{a}_{3}$ | = | $\left(a x_{42} + c z_{42} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{42} \,\mathbf{\hat{y}}+c z_{42} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XVIII |
| $\mathbf{B_{84}}$ | = | $x_{42} \, \mathbf{a}_{1}- y_{42} \, \mathbf{a}_{2}+\left(z_{42} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{42} + c \left(z_{42} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{42} \,\mathbf{\hat{y}}+c \left(z_{42} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XVIII |
| $\mathbf{B_{85}}$ | = | $x_{43} \, \mathbf{a}_{1}+y_{43} \, \mathbf{a}_{2}+z_{43} \, \mathbf{a}_{3}$ | = | $\left(a x_{43} + c z_{43} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{43} \,\mathbf{\hat{y}}+c z_{43} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XIX |
| $\mathbf{B_{86}}$ | = | $x_{43} \, \mathbf{a}_{1}- y_{43} \, \mathbf{a}_{2}+\left(z_{43} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{43} + c \left(z_{43} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{43} \,\mathbf{\hat{y}}+c \left(z_{43} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XIX |
| $\mathbf{B_{87}}$ | = | $x_{44} \, \mathbf{a}_{1}+y_{44} \, \mathbf{a}_{2}+z_{44} \, \mathbf{a}_{3}$ | = | $\left(a x_{44} + c z_{44} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{44} \,\mathbf{\hat{y}}+c z_{44} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XX |
| $\mathbf{B_{88}}$ | = | $x_{44} \, \mathbf{a}_{1}- y_{44} \, \mathbf{a}_{2}+\left(z_{44} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{44} + c \left(z_{44} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{44} \,\mathbf{\hat{y}}+c \left(z_{44} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XX |
| $\mathbf{B_{89}}$ | = | $x_{45} \, \mathbf{a}_{1}+y_{45} \, \mathbf{a}_{2}+z_{45} \, \mathbf{a}_{3}$ | = | $\left(a x_{45} + c z_{45} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{45} \,\mathbf{\hat{y}}+c z_{45} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXI |
| $\mathbf{B_{90}}$ | = | $x_{45} \, \mathbf{a}_{1}- y_{45} \, \mathbf{a}_{2}+\left(z_{45} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{45} + c \left(z_{45} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{45} \,\mathbf{\hat{y}}+c \left(z_{45} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXI |
| $\mathbf{B_{91}}$ | = | $x_{46} \, \mathbf{a}_{1}+y_{46} \, \mathbf{a}_{2}+z_{46} \, \mathbf{a}_{3}$ | = | $\left(a x_{46} + c z_{46} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{46} \,\mathbf{\hat{y}}+c z_{46} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXII |
| $\mathbf{B_{92}}$ | = | $x_{46} \, \mathbf{a}_{1}- y_{46} \, \mathbf{a}_{2}+\left(z_{46} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{46} + c \left(z_{46} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{46} \,\mathbf{\hat{y}}+c \left(z_{46} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXII |
| $\mathbf{B_{93}}$ | = | $x_{47} \, \mathbf{a}_{1}+y_{47} \, \mathbf{a}_{2}+z_{47} \, \mathbf{a}_{3}$ | = | $\left(a x_{47} + c z_{47} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{47} \,\mathbf{\hat{y}}+c z_{47} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXIII |
| $\mathbf{B_{94}}$ | = | $x_{47} \, \mathbf{a}_{1}- y_{47} \, \mathbf{a}_{2}+\left(z_{47} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{47} + c \left(z_{47} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{47} \,\mathbf{\hat{y}}+c \left(z_{47} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXIII |
| $\mathbf{B_{95}}$ | = | $x_{48} \, \mathbf{a}_{1}+y_{48} \, \mathbf{a}_{2}+z_{48} \, \mathbf{a}_{3}$ | = | $\left(a x_{48} + c z_{48} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{48} \,\mathbf{\hat{y}}+c z_{48} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXIV |
| $\mathbf{B_{96}}$ | = | $x_{48} \, \mathbf{a}_{1}- y_{48} \, \mathbf{a}_{2}+\left(z_{48} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{48} + c \left(z_{48} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{48} \,\mathbf{\hat{y}}+c \left(z_{48} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXIV |
| $\mathbf{B_{97}}$ | = | $x_{49} \, \mathbf{a}_{1}+y_{49} \, \mathbf{a}_{2}+z_{49} \, \mathbf{a}_{3}$ | = | $\left(a x_{49} + c z_{49} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{49} \,\mathbf{\hat{y}}+c z_{49} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXV |
| $\mathbf{B_{98}}$ | = | $x_{49} \, \mathbf{a}_{1}- y_{49} \, \mathbf{a}_{2}+\left(z_{49} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{49} + c \left(z_{49} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{49} \,\mathbf{\hat{y}}+c \left(z_{49} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXV |
| $\mathbf{B_{99}}$ | = | $x_{50} \, \mathbf{a}_{1}+y_{50} \, \mathbf{a}_{2}+z_{50} \, \mathbf{a}_{3}$ | = | $\left(a x_{50} + c z_{50} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{50} \,\mathbf{\hat{y}}+c z_{50} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXVI |
| $\mathbf{B_{100}}$ | = | $x_{50} \, \mathbf{a}_{1}- y_{50} \, \mathbf{a}_{2}+\left(z_{50} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{50} + c \left(z_{50} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{50} \,\mathbf{\hat{y}}+c \left(z_{50} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXVI |
| $\mathbf{B_{101}}$ | = | $x_{51} \, \mathbf{a}_{1}+y_{51} \, \mathbf{a}_{2}+z_{51} \, \mathbf{a}_{3}$ | = | $\left(a x_{51} + c z_{51} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{51} \,\mathbf{\hat{y}}+c z_{51} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXVII |
| $\mathbf{B_{102}}$ | = | $x_{51} \, \mathbf{a}_{1}- y_{51} \, \mathbf{a}_{2}+\left(z_{51} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{51} + c \left(z_{51} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{51} \,\mathbf{\hat{y}}+c \left(z_{51} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXVII |
| $\mathbf{B_{103}}$ | = | $x_{52} \, \mathbf{a}_{1}+y_{52} \, \mathbf{a}_{2}+z_{52} \, \mathbf{a}_{3}$ | = | $\left(a x_{52} + c z_{52} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{52} \,\mathbf{\hat{y}}+c z_{52} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXVIII |
| $\mathbf{B_{104}}$ | = | $x_{52} \, \mathbf{a}_{1}- y_{52} \, \mathbf{a}_{2}+\left(z_{52} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{52} + c \left(z_{52} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{52} \,\mathbf{\hat{y}}+c \left(z_{52} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXVIII |
| $\mathbf{B_{105}}$ | = | $x_{53} \, \mathbf{a}_{1}+y_{53} \, \mathbf{a}_{2}+z_{53} \, \mathbf{a}_{3}$ | = | $\left(a x_{53} + c z_{53} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{53} \,\mathbf{\hat{y}}+c z_{53} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXIX |
| $\mathbf{B_{106}}$ | = | $x_{53} \, \mathbf{a}_{1}- y_{53} \, \mathbf{a}_{2}+\left(z_{53} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{53} + c \left(z_{53} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{53} \,\mathbf{\hat{y}}+c \left(z_{53} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXIX |
| $\mathbf{B_{107}}$ | = | $x_{54} \, \mathbf{a}_{1}+y_{54} \, \mathbf{a}_{2}+z_{54} \, \mathbf{a}_{3}$ | = | $\left(a x_{54} + c z_{54} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{54} \,\mathbf{\hat{y}}+c z_{54} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXX |
| $\mathbf{B_{108}}$ | = | $x_{54} \, \mathbf{a}_{1}- y_{54} \, \mathbf{a}_{2}+\left(z_{54} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{54} + c \left(z_{54} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{54} \,\mathbf{\hat{y}}+c \left(z_{54} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXX |
| $\mathbf{B_{109}}$ | = | $x_{55} \, \mathbf{a}_{1}+y_{55} \, \mathbf{a}_{2}+z_{55} \, \mathbf{a}_{3}$ | = | $\left(a x_{55} + c z_{55} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{55} \,\mathbf{\hat{y}}+c z_{55} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXI |
| $\mathbf{B_{110}}$ | = | $x_{55} \, \mathbf{a}_{1}- y_{55} \, \mathbf{a}_{2}+\left(z_{55} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{55} + c \left(z_{55} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{55} \,\mathbf{\hat{y}}+c \left(z_{55} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXI |
