Triclinic tridymite (295K) AlPO$_{4}$ Structure: AB4C_aP240_1_40a_160a_40a-001
| Prototype | AlO$_{4}$P |
| AFLOW prototype label | AB4C_aP240_1_40a_160a_40a-001 |
| ICSD | 280307 |
| CCDC | 1721023 |
| Pearson symbol | aP240 |
| Space group number | 1 |
| Space group symbol | $P1$ |
| AFLOW prototype command |
aflow --proto=AB4C_aP240_1_40a_160a_40a-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \alpha, \allowbreak \beta, \allowbreak \gamma, \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}, \allowbreak x_{145}, \allowbreak y_{145}, \allowbreak z_{145}, \allowbreak x_{146}, \allowbreak y_{146}, \allowbreak z_{146}, \allowbreak x_{147}, \allowbreak y_{147}, \allowbreak z_{147}, \allowbreak x_{148}, \allowbreak y_{148}, \allowbreak z_{148}, \allowbreak x_{149}, \allowbreak y_{149}, \allowbreak z_{149}, \allowbreak x_{150}, \allowbreak y_{150}, \allowbreak z_{150}, \allowbreak x_{151}, \allowbreak y_{151}, \allowbreak z_{151}, \allowbreak x_{152}, \allowbreak y_{152}, \allowbreak z_{152}, \allowbreak x_{153}, \allowbreak y_{153}, \allowbreak z_{153}, \allowbreak x_{154}, \allowbreak y_{154}, \allowbreak z_{154}, \allowbreak x_{155}, \allowbreak y_{155}, \allowbreak z_{155}, \allowbreak x_{156}, \allowbreak y_{156}, \allowbreak z_{156}, \allowbreak x_{157}, \allowbreak y_{157}, \allowbreak z_{157}, \allowbreak x_{158}, \allowbreak y_{158}, \allowbreak z_{158}, \allowbreak x_{159}, \allowbreak y_{159}, \allowbreak z_{159}, \allowbreak x_{160}, \allowbreak y_{160}, \allowbreak z_{160}, \allowbreak x_{161}, \allowbreak y_{161}, \allowbreak z_{161}, \allowbreak x_{162}, \allowbreak y_{162}, \allowbreak z_{162}, \allowbreak x_{163}, \allowbreak y_{163}, \allowbreak z_{163}, \allowbreak x_{164}, \allowbreak y_{164}, \allowbreak z_{164}, \allowbreak x_{165}, \allowbreak y_{165}, \allowbreak z_{165}, \allowbreak x_{166}, \allowbreak y_{166}, \allowbreak z_{166}, \allowbreak x_{167}, \allowbreak y_{167}, \allowbreak z_{167}, \allowbreak x_{168}, \allowbreak y_{168}, \allowbreak z_{168}, \allowbreak x_{169}, \allowbreak y_{169}, \allowbreak z_{169}, \allowbreak x_{170}, \allowbreak y_{170}, \allowbreak z_{170}, \allowbreak x_{171}, \allowbreak y_{171}, \allowbreak z_{171}, \allowbreak x_{172}, \allowbreak y_{172}, \allowbreak z_{172}, \allowbreak x_{173}, \allowbreak y_{173}, \allowbreak z_{173}, \allowbreak x_{174}, \allowbreak y_{174}, \allowbreak z_{174}, \allowbreak x_{175}, \allowbreak y_{175}, \allowbreak z_{175}, \allowbreak x_{176}, \allowbreak y_{176}, \allowbreak z_{176}, \allowbreak x_{177}, \allowbreak y_{177}, \allowbreak z_{177}, \allowbreak x_{178}, \allowbreak y_{178}, \allowbreak z_{178}, \allowbreak x_{179}, \allowbreak y_{179}, \allowbreak z_{179}, \allowbreak x_{180}, \allowbreak y_{180}, \allowbreak z_{180}, \allowbreak x_{181}, \allowbreak y_{181}, \allowbreak z_{181}, \allowbreak x_{182}, \allowbreak y_{182}, \allowbreak z_{182}, \allowbreak x_{183}, \allowbreak y_{183}, \allowbreak z_{183}, \allowbreak x_{184}, \allowbreak y_{184}, \allowbreak z_{184}, \allowbreak x_{185}, \allowbreak y_{185}, \allowbreak z_{185}, \allowbreak x_{186}, \allowbreak y_{186}, \allowbreak z_{186}, \allowbreak x_{187}, \allowbreak y_{187}, \allowbreak