| $\mathbf{B_{111}}$ | = | $x_{56} \, \mathbf{a}_{1}+y_{56} \, \mathbf{a}_{2}+z_{56} \, \mathbf{a}_{3}$ | = | $\left(a x_{56} + c z_{56} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{56} \,\mathbf{\hat{y}}+c z_{56} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXII |
| $\mathbf{B_{112}}$ | = | $x_{56} \, \mathbf{a}_{1}- y_{56} \, \mathbf{a}_{2}+\left(z_{56} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{56} + c \left(z_{56} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{56} \,\mathbf{\hat{y}}+c \left(z_{56} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXII |
| $\mathbf{B_{113}}$ | = | $x_{57} \, \mathbf{a}_{1}+y_{57} \, \mathbf{a}_{2}+z_{57} \, \mathbf{a}_{3}$ | = | $\left(a x_{57} + c z_{57} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{57} \,\mathbf{\hat{y}}+c z_{57} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXIII |
| $\mathbf{B_{114}}$ | = | $x_{57} \, \mathbf{a}_{1}- y_{57} \, \mathbf{a}_{2}+\left(z_{57} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{57} + c \left(z_{57} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{57} \,\mathbf{\hat{y}}+c \left(z_{57} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXIII |
| $\mathbf{B_{115}}$ | = | $x_{58} \, \mathbf{a}_{1}+y_{58} \, \mathbf{a}_{2}+z_{58} \, \mathbf{a}_{3}$ | = | $\left(a x_{58} + c z_{58} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{58} \,\mathbf{\hat{y}}+c z_{58} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXIV |
| $\mathbf{B_{116}}$ | = | $x_{58} \, \mathbf{a}_{1}- y_{58} \, \mathbf{a}_{2}+\left(z_{58} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{58} + c \left(z_{58} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{58} \,\mathbf{\hat{y}}+c \left(z_{58} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXIV |
| $\mathbf{B_{117}}$ | = | $x_{59} \, \mathbf{a}_{1}+y_{59} \, \mathbf{a}_{2}+z_{59} \, \mathbf{a}_{3}$ | = | $\left(a x_{59} + c z_{59} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{59} \,\mathbf{\hat{y}}+c z_{59} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXV |
| $\mathbf{B_{118}}$ | = | $x_{59} \, \mathbf{a}_{1}- y_{59} \, \mathbf{a}_{2}+\left(z_{59} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{59} + c \left(z_{59} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{59} \,\mathbf{\hat{y}}+c \left(z_{59} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXV |
| $\mathbf{B_{119}}$ | = | $x_{60} \, \mathbf{a}_{1}+y_{60} \, \mathbf{a}_{2}+z_{60} \, \mathbf{a}_{3}$ | = | $\left(a x_{60} + c z_{60} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{60} \,\mathbf{\hat{y}}+c z_{60} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXVI |
| $\mathbf{B_{120}}$ | = | $x_{60} \, \mathbf{a}_{1}- y_{60} \, \mathbf{a}_{2}+\left(z_{60} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{60} + c \left(z_{60} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{60} \,\mathbf{\hat{y}}+c \left(z_{60} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXVI |
| $\mathbf{B_{121}}$ | = | $x_{61} \, \mathbf{a}_{1}+y_{61} \, \mathbf{a}_{2}+z_{61} \, \mathbf{a}_{3}$ | = | $\left(a x_{61} + c z_{61} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{61} \,\mathbf{\hat{y}}+c z_{61} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXVII |
| $\mathbf{B_{122}}$ | = | $x_{61} \, \mathbf{a}_{1}- y_{61} \, \mathbf{a}_{2}+\left(z_{61} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{61} + c \left(z_{61} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{61} \,\mathbf{\hat{y}}+c \left(z_{61} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXVII |
| $\mathbf{B_{123}}$ | = | $x_{62} \, \mathbf{a}_{1}+y_{62} \, \mathbf{a}_{2}+z_{62} \, \mathbf{a}_{3}$ | = | $\left(a x_{62} + c z_{62} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{62} \,\mathbf{\hat{y}}+c z_{62} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXVIII |
| $\mathbf{B_{124}}$ | = | $x_{62} \, \mathbf{a}_{1}- y_{62} \, \mathbf{a}_{2}+\left(z_{62} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{62} + c \left(z_{62} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{62} \,\mathbf{\hat{y}}+c \left(z_{62} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXVIII |
| $\mathbf{B_{125}}$ | = | $x_{63} \, \mathbf{a}_{1}+y_{63} \, \mathbf{a}_{2}+z_{63} \, \mathbf{a}_{3}$ | = | $\left(a x_{63} + c z_{63} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{63} \,\mathbf{\hat{y}}+c z_{63} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXIX |
| $\mathbf{B_{126}}$ | = | $x_{63} \, \mathbf{a}_{1}- y_{63} \, \mathbf{a}_{2}+\left(z_{63} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{63} + c \left(z_{63} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{63} \,\mathbf{\hat{y}}+c \left(z_{63} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XXXIX |
| $\mathbf{B_{127}}$ | = | $x_{64} \, \mathbf{a}_{1}+y_{64} \, \mathbf{a}_{2}+z_{64} \, \mathbf{a}_{3}$ | = | $\left(a x_{64} + c z_{64} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{64} \,\mathbf{\hat{y}}+c z_{64} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XL |
| $\mathbf{B_{128}}$ | = | $x_{64} \, \mathbf{a}_{1}- y_{64} \, \mathbf{a}_{2}+\left(z_{64} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{64} + c \left(z_{64} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{64} \,\mathbf{\hat{y}}+c \left(z_{64} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XL |
| $\mathbf{B_{129}}$ | = | $x_{65} \, \mathbf{a}_{1}+y_{65} \, \mathbf{a}_{2}+z_{65} \, \mathbf{a}_{3}$ | = | $\left(a x_{65} + c z_{65} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{65} \,\mathbf{\hat{y}}+c z_{65} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLI |
| $\mathbf{B_{130}}$ | = | $x_{65} \, \mathbf{a}_{1}- y_{65} \, \mathbf{a}_{2}+\left(z_{65} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{65} + c \left(z_{65} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{65} \,\mathbf{\hat{y}}+c \left(z_{65} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLI |
| $\mathbf{B_{131}}$ | = | $x_{66} \, \mathbf{a}_{1}+y_{66} \, \mathbf{a}_{2}+z_{66} \, \mathbf{a}_{3}$ | = | $\left(a x_{66} + c z_{66} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{66} \,\mathbf{\hat{y}}+c z_{66} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLII |
| $\mathbf{B_{132}}$ | = | $x_{66} \, \mathbf{a}_{1}- y_{66} \, \mathbf{a}_{2}+\left(z_{66} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{66} + c \left(z_{66} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{66} \,\mathbf{\hat{y}}+c \left(z_{66} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLII |
| $\mathbf{B_{133}}$ | = | $x_{67} \, \mathbf{a}_{1}+y_{67} \, \mathbf{a}_{2}+z_{67} \, \mathbf{a}_{3}$ | = | $\left(a x_{67} + c z_{67} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{67} \,\mathbf{\hat{y}}+c z_{67} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLIII |
| $\mathbf{B_{134}}$ | = | $x_{67} \, \mathbf{a}_{1}- y_{67} \, \mathbf{a}_{2}+\left(z_{67} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{67} + c \left(z_{67} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{67} \,\mathbf{\hat{y}}+c \left(z_{67} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLIII |
| $\mathbf{B_{135}}$ | = | $x_{68} \, \mathbf{a}_{1}+y_{68} \, \mathbf{a}_{2}+z_{68} \, \mathbf{a}_{3}$ | = | $\left(a x_{68} + c z_{68} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{68} \,\mathbf{\hat{y}}+c z_{68} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLIV |
| $\mathbf{B_{136}}$ | = | $x_{68} \, \mathbf{a}_{1}- y_{68} \, \mathbf{a}_{2}+\left(z_{68} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{68} + c \left(z_{68} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{68} \,\mathbf{\hat{y}}+c \left(z_{68} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLIV |
| $\mathbf{B_{137}}$ | = | $x_{69} \, \mathbf{a}_{1}+y_{69} \, \mathbf{a}_{2}+z_{69} \, \mathbf{a}_{3}$ | = | $\left(a x_{69} + c z_{69} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{69} \,\mathbf{\hat{y}}+c z_{69} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLV |
| $\mathbf{B_{138}}$ | = | $x_{69} \, \mathbf{a}_{1}- y_{69} \, \mathbf{a}_{2}+\left(z_{69} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{69} + c \left(z_{69} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{69} \,\mathbf{\hat{y}}+c \left(z_{69} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLV |
| $\mathbf{B_{139}}$ | = | $x_{70} \, \mathbf{a}_{1}+y_{70} \, \mathbf{a}_{2}+z_{70} \, \mathbf{a}_{3}$ | = | $\left(a x_{70} + c z_{70} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{70} \,\mathbf{\hat{y}}+c z_{70} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLVI |
| $\mathbf{B_{140}}$ | = | $x_{70} \, \mathbf{a}_{1}- y_{70} \, \mathbf{a}_{2}+\left(z_{70} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{70} + c \left(z_{70} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{70} \,\mathbf{\hat{y}}+c \left(z_{70} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLVI |
| $\mathbf{B_{141}}$ | = | $x_{71} \, \mathbf{a}_{1}+y_{71} \, \mathbf{a}_{2}+z_{71} \, \mathbf{a}_{3}$ | = | $\left(a x_{71} + c z_{71} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{71} \,\mathbf{\hat{y}}+c z_{71} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLVII |
| $\mathbf{B_{142}}$ | = | $x_{71} \, \mathbf{a}_{1}- y_{71} \, \mathbf{a}_{2}+\left(z_{71} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{71} + c \left(z_{71} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{71} \,\mathbf{\hat{y}}+c \left(z_{71} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLVII |
| $\mathbf{B_{143}}$ | = | $x_{72} \, \mathbf{a}_{1}+y_{72} \, \mathbf{a}_{2}+z_{72} \, \mathbf{a}_{3}$ | = | $\left(a x_{72} + c z_{72} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{72} \,\mathbf{\hat{y}}+c z_{72} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLVIII |
| $\mathbf{B_{144}}$ | = | $x_{72} \, \mathbf{a}_{1}- y_{72} \, \mathbf{a}_{2}+\left(z_{72} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{72} + c \left(z_{72} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{72} \,\mathbf{\hat{y}}+c \left(z_{72} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLVIII |
| $\mathbf{B_{145}}$ | = | $x_{73} \, \mathbf{a}_{1}+y_{73} \, \mathbf{a}_{2}+z_{73} \, \mathbf{a}_{3}$ | = | $\left(a x_{73} + c z_{73} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{73} \,\mathbf{\hat{y}}+c z_{73} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLIX |
| $\mathbf{B_{146}}$ | = | $x_{73} \, \mathbf{a}_{1}- y_{73} \, \mathbf{a}_{2}+\left(z_{73} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{73} + c \left(z_{73} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{73} \,\mathbf{\hat{y}}+c \left(z_{73} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XLIX |
| $\mathbf{B_{147}}$ | = | $x_{74} \, \mathbf{a}_{1}+y_{74} \, \mathbf{a}_{2}+z_{74} \, \mathbf{a}_{3}$ | = | $\left(a x_{74} + c z_{74} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{74} \,\mathbf{\hat{y}}+c z_{74} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O L |
| $\mathbf{B_{148}}$ | = | $x_{74} \, \mathbf{a}_{1}- y_{74} \, \mathbf{a}_{2}+\left(z_{74} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{74} + c \left(z_{74} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{74} \,\mathbf{\hat{y}}+c \left(z_{74} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O L |
| $\mathbf{B_{149}}$ | = | $x_{75} \, \mathbf{a}_{1}+y_{75} \, \mathbf{a}_{2}+z_{75} \, \mathbf{a}_{3}$ | = | $\left(a x_{75} + c z_{75} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{75} \,\mathbf{\hat{y}}+c z_{75} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LI |
| $\mathbf{B_{150}}$ | = | $x_{75} \, \mathbf{a}_{1}- y_{75} \, \mathbf{a}_{2}+\left(z_{75} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{75} + c \left(z_{75} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{75} \,\mathbf{\hat{y}}+c \left(z_{75} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LI |
| $\mathbf{B_{151}}$ | = | $x_{76} \, \mathbf{a}_{1}+y_{76} \, \mathbf{a}_{2}+z_{76} \, \mathbf{a}_{3}$ | = | $\left(a x_{76} + c z_{76} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{76} \,\mathbf{\hat{y}}+c z_{76} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LII |
| $\mathbf{B_{152}}$ | = | $x_{76} \, \mathbf{a}_{1}- y_{76} \, \mathbf{a}_{2}+\left(z_{76} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{76} + c \left(z_{76} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{76} \,\mathbf{\hat{y}}+c \left(z_{76} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LII |
| $\mathbf{B_{153}}$ | = | $x_{77} \, \mathbf{a}_{1}+y_{77} \, \mathbf{a}_{2}+z_{77} \, \mathbf{a}_{3}$ | = | $\left(a x_{77} + c z_{77} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{77} \,\mathbf{\hat{y}}+c z_{77} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LIII |
| $\mathbf{B_{154}}$ | = | $x_{77} \, \mathbf{a}_{1}- y_{77} \, \mathbf{a}_{2}+\left(z_{77} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{77} + c \left(z_{77} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{77} \,\mathbf{\hat{y}}+c \left(z_{77} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LIII |
| $\mathbf{B_{155}}$ | = | $x_{78} \, \mathbf{a}_{1}+y_{78} \, \mathbf{a}_{2}+z_{78} \, \mathbf{a}_{3}$ | = | $\left(a x_{78} + c z_{78} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{78} \,\mathbf{\hat{y}}+c z_{78} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LIV |
| $\mathbf{B_{156}}$ | = | $x_{78} \, \mathbf{a}_{1}- y_{78} \, \mathbf{a}_{2}+\left(z_{78} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{78} + c \left(z_{78} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{78} \,\mathbf{\hat{y}}+c \left(z_{78} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LIV |
| $\mathbf{B_{157}}$ | = | $x_{79} \, \mathbf{a}_{1}+y_{79} \, \mathbf{a}_{2}+z_{79} \, \mathbf{a}_{3}$ | = | $\left(a x_{79} + c z_{79} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{79} \,\mathbf{\hat{y}}+c z_{79} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LV |
| $\mathbf{B_{158}}$ | = | $x_{79} \, \mathbf{a}_{1}- y_{79} \, \mathbf{a}_{2}+\left(z_{79} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{79} + c \left(z_{79} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{79} \,\mathbf{\hat{y}}+c \left(z_{79} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LV |
| $\mathbf{B_{159}}$ | = | $x_{80} \, \mathbf{a}_{1}+y_{80} \, \mathbf{a}_{2}+z_{80} \, \mathbf{a}_{3}$ | = | $\left(a x_{80} + c z_{80} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{80} \,\mathbf{\hat{y}}+c z_{80} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LVI |
| $\mathbf{B_{160}}$ | = | $x_{80} \, \mathbf{a}_{1}- y_{80} \, \mathbf{a}_{2}+\left(z_{80} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{80} + c \left(z_{80} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{80} \,\mathbf{\hat{y}}+c \left(z_{80} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LVI |
| $\mathbf{B_{161}}$ | = | $x_{81} \, \mathbf{a}_{1}+y_{81} \, \mathbf{a}_{2}+z_{81} \, \mathbf{a}_{3}$ | = | $\left(a x_{81} + c z_{81} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{81} \,\mathbf{\hat{y}}+c z_{81} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LVII |
| $\mathbf{B_{162}}$ | = | $x_{81} \, \mathbf{a}_{1}- y_{81} \, \mathbf{a}_{2}+\left(z_{81} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{81} + c \left(z_{81} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{81} \,\mathbf{\hat{y}}+c \left(z_{81} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LVII |
| $\mathbf{B_{163}}$ | = | $x_{82} \, \mathbf{a}_{1}+y_{82} \, \mathbf{a}_{2}+z_{82} \, \mathbf{a}_{3}$ | = | $\left(a x_{82} + c z_{82} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{82} \,\mathbf{\hat{y}}+c z_{82} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LVIII |
| $\mathbf{B_{164}}$ | = | $x_{82} \, \mathbf{a}_{1}- y_{82} \, \mathbf{a}_{2}+\left(z_{82} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{82} + c \left(z_{82} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{82} \,\mathbf{\hat{y}}+c \left(z_{82} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LVIII |