z_{187}, \allowbreak x_{188}, \allowbreak y_{188}, \allowbreak z_{188}, \allowbreak x_{189}, \allowbreak y_{189}, \allowbreak z_{189}, \allowbreak x_{190}, \allowbreak y_{190}, \allowbreak z_{190}, \allowbreak x_{191}, \allowbreak y_{191}, \allowbreak z_{191}, \allowbreak x_{192}, \allowbreak y_{192}, \allowbreak z_{192}, \allowbreak x_{193}, \allowbreak y_{193}, \allowbreak z_{193}, \allowbreak x_{194}, \allowbreak y_{194}, \allowbreak z_{194}, \allowbreak x_{195}, \allowbreak y_{195}, \allowbreak z_{195}, \allowbreak x_{196}, \allowbreak y_{196}, \allowbreak z_{196}, \allowbreak x_{197}, \allowbreak y_{197}, \allowbreak z_{197}, \allowbreak x_{198}, \allowbreak y_{198}, \allowbreak z_{198}, \allowbreak x_{199}, \allowbreak y_{199}, \allowbreak z_{199}, \allowbreak x_{200}, \allowbreak y_{200}, \allowbreak z_{200}, \allowbreak x_{201}, \allowbreak y_{201}, \allowbreak z_{201}, \allowbreak x_{202}, \allowbreak y_{202}, \allowbreak z_{202}, \allowbreak x_{203}, \allowbreak y_{203}, \allowbreak z_{203}, \allowbreak x_{204}, \allowbreak y_{204}, \allowbreak z_{204}, \allowbreak x_{205}, \allowbreak y_{205}, \allowbreak z_{205}, \allowbreak x_{206}, \allowbreak y_{206}, \allowbreak z_{206}, \allowbreak x_{207}, \allowbreak y_{207}, \allowbreak z_{207}, \allowbreak x_{208}, \allowbreak y_{208}, \allowbreak z_{208}, \allowbreak x_{209}, \allowbreak y_{209}, \allowbreak z_{209}, \allowbreak x_{210}, \allowbreak y_{210}, \allowbreak z_{210}, \allowbreak x_{211}, \allowbreak y_{211}, \allowbreak z_{211}, \allowbreak x_{212}, \allowbreak y_{212}, \allowbreak z_{212}, \allowbreak x_{213}, \allowbreak y_{213}, \allowbreak z_{213}, \allowbreak x_{214}, \allowbreak y_{214}, \allowbreak z_{214}, \allowbreak x_{215}, \allowbreak y_{215}, \allowbreak z_{215}, \allowbreak x_{216}, \allowbreak y_{216}, \allowbreak z_{216}, \allowbreak x_{217}, \allowbreak y_{217}, \allowbreak z_{217}, \allowbreak x_{218}, \allowbreak y_{218}, \allowbreak z_{218}, \allowbreak x_{219}, \allowbreak y_{219}, \allowbreak z_{219}, \allowbreak x_{220}, \allowbreak y_{220}, \allowbreak z_{220}, \allowbreak x_{221}, \allowbreak y_{221}, \allowbreak z_{221}, \allowbreak x_{222}, \allowbreak y_{222}, \allowbreak z_{222}, \allowbreak x_{223}, \allowbreak y_{223}, \allowbreak z_{223}, \allowbreak x_{224}, \allowbreak y_{224}, \allowbreak z_{224}, \allowbreak x_{225}, \allowbreak y_{225}, \allowbreak z_{225}, \allowbreak x_{226}, \allowbreak y_{226}, \allowbreak z_{226}, \allowbreak x_{227}, \allowbreak y_{227}, \allowbreak z_{227}, \allowbreak x_{228}, \allowbreak y_{228}, \allowbreak z_{228}, \allowbreak x_{229}, \allowbreak y_{229}, \allowbreak z_{229}, \allowbreak x_{230}, \allowbreak y_{230}, \allowbreak z_{230}, \allowbreak x_{231}, \allowbreak y_{231}, \allowbreak z_{231}, \allowbreak x_{232}, \allowbreak y_{232}, \allowbreak z_{232}, \allowbreak x_{233}, \allowbreak y_{233}, \allowbreak z_{233}, \allowbreak x_{234}, \allowbreak y_{234}, \allowbreak z_{234}, \allowbreak x_{235}, \allowbreak y_{235}, \allowbreak z_{235}, \allowbreak x_{236}, \allowbreak y_{236}, \allowbreak z_{236}, \allowbreak x_{237}, \allowbreak y_{237}, \allowbreak z_{237}, \allowbreak x_{238}, \allowbreak y_{238}, \allowbreak z_{238}, \allowbreak x_{239}, \allowbreak y_{239}, \allowbreak z_{239}, \allowbreak x_{240}, \allowbreak y_{240}, \allowbreak z_{240}$ |