| $\mathbf{B_{165}}$ | = | $x_{83} \, \mathbf{a}_{1}+y_{83} \, \mathbf{a}_{2}+z_{83} \, \mathbf{a}_{3}$ | = | $\left(a x_{83} + c z_{83} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{83} \,\mathbf{\hat{y}}+c z_{83} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LIX |
| $\mathbf{B_{166}}$ | = | $x_{83} \, \mathbf{a}_{1}- y_{83} \, \mathbf{a}_{2}+\left(z_{83} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{83} + c \left(z_{83} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{83} \,\mathbf{\hat{y}}+c \left(z_{83} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LIX |
| $\mathbf{B_{167}}$ | = | $x_{84} \, \mathbf{a}_{1}+y_{84} \, \mathbf{a}_{2}+z_{84} \, \mathbf{a}_{3}$ | = | $\left(a x_{84} + c z_{84} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{84} \,\mathbf{\hat{y}}+c z_{84} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LX |
| $\mathbf{B_{168}}$ | = | $x_{84} \, \mathbf{a}_{1}- y_{84} \, \mathbf{a}_{2}+\left(z_{84} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{84} + c \left(z_{84} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{84} \,\mathbf{\hat{y}}+c \left(z_{84} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LX |
| $\mathbf{B_{169}}$ | = | $x_{85} \, \mathbf{a}_{1}+y_{85} \, \mathbf{a}_{2}+z_{85} \, \mathbf{a}_{3}$ | = | $\left(a x_{85} + c z_{85} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{85} \,\mathbf{\hat{y}}+c z_{85} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXI |
| $\mathbf{B_{170}}$ | = | $x_{85} \, \mathbf{a}_{1}- y_{85} \, \mathbf{a}_{2}+\left(z_{85} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{85} + c \left(z_{85} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{85} \,\mathbf{\hat{y}}+c \left(z_{85} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXI |
| $\mathbf{B_{171}}$ | = | $x_{86} \, \mathbf{a}_{1}+y_{86} \, \mathbf{a}_{2}+z_{86} \, \mathbf{a}_{3}$ | = | $\left(a x_{86} + c z_{86} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{86} \,\mathbf{\hat{y}}+c z_{86} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXII |
| $\mathbf{B_{172}}$ | = | $x_{86} \, \mathbf{a}_{1}- y_{86} \, \mathbf{a}_{2}+\left(z_{86} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{86} + c \left(z_{86} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{86} \,\mathbf{\hat{y}}+c \left(z_{86} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXII |
| $\mathbf{B_{173}}$ | = | $x_{87} \, \mathbf{a}_{1}+y_{87} \, \mathbf{a}_{2}+z_{87} \, \mathbf{a}_{3}$ | = | $\left(a x_{87} + c z_{87} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{87} \,\mathbf{\hat{y}}+c z_{87} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXIII |
| $\mathbf{B_{174}}$ | = | $x_{87} \, \mathbf{a}_{1}- y_{87} \, \mathbf{a}_{2}+\left(z_{87} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{87} + c \left(z_{87} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{87} \,\mathbf{\hat{y}}+c \left(z_{87} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXIII |
| $\mathbf{B_{175}}$ | = | $x_{88} \, \mathbf{a}_{1}+y_{88} \, \mathbf{a}_{2}+z_{88} \, \mathbf{a}_{3}$ | = | $\left(a x_{88} + c z_{88} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{88} \,\mathbf{\hat{y}}+c z_{88} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXIV |
| $\mathbf{B_{176}}$ | = | $x_{88} \, \mathbf{a}_{1}- y_{88} \, \mathbf{a}_{2}+\left(z_{88} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{88} + c \left(z_{88} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{88} \,\mathbf{\hat{y}}+c \left(z_{88} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXIV |
| $\mathbf{B_{177}}$ | = | $x_{89} \, \mathbf{a}_{1}+y_{89} \, \mathbf{a}_{2}+z_{89} \, \mathbf{a}_{3}$ | = | $\left(a x_{89} + c z_{89} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{89} \,\mathbf{\hat{y}}+c z_{89} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXV |
| $\mathbf{B_{178}}$ | = | $x_{89} \, \mathbf{a}_{1}- y_{89} \, \mathbf{a}_{2}+\left(z_{89} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{89} + c \left(z_{89} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{89} \,\mathbf{\hat{y}}+c \left(z_{89} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXV |
| $\mathbf{B_{179}}$ | = | $x_{90} \, \mathbf{a}_{1}+y_{90} \, \mathbf{a}_{2}+z_{90} \, \mathbf{a}_{3}$ | = | $\left(a x_{90} + c z_{90} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{90} \,\mathbf{\hat{y}}+c z_{90} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXVI |
| $\mathbf{B_{180}}$ | = | $x_{90} \, \mathbf{a}_{1}- y_{90} \, \mathbf{a}_{2}+\left(z_{90} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{90} + c \left(z_{90} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{90} \,\mathbf{\hat{y}}+c \left(z_{90} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXVI |
| $\mathbf{B_{181}}$ | = | $x_{91} \, \mathbf{a}_{1}+y_{91} \, \mathbf{a}_{2}+z_{91} \, \mathbf{a}_{3}$ | = | $\left(a x_{91} + c z_{91} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{91} \,\mathbf{\hat{y}}+c z_{91} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXVII |
| $\mathbf{B_{182}}$ | = | $x_{91} \, \mathbf{a}_{1}- y_{91} \, \mathbf{a}_{2}+\left(z_{91} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{91} + c \left(z_{91} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{91} \,\mathbf{\hat{y}}+c \left(z_{91} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXVII |
| $\mathbf{B_{183}}$ | = | $x_{92} \, \mathbf{a}_{1}+y_{92} \, \mathbf{a}_{2}+z_{92} \, \mathbf{a}_{3}$ | = | $\left(a x_{92} + c z_{92} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{92} \,\mathbf{\hat{y}}+c z_{92} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXVIII |
| $\mathbf{B_{184}}$ | = | $x_{92} \, \mathbf{a}_{1}- y_{92} \, \mathbf{a}_{2}+\left(z_{92} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{92} + c \left(z_{92} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{92} \,\mathbf{\hat{y}}+c \left(z_{92} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXVIII |
| $\mathbf{B_{185}}$ | = | $x_{93} \, \mathbf{a}_{1}+y_{93} \, \mathbf{a}_{2}+z_{93} \, \mathbf{a}_{3}$ | = | $\left(a x_{93} + c z_{93} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{93} \,\mathbf{\hat{y}}+c z_{93} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXIX |
| $\mathbf{B_{186}}$ | = | $x_{93} \, \mathbf{a}_{1}- y_{93} \, \mathbf{a}_{2}+\left(z_{93} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{93} + c \left(z_{93} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{93} \,\mathbf{\hat{y}}+c \left(z_{93} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXIX |
| $\mathbf{B_{187}}$ | = | $x_{94} \, \mathbf{a}_{1}+y_{94} \, \mathbf{a}_{2}+z_{94} \, \mathbf{a}_{3}$ | = | $\left(a x_{94} + c z_{94} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{94} \,\mathbf{\hat{y}}+c z_{94} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXX |
| $\mathbf{B_{188}}$ | = | $x_{94} \, \mathbf{a}_{1}- y_{94} \, \mathbf{a}_{2}+\left(z_{94} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{94} + c \left(z_{94} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{94} \,\mathbf{\hat{y}}+c \left(z_{94} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXX |
| $\mathbf{B_{189}}$ | = | $x_{95} \, \mathbf{a}_{1}+y_{95} \, \mathbf{a}_{2}+z_{95} \, \mathbf{a}_{3}$ | = | $\left(a x_{95} + c z_{95} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{95} \,\mathbf{\hat{y}}+c z_{95} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXI |
| $\mathbf{B_{190}}$ | = | $x_{95} \, \mathbf{a}_{1}- y_{95} \, \mathbf{a}_{2}+\left(z_{95} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{95} + c \left(z_{95} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{95} \,\mathbf{\hat{y}}+c \left(z_{95} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXI |
| $\mathbf{B_{191}}$ | = | $x_{96} \, \mathbf{a}_{1}+y_{96} \, \mathbf{a}_{2}+z_{96} \, \mathbf{a}_{3}$ | = | $\left(a x_{96} + c z_{96} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{96} \,\mathbf{\hat{y}}+c z_{96} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXII |
| $\mathbf{B_{192}}$ | = | $x_{96} \, \mathbf{a}_{1}- y_{96} \, \mathbf{a}_{2}+\left(z_{96} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{96} + c \left(z_{96} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{96} \,\mathbf{\hat{y}}+c \left(z_{96} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXII |
| $\mathbf{B_{193}}$ | = | $x_{97} \, \mathbf{a}_{1}+y_{97} \, \mathbf{a}_{2}+z_{97} \, \mathbf{a}_{3}$ | = | $\left(a x_{97} + c z_{97} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{97} \,\mathbf{\hat{y}}+c z_{97} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXIII |
| $\mathbf{B_{194}}$ | = | $x_{97} \, \mathbf{a}_{1}- y_{97} \, \mathbf{a}_{2}+\left(z_{97} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{97} + c \left(z_{97} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{97} \,\mathbf{\hat{y}}+c \left(z_{97} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXIII |
| $\mathbf{B_{195}}$ | = | $x_{98} \, \mathbf{a}_{1}+y_{98} \, \mathbf{a}_{2}+z_{98} \, \mathbf{a}_{3}$ | = | $\left(a x_{98} + c z_{98} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{98} \,\mathbf{\hat{y}}+c z_{98} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXIV |
| $\mathbf{B_{196}}$ | = | $x_{98} \, \mathbf{a}_{1}- y_{98} \, \mathbf{a}_{2}+\left(z_{98} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{98} + c \left(z_{98} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{98} \,\mathbf{\hat{y}}+c \left(z_{98} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXIV |
| $\mathbf{B_{197}}$ | = | $x_{99} \, \mathbf{a}_{1}+y_{99} \, \mathbf{a}_{2}+z_{99} \, \mathbf{a}_{3}$ | = | $\left(a x_{99} + c z_{99} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{99} \,\mathbf{\hat{y}}+c z_{99} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXV |
| $\mathbf{B_{198}}$ | = | $x_{99} \, \mathbf{a}_{1}- y_{99} \, \mathbf{a}_{2}+\left(z_{99} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{99} + c \left(z_{99} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{99} \,\mathbf{\hat{y}}+c \left(z_{99} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXV |
| $\mathbf{B_{199}}$ | = | $x_{100} \, \mathbf{a}_{1}+y_{100} \, \mathbf{a}_{2}+z_{100} \, \mathbf{a}_{3}$ | = | $\left(a x_{100} + c z_{100} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{100} \,\mathbf{\hat{y}}+c z_{100} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXVI |
| $\mathbf{B_{200}}$ | = | $x_{100} \, \mathbf{a}_{1}- y_{100} \, \mathbf{a}_{2}+\left(z_{100} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{100} + c \left(z_{100} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{100} \,\mathbf{\hat{y}}+c \left(z_{100} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXVI |
| $\mathbf{B_{201}}$ | = | $x_{101} \, \mathbf{a}_{1}+y_{101} \, \mathbf{a}_{2}+z_{101} \, \mathbf{a}_{3}$ | = | $\left(a x_{101} + c z_{101} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{101} \,\mathbf{\hat{y}}+c z_{101} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXVII |
| $\mathbf{B_{202}}$ | = | $x_{101} \, \mathbf{a}_{1}- y_{101} \, \mathbf{a}_{2}+\left(z_{101} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{101} + c \left(z_{101} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{101} \,\mathbf{\hat{y}}+c \left(z_{101} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXVII |
| $\mathbf{B_{203}}$ | = | $x_{102} \, \mathbf{a}_{1}+y_{102} \, \mathbf{a}_{2}+z_{102} \, \mathbf{a}_{3}$ | = | $\left(a x_{102} + c z_{102} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{102} \,\mathbf{\hat{y}}+c z_{102} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXVIII |
| $\mathbf{B_{204}}$ | = | $x_{102} \, \mathbf{a}_{1}- y_{102} \, \mathbf{a}_{2}+\left(z_{102} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{102} + c \left(z_{102} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{102} \,\mathbf{\hat{y}}+c \left(z_{102} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXVIII |
| $\mathbf{B_{205}}$ | = | $x_{103} \, \mathbf{a}_{1}+y_{103} \, \mathbf{a}_{2}+z_{103} \, \mathbf{a}_{3}$ | = | $\left(a x_{103} + c z_{103} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{103} \,\mathbf{\hat{y}}+c z_{103} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXIX |
| $\mathbf{B_{206}}$ | = | $x_{103} \, \mathbf{a}_{1}- y_{103} \, \mathbf{a}_{2}+\left(z_{103} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{103} + c \left(z_{103} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{103} \,\mathbf{\hat{y}}+c \left(z_{103} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXIX |
| $\mathbf{B_{207}}$ | = | $x_{104} \, \mathbf{a}_{1}+y_{104} \, \mathbf{a}_{2}+z_{104} \, \mathbf{a}_{3}$ | = | $\left(a x_{104} + c z_{104} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{104} \,\mathbf{\hat{y}}+c z_{104} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXX |
| $\mathbf{B_{208}}$ | = | $x_{104} \, \mathbf{a}_{1}- y_{104} \, \mathbf{a}_{2}+\left(z_{104} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{104} + c \left(z_{104} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{104} \,\mathbf{\hat{y}}+c \left(z_{104} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXX |
| $\mathbf{B_{209}}$ | = | $x_{105} \, \mathbf{a}_{1}+y_{105} \, \mathbf{a}_{2}+z_{105} \, \mathbf{a}_{3}$ | = | $\left(a x_{105} + c z_{105} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{105} \,\mathbf{\hat{y}}+c z_{105} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXI |
| $\mathbf{B_{210}}$ | = | $x_{105} \, \mathbf{a}_{1}- y_{105} \, \mathbf{a}_{2}+\left(z_{105} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{105} + c \left(z_{105} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{105} \,\mathbf{\hat{y}}+c \left(z_{105} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXI |
| $\mathbf{B_{211}}$ | = | $x_{106} \, \mathbf{a}_{1}+y_{106} \, \mathbf{a}_{2}+z_{106} \, \mathbf{a}_{3}$ | = | $\left(a x_{106} + c z_{106} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{106} \,\mathbf{\hat{y}}+c z_{106} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXII |
| $\mathbf{B_{212}}$ | = | $x_{106} \, \mathbf{a}_{1}- y_{106} \, \mathbf{a}_{2}+\left(z_{106} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{106} + c \left(z_{106} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{106} \,\mathbf{\hat{y}}+c \left(z_{106} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXII |
| $\mathbf{B_{213}}$ | = | $x_{107} \, \mathbf{a}_{1}+y_{107} \, \mathbf{a}_{2}+z_{107} \, \mathbf{a}_{3}$ | = | $\left(a x_{107} + c z_{107} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{107} \,\mathbf{\hat{y}}+c z_{107} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXIII |
| $\mathbf{B_{214}}$ | = | $x_{107} \, \mathbf{a}_{1}- y_{107} \, \mathbf{a}_{2}+\left(z_{107} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{107} + c \left(z_{107} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{107} \,\mathbf{\hat{y}}+c \left(z_{107} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXIII |
| $\mathbf{B_{215}}$ | = | $x_{108} \, \mathbf{a}_{1}+y_{108} \, \mathbf{a}_{2}+z_{108} \, \mathbf{a}_{3}$ | = | $\left(a x_{108} + c z_{108} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{108} \,\mathbf{\hat{y}}+c z_{108} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXIV |
| $\mathbf{B_{216}}$ | = | $x_{108} \, \mathbf{a}_{1}- y_{108} \, \mathbf{a}_{2}+\left(z_{108} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{108} + c \left(z_{108} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{108} \,\mathbf{\hat{y}}+c \left(z_{108} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXIV |
| $\mathbf{B_{217}}$ | = | $x_{109} \, \mathbf{a}_{1}+y_{109} \, \mathbf{a}_{2}+z_{109} \, \mathbf{a}_{3}$ | = | $\left(a x_{109} + c z_{109} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{109} \,\mathbf{\hat{y}}+c z_{109} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXV |
| $\mathbf{B_{218}}$ | = | $x_{109} \, \mathbf{a}_{1}- y_{109} \, \mathbf{a}_{2}+\left(z_{109} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{109} + c \left(z_{109} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{109} \,\mathbf{\hat{y}}+c \left(z_{109} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXV |
| $\mathbf{B_{219}}$ | = | $x_{110} \, \mathbf{a}_{1}+y_{110} \, \mathbf{a}_{2}+z_{110} \, \mathbf{a}_{3}$ | = | $\left(a x_{110} + c z_{110} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{110} \,\mathbf{\hat{y}}+c z_{110} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXVI |
| $\mathbf{B_{220}}$ | = | $x_{110} \, \mathbf{a}_{1}- y_{110} \, \mathbf{a}_{2}+\left(z_{110} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{110} + c \left(z_{110} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{110} \,\mathbf{\hat{y}}+c \left(z_{110} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXVI |
| $\mathbf{B_{221}}$ | = | $x_{111} \, \mathbf{a}_{1}+y_{111} \, \mathbf{a}_{2}+z_{111} \, \mathbf{a}_{3}$ | = | $\left(a x_{111} + c z_{111} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{111} \,\mathbf{\hat{y}}+c z_{111} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXVII |
| $\mathbf{B_{222}}$ | = | $x_{111} \, \mathbf{a}_{1}- y_{111} \, \mathbf{a}_{2}+\left(z_{111} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{111} + c \left(z_{111} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{111} \,\mathbf{\hat{y}}+c \left(z_{111} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXVII |
| $\mathbf{B_{223}}$ | = | $x_{112} \, \mathbf{a}_{1}+y_{112} \, \mathbf{a}_{2}+z_{112} \, \mathbf{a}_{3}$ | = | $\left(a x_{112} + c z_{112} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{112} \,\mathbf{\hat{y}}+c z_{112} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXVIII |
| $\mathbf{B_{224}}$ | = | $x_{112} \, \mathbf{a}_{1}- y_{112} \, \mathbf{a}_{2}+\left(z_{112} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{112} + c \left(z_{112} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{112} \,\mathbf{\hat{y}}+c \left(z_{112} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXVIII |
| $\mathbf{B_{225}}$ | = | $x_{113} \, \mathbf{a}_{1}+y_{113} \, \mathbf{a}_{2}+z_{113} \, \mathbf{a}_{3}$ | = | $\left(a x_{113} + c z_{113} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{113} \,\mathbf{\hat{y}}+c z_{113} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXIX |
| $\mathbf{B_{226}}$ | = | $x_{113} \, \mathbf{a}_{1}- y_{113} \, \mathbf{a}_{2}+\left(z_{113} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{113} + c \left(z_{113} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{113} \,\mathbf{\hat{y}}+c \left(z_{113} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O LXXXIX |
| $\mathbf{B_{227}}$ | = | $x_{114} \, \mathbf{a}_{1}+y_{114} \, \mathbf{a}_{2}+z_{114} \, \mathbf{a}_{3}$ | = | $\left(a x_{114} + c z_{114} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{114} \,\mathbf{\hat{y}}+c z_{114} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XC |
| $\mathbf{B_{228}}$ | = | $x_{114} \, \mathbf{a}_{1}- y_{114} \, \mathbf{a}_{2}+\left(z_{114} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{114} + c \left(z_{114} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{114} \,\mathbf{\hat{y}}+c \left(z_{114} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XC |
| $\mathbf{B_{229}}$ | = | $x_{115} \, \mathbf{a}_{1}+y_{115} \, \mathbf{a}_{2}+z_{115} \, \mathbf{a}_{3}$ | = | $\left(a x_{115} + c z_{115} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{115} \,\mathbf{\hat{y}}+c z_{115} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XCI |
| $\mathbf{B_{230}}$ | = | $x_{115} \, \mathbf{a}_{1}- y_{115} \, \mathbf{a}_{2}+\left(z_{115} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{115} + c \left(z_{115} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{115} \,\mathbf{\hat{y}}+c \left(z_{115} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XCI |
| $\mathbf{B_{231}}$ | = | $x_{116} \, \mathbf{a}_{1}+y_{116} \, \mathbf{a}_{2}+z_{116} \, \mathbf{a}_{3}$ | = | $\left(a x_{116} + c z_{116} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{116} \,\mathbf{\hat{y}}+c z_{116} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XCII |
| $\mathbf{B_{232}}$ | = | $x_{116} \, \mathbf{a}_{1}- y_{116} \, \mathbf{a}_{2}+\left(z_{116} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{116} + c \left(z_{116} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{116} \,\mathbf{\hat{y}}+c \left(z_{116} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XCII |
| $\mathbf{B_{233}}$ | = | $x_{117} \, \mathbf{a}_{1}+y_{117} \, \mathbf{a}_{2}+z_{117} \, \mathbf{a}_{3}$ | = | $\left(a x_{117} + c z_{117} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{117} \,\mathbf{\hat{y}}+c z_{117} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XCIII |
| $\mathbf{B_{234}}$ | = | $x_{117} \, \mathbf{a}_{1}- y_{117} \, \mathbf{a}_{2}+\left(z_{117} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{117} + c \left(z_{117} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{117} \,\mathbf{\hat{y}}+c \left(z_{117} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XCIII |
| $\mathbf{B_{235}}$ | = | $x_{118} \, \mathbf{a}_{1}+y_{118} \, \mathbf{a}_{2}+z_{118} \, \mathbf{a}_{3}$ | = | $\left(a x_{118} + c z_{118} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{118} \,\mathbf{\hat{y}}+c z_{118} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XCIV |
| $\mathbf{B_{236}}$ | = | $x_{118} \, \mathbf{a}_{1}- y_{118} \, \mathbf{a}_{2}+\left(z_{118} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{118} + c \left(z_{118} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{118} \,\mathbf{\hat{y}}+c \left(z_{118} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XCIV |
| $\mathbf{B_{237}}$ | = | $x_{119} \, \mathbf{a}_{1}+y_{119} \, \mathbf{a}_{2}+z_{119} \, \mathbf{a}_{3}$ | = | $\left(a x_{119} + c z_{119} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{119} \,\mathbf{\hat{y}}+c z_{119} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XCV |
| $\mathbf{B_{238}}$ | = | $x_{119} \, \mathbf{a}_{1}- y_{119} \, \mathbf{a}_{2}+\left(z_{119} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{119} + c \left(z_{119} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{119} \,\mathbf{\hat{y}}+c \left(z_{119} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XCV |
| $\mathbf{B_{239}}$ | = | $x_{120} \, \mathbf{a}_{1}+y_{120} \, \mathbf{a}_{2}+z_{120} \, \mathbf{a}_{3}$ | = | $\left(a x_{120} + c z_{120} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{120} \,\mathbf{\hat{y}}+c z_{120} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XCVI |
| $\mathbf{B_{240}}$ | = | $x_{120} \, \mathbf{a}_{1}- y_{120} \, \mathbf{a}_{2}+\left(z_{120} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{120} + c \left(z_{120} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{120} \,\mathbf{\hat{y}}+c \left(z_{120} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | O XCVI |
| $\mathbf{B_{241}}$ | = | $x_{121} \, \mathbf{a}_{1}+y_{121} \, \mathbf{a}_{2}+z_{121} \, \mathbf{a}_{3}$ | = | $\left(a x_{121} + c z_{121} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{121} \,\mathbf{\hat{y}}+c z_{121} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P I |
| $\mathbf{B_{242}}$ | = | $x_{121} \, \mathbf{a}_{1}- y_{121} \, \mathbf{a}_{2}+\left(z_{121} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{121} + c \left(z_{121} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{121} \,\mathbf{\hat{y}}+c \left(z_{121} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P I |
| $\mathbf{B_{243}}$ | = | $x_{122} \, \mathbf{a}_{1}+y_{122} \, \mathbf{a}_{2}+z_{122} \, \mathbf{a}_{3}$ | = | $\left(a x_{122} + c z_{122} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{122} \,\mathbf{\hat{y}}+c z_{122} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P II |
| $\mathbf{B_{244}}$ | = | $x_{122} \, \mathbf{a}_{1}- y_{122} \, \mathbf{a}_{2}+\left(z_{122} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{122} + c \left(z_{122} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{122} \,\mathbf{\hat{y}}+c \left(z_{122} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P II |
| $\mathbf{B_{245}}$ | = | $x_{123} \, \mathbf{a}_{1}+y_{123} \, \mathbf{a}_{2}+z_{123} \, \mathbf{a}_{3}$ | = | $\left(a x_{123} + c z_{123} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{123} \,\mathbf{\hat{y}}+c z_{123} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P III |