- 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
- The low temperature structure is triclinic, space group $P1$ #1 (this structure), 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 given in the $F1$ setting of space group #1. This gives a conventional unit cell which is four times larger than the primitive cell and is very close to an orthorhombic cell. We used AFLOW to convert this to the standard $P1$ setting, which produces a cell equivalent to the primitive unit cell in the $F1$ setting.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \cos{\gamma} \,\mathbf{\hat{x}}+b \sin{\gamma} \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c_{x} \,\mathbf{\hat{x}}+c_{y} \,\mathbf{\hat{y}}+c_{z} \,\mathbf{\hat{z}}\\c_{x} & = & c \cos{\beta} \\ c_{y} & = & c (\cos{\alpha} - \cos{\beta}\cos{\gamma}) / {\sin{\gamma}} \\ c_{z} & = & \sqrt{c^2 - c_{x}^2- c_{y}^2}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\left(a x_{1} + b y_{1} \cos{\gamma} + c_{x} z_{1}\right) \,\mathbf{\hat{x}}+\left(b y_{1} \sin{\gamma} + c_{y} z_{1}\right) \,\mathbf{\hat{y}}+c_{z} z_{1} \,\mathbf{\hat{z}}$ | (1a) | Al I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\left(a x_{2} + b y_{2} \cos{\gamma} + c_{x} z_{2}\right) \,\mathbf{\hat{x}}+\left(b y_{2} \sin{\gamma} + c_{y} z_{2}\right) \,\mathbf{\hat{y}}+c_{z} z_{2} \,\mathbf{\hat{z}}$ | (1a) | Al II |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + b y_{3} \cos{\gamma} + c_{x} z_{3}\right) \,\mathbf{\hat{x}}+\left(b y_{3} \sin{\gamma} + c_{y} z_{3}\right) \,\mathbf{\hat{y}}+c_{z} z_{3} \,\mathbf{\hat{z}}$ | (1a) | Al III |
| $\mathbf{B_{4}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + b y_{4} \cos{\gamma} + c_{x} z_{4}\right) \,\mathbf{\hat{x}}+\left(b y_{4} \sin{\gamma} + c_{y} z_{4}\right) \,\mathbf{\hat{y}}+c_{z} z_{4} \,\mathbf{\hat{z}}$ | (1a) | Al IV |
| $\mathbf{B_{5}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + b y_{5} \cos{\gamma} + c_{x} z_{5}\right) \,\mathbf{\hat{x}}+\left(b y_{5} \sin{\gamma} + c_{y} z_{5}\right) \,\mathbf{\hat{y}}+c_{z} z_{5} \,\mathbf{\hat{z}}$ | (1a) | Al V |
| $\mathbf{B_{6}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + b y_{6} \cos{\gamma} + c_{x} z_{6}\right) \,\mathbf{\hat{x}}+\left(b y_{6} \sin{\gamma} + c_{y} z_{6}\right) \,\mathbf{\hat{y}}+c_{z} z_{6} \,\mathbf{\hat{z}}$ | (1a) | Al VI |
| $\mathbf{B_{7}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\left(a x_{7} + b y_{7} \cos{\gamma} + c_{x} z_{7}\right) \,\mathbf{\hat{x}}+\left(b y_{7} \sin{\gamma} + c_{y} z_{7}\right) \,\mathbf{\hat{y}}+c_{z} z_{7} \,\mathbf{\hat{z}}$ | (1a) | Al VII |
| $\mathbf{B_{8}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\left(a x_{8} + b y_{8} \cos{\gamma} + c_{x} z_{8}\right) \,\mathbf{\hat{x}}+\left(b y_{8} \sin{\gamma} + c_{y} z_{8}\right) \,\mathbf{\hat{y}}+c_{z} z_{8} \,\mathbf{\hat{z}}$ | (1a) | Al VIII |
| $\mathbf{B_{9}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\left(a x_{9} + b y_{9} \cos{\gamma} + c_{x} z_{9}\right) \,\mathbf{\hat{x}}+\left(b y_{9} \sin{\gamma} + c_{y} z_{9}\right) \,\mathbf{\hat{y}}+c_{z} z_{9} \,