| $\mathbf{B_{246}}$ | = | $x_{123} \, \mathbf{a}_{1}- y_{123} \, \mathbf{a}_{2}+\left(z_{123} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{123} + c \left(z_{123} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{123} \,\mathbf{\hat{y}}+c \left(z_{123} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P III |
| $\mathbf{B_{247}}$ | = | $x_{124} \, \mathbf{a}_{1}+y_{124} \, \mathbf{a}_{2}+z_{124} \, \mathbf{a}_{3}$ | = | $\left(a x_{124} + c z_{124} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{124} \,\mathbf{\hat{y}}+c z_{124} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P IV |
| $\mathbf{B_{248}}$ | = | $x_{124} \, \mathbf{a}_{1}- y_{124} \, \mathbf{a}_{2}+\left(z_{124} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{124} + c \left(z_{124} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{124} \,\mathbf{\hat{y}}+c \left(z_{124} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P IV |
| $\mathbf{B_{249}}$ | = | $x_{125} \, \mathbf{a}_{1}+y_{125} \, \mathbf{a}_{2}+z_{125} \, \mathbf{a}_{3}$ | = | $\left(a x_{125} + c z_{125} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{125} \,\mathbf{\hat{y}}+c z_{125} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P V |
| $\mathbf{B_{250}}$ | = | $x_{125} \, \mathbf{a}_{1}- y_{125} \, \mathbf{a}_{2}+\left(z_{125} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{125} + c \left(z_{125} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{125} \,\mathbf{\hat{y}}+c \left(z_{125} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P V |
| $\mathbf{B_{251}}$ | = | $x_{126} \, \mathbf{a}_{1}+y_{126} \, \mathbf{a}_{2}+z_{126} \, \mathbf{a}_{3}$ | = | $\left(a x_{126} + c z_{126} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{126} \,\mathbf{\hat{y}}+c z_{126} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P VI |
| $\mathbf{B_{252}}$ | = | $x_{126} \, \mathbf{a}_{1}- y_{126} \, \mathbf{a}_{2}+\left(z_{126} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{126} + c \left(z_{126} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{126} \,\mathbf{\hat{y}}+c \left(z_{126} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P VI |
| $\mathbf{B_{253}}$ | = | $x_{127} \, \mathbf{a}_{1}+y_{127} \, \mathbf{a}_{2}+z_{127} \, \mathbf{a}_{3}$ | = | $\left(a x_{127} + c z_{127} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{127} \,\mathbf{\hat{y}}+c z_{127} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P VII |
| $\mathbf{B_{254}}$ | = | $x_{127} \, \mathbf{a}_{1}- y_{127} \, \mathbf{a}_{2}+\left(z_{127} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{127} + c \left(z_{127} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{127} \,\mathbf{\hat{y}}+c \left(z_{127} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P VII |
| $\mathbf{B_{255}}$ | = | $x_{128} \, \mathbf{a}_{1}+y_{128} \, \mathbf{a}_{2}+z_{128} \, \mathbf{a}_{3}$ | = | $\left(a x_{128} + c z_{128} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{128} \,\mathbf{\hat{y}}+c z_{128} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P VIII |
| $\mathbf{B_{256}}$ | = | $x_{128} \, \mathbf{a}_{1}- y_{128} \, \mathbf{a}_{2}+\left(z_{128} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{128} + c \left(z_{128} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{128} \,\mathbf{\hat{y}}+c \left(z_{128} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P VIII |
| $\mathbf{B_{257}}$ | = | $x_{129} \, \mathbf{a}_{1}+y_{129} \, \mathbf{a}_{2}+z_{129} \, \mathbf{a}_{3}$ | = | $\left(a x_{129} + c z_{129} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{129} \,\mathbf{\hat{y}}+c z_{129} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P IX |
| $\mathbf{B_{258}}$ | = | $x_{129} \, \mathbf{a}_{1}- y_{129} \, \mathbf{a}_{2}+\left(z_{129} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{129} + c \left(z_{129} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{129} \,\mathbf{\hat{y}}+c \left(z_{129} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P IX |
| $\mathbf{B_{259}}$ | = | $x_{130} \, \mathbf{a}_{1}+y_{130} \, \mathbf{a}_{2}+z_{130} \, \mathbf{a}_{3}$ | = | $\left(a x_{130} + c z_{130} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{130} \,\mathbf{\hat{y}}+c z_{130} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P X |
| $\mathbf{B_{260}}$ | = | $x_{130} \, \mathbf{a}_{1}- y_{130} \, \mathbf{a}_{2}+\left(z_{130} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{130} + c \left(z_{130} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{130} \,\mathbf{\hat{y}}+c \left(z_{130} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P X |
| $\mathbf{B_{261}}$ | = | $x_{131} \, \mathbf{a}_{1}+y_{131} \, \mathbf{a}_{2}+z_{131} \, \mathbf{a}_{3}$ | = | $\left(a x_{131} + c z_{131} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{131} \,\mathbf{\hat{y}}+c z_{131} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XI |
| $\mathbf{B_{262}}$ | = | $x_{131} \, \mathbf{a}_{1}- y_{131} \, \mathbf{a}_{2}+\left(z_{131} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{131} + c \left(z_{131} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{131} \,\mathbf{\hat{y}}+c \left(z_{131} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XI |
| $\mathbf{B_{263}}$ | = | $x_{132} \, \mathbf{a}_{1}+y_{132} \, \mathbf{a}_{2}+z_{132} \, \mathbf{a}_{3}$ | = | $\left(a x_{132} + c z_{132} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{132} \,\mathbf{\hat{y}}+c z_{132} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XII |
| $\mathbf{B_{264}}$ | = | $x_{132} \, \mathbf{a}_{1}- y_{132} \, \mathbf{a}_{2}+\left(z_{132} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{132} + c \left(z_{132} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{132} \,\mathbf{\hat{y}}+c \left(z_{132} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XII |
| $\mathbf{B_{265}}$ | = | $x_{133} \, \mathbf{a}_{1}+y_{133} \, \mathbf{a}_{2}+z_{133} \, \mathbf{a}_{3}$ | = | $\left(a x_{133} + c z_{133} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{133} \,\mathbf{\hat{y}}+c z_{133} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XIII |
| $\mathbf{B_{266}}$ | = | $x_{133} \, \mathbf{a}_{1}- y_{133} \, \mathbf{a}_{2}+\left(z_{133} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{133} + c \left(z_{133} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{133} \,\mathbf{\hat{y}}+c \left(z_{133} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XIII |
| $\mathbf{B_{267}}$ | = | $x_{134} \, \mathbf{a}_{1}+y_{134} \, \mathbf{a}_{2}+z_{134} \, \mathbf{a}_{3}$ | = | $\left(a x_{134} + c z_{134} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{134} \,\mathbf{\hat{y}}+c z_{134} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XIV |
| $\mathbf{B_{268}}$ | = | $x_{134} \, \mathbf{a}_{1}- y_{134} \, \mathbf{a}_{2}+\left(z_{134} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{134} + c \left(z_{134} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{134} \,\mathbf{\hat{y}}+c \left(z_{134} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XIV |
| $\mathbf{B_{269}}$ | = | $x_{135} \, \mathbf{a}_{1}+y_{135} \, \mathbf{a}_{2}+z_{135} \, \mathbf{a}_{3}$ | = | $\left(a x_{135} + c z_{135} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{135} \,\mathbf{\hat{y}}+c z_{135} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XV |
| $\mathbf{B_{270}}$ | = | $x_{135} \, \mathbf{a}_{1}- y_{135} \, \mathbf{a}_{2}+\left(z_{135} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{135} + c \left(z_{135} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{135} \,\mathbf{\hat{y}}+c \left(z_{135} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XV |
| $\mathbf{B_{271}}$ | = | $x_{136} \, \mathbf{a}_{1}+y_{136} \, \mathbf{a}_{2}+z_{136} \, \mathbf{a}_{3}$ | = | $\left(a x_{136} + c z_{136} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{136} \,\mathbf{\hat{y}}+c z_{136} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XVI |
| $\mathbf{B_{272}}$ | = | $x_{136} \, \mathbf{a}_{1}- y_{136} \, \mathbf{a}_{2}+\left(z_{136} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{136} + c \left(z_{136} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{136} \,\mathbf{\hat{y}}+c \left(z_{136} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XVI |
| $\mathbf{B_{273}}$ | = | $x_{137} \, \mathbf{a}_{1}+y_{137} \, \mathbf{a}_{2}+z_{137} \, \mathbf{a}_{3}$ | = | $\left(a x_{137} + c z_{137} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{137} \,\mathbf{\hat{y}}+c z_{137} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XVII |
| $\mathbf{B_{274}}$ | = | $x_{137} \, \mathbf{a}_{1}- y_{137} \, \mathbf{a}_{2}+\left(z_{137} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{137} + c \left(z_{137} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{137} \,\mathbf{\hat{y}}+c \left(z_{137} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XVII |
| $\mathbf{B_{275}}$ | = | $x_{138} \, \mathbf{a}_{1}+y_{138} \, \mathbf{a}_{2}+z_{138} \, \mathbf{a}_{3}$ | = | $\left(a x_{138} + c z_{138} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{138} \,\mathbf{\hat{y}}+c z_{138} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XVIII |
| $\mathbf{B_{276}}$ | = | $x_{138} \, \mathbf{a}_{1}- y_{138} \, \mathbf{a}_{2}+\left(z_{138} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{138} + c \left(z_{138} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{138} \,\mathbf{\hat{y}}+c \left(z_{138} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XVIII |
| $\mathbf{B_{277}}$ | = | $x_{139} \, \mathbf{a}_{1}+y_{139} \, \mathbf{a}_{2}+z_{139} \, \mathbf{a}_{3}$ | = | $\left(a x_{139} + c z_{139} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{139} \,\mathbf{\hat{y}}+c z_{139} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XIX |
| $\mathbf{B_{278}}$ | = | $x_{139} \, \mathbf{a}_{1}- y_{139} \, \mathbf{a}_{2}+\left(z_{139} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{139} + c \left(z_{139} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{139} \,\mathbf{\hat{y}}+c \left(z_{139} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XIX |
| $\mathbf{B_{279}}$ | = | $x_{140} \, \mathbf{a}_{1}+y_{140} \, \mathbf{a}_{2}+z_{140} \, \mathbf{a}_{3}$ | = | $\left(a x_{140} + c z_{140} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{140} \,\mathbf{\hat{y}}+c z_{140} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XX |
| $\mathbf{B_{280}}$ | = | $x_{140} \, \mathbf{a}_{1}- y_{140} \, \mathbf{a}_{2}+\left(z_{140} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{140} + c \left(z_{140} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{140} \,\mathbf{\hat{y}}+c \left(z_{140} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XX |
| $\mathbf{B_{281}}$ | = | $x_{141} \, \mathbf{a}_{1}+y_{141} \, \mathbf{a}_{2}+z_{141} \, \mathbf{a}_{3}$ | = | $\left(a x_{141} + c z_{141} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{141} \,\mathbf{\hat{y}}+c z_{141} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XXI |
| $\mathbf{B_{282}}$ | = | $x_{141} \, \mathbf{a}_{1}- y_{141} \, \mathbf{a}_{2}+\left(z_{141} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{141} + c \left(z_{141} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{141} \,\mathbf{\hat{y}}+c \left(z_{141} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XXI |
| $\mathbf{B_{283}}$ | = | $x_{142} \, \mathbf{a}_{1}+y_{142} \, \mathbf{a}_{2}+z_{142} \, \mathbf{a}_{3}$ | = | $\left(a x_{142} + c z_{142} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{142} \,\mathbf{\hat{y}}+c z_{142} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XXII |
| $\mathbf{B_{284}}$ | = | $x_{142} \, \mathbf{a}_{1}- y_{142} \, \mathbf{a}_{2}+\left(z_{142} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{142} + c \left(z_{142} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{142} \,\mathbf{\hat{y}}+c \left(z_{142} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XXII |
| $\mathbf{B_{285}}$ | = | $x_{143} \, \mathbf{a}_{1}+y_{143} \, \mathbf{a}_{2}+z_{143} \, \mathbf{a}_{3}$ | = | $\left(a x_{143} + c z_{143} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{143} \,\mathbf{\hat{y}}+c z_{143} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XXIII |
| $\mathbf{B_{286}}$ | = | $x_{143} \, \mathbf{a}_{1}- y_{143} \, \mathbf{a}_{2}+\left(z_{143} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{143} + c \left(z_{143} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{143} \,\mathbf{\hat{y}}+c \left(z_{143} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XXIII |
| $\mathbf{B_{287}}$ | = | $x_{144} \, \mathbf{a}_{1}+y_{144} \, \mathbf{a}_{2}+z_{144} \, \mathbf{a}_{3}$ | = | $\left(a x_{144} + c z_{144} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{144} \,\mathbf{\hat{y}}+c z_{144} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XXIV |
| $\mathbf{B_{288}}$ | = | $x_{144} \, \mathbf{a}_{1}- y_{144} \, \mathbf{a}_{2}+\left(z_{144} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{144} + c \left(z_{144} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{144} \,\mathbf{\hat{y}}+c \left(z_{144} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | P XXIV |
References
- H. Graetsch, Two forms of aluminium phosphate tridymite from X-ray powder data, Acta Crystallogr. Sect. C 56, 401–403 (2000), doi:10.1107/S0108270199015164.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=AB4C_mP288_7_24a_96a_24a --params=$a,b/a,c/a,\beta,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16},x_{17},y_{17},z_{17},x_{18},y_{18},z_{18},x_{19},y_{19},z_{19},x_{20},y_{20},z_{20},x_{21},y_{21},z_{21},x_{22},y_{22},z_{22},x_{23},y_{23},z_{23},x_{24},y_{24},z_{24},x_{25},y_{25},z_{25},x_{26},y_{26},z_{26},x_{27},y_{27},z_{27},x_{28},y_{28},z_{28},x_{29},y_{29},z_{29},x_{30},y_{30},z_{30},x_{31},y_{31},z_{31},x_{32},y_{32},z_{32},x_{33},y_{33},z_{33},x_{34},y_{34},z_{34},x_{35},y_{35},z_{35},x_{36},y_{36},z_{36},x_{37},y_{37},z_{37},x_{38},y_{38},z_{38},x_{39},y_{39},z_{39},x_{40},y_{40},z_{40},x_{41},y_{41},z_{41},x_{42},y_{42},z_{42},x_{43},y_{43},z_{43},x_{44},y_{44},z_{44},x_{45},y_{45},z_{45},x_{46},y_{46},z_{46},x_{47},y_{47},z_{47},x_{48},y_{48},z_{48},x_{49},y_{49},z_{49},x_{50},y_{50},z_{50},x_{51},y_{51},z_{51},x_{52},y_{52},z_{52},x_{53},y_{53},z_{53},x_{54},y_{54},z_{54},x_{55},y_{55},z_{55},x_{56},y_{56},z_{56},x_{57},y_{57},z_{57},x_{58},y_{58},z_{58},x_{59},y_{59},z_{59},x_{60},y_{60},z_{60},x_{61},y_{61},z_{61},x_{62},y_{62},z_{62},x_{63},y_{63},z_{63},x_{64},y_{64},z_{64},x_{65},y_{65},z_{65},x_{66},y_{66},z_{66},x_{67},y_{67},z_{67},x_{68},y_{68},z_{68},x_{69},y_{69},z_{69},x_{70},y_{70},z_{70},x_{71},y_{71},z_{71},x_{72},y_{72},z_{72},x_{73},y_{73},z_{73},x_{74},y_{74},z_{74},x_{75},y_{75},z_{75},x_{76},y_{76},z_{76},x_{77},y_{77},z_{77},x_{78},y_{78},z_{78},x_{79},y_{79},z_{79},x_{80},y_{80},z_{80},x_{81},y_{81},z_{81},x_{82},y_{82},z_{82},x_{83},y_{83},z_{83},x_{84},y_{84},z_{84},x_{85},y_{85},z_{85},x_{86},y_{86},z_{86},x_{87},y_{87},z_{87},x_{88},y_{88},z_{88},x_{89},y_{89},z_{89},x_{90},y_{90},z_{90},x_{91},y_{91},z_{91},x_{92},y_{92},z_{92},x_{93},y_{93},z_{93},x_{94},y_{94},z_{94},x_{95},y_{95},z_{95},x_{96},y_{96},z_{96},x_{97},y_{97},z_{97},x_{98},y_{98},z_{98},x_{99},y_{99},z_{99},x_{100},y_{100},z_{100},x_{101},y_{101},z_{101},x_{102},y_{102},z_{102},x_{103},y_{103},z_{103},x_{104},y_{104},z_{104},x_{105},y_{105},z_{105},x_{106},y_{106},z_{106},x_{107},y_{107},z_{107},x_{108},y_{108},z_{108},x_{109},y_{109},z_{109},x_{110},y_{110},z_{110},x_{111},y_{111},z_{111},x_{112},y_{112},z_{112},x_{113},y_{113},z_{113},x_{114},y_{114},z_{114},x_{115},y_{115},z_{115},x_{116},y_{116},z_{116},x_{117},y_{117},z_{117},x_{118},y_{118},z_{118},x_{119},y_{119},z_{119},x_{120},y_{120},z_{120},x_{121},y_{121},z_{121},x_{122},y_{122},z_{122},x_{123},y_{123},z_{123},x_{124},y_{124},z_{124},x_{125},y_{125},z_{125},x_{126},y_{126},z_{126},x_{127},y_{127},z_{127},x_{128},y_{128},z_{128},x_{129},y_{129},z_{129},x_{130},y_{130},z_{130},x_{131},y_{131},z_{131},x_{132},y_{132},z_{132},x_{133},y_{133},z_{133},x_{134},y_{134},z_{134},x_{135},y_{135},z_{135},x_{136},y_{136},z_{136},x_{137},y_{137},z_{137},x_{138},y_{138},z_{138},x_{139},y_{139},z_{139},x_{140},y_{140},z_{140},x_{141},y_{141},z_{141},x_{142},y_{142},z_{142},x_{143},y_{143},z_{143},x_{144},y_{144},z_{144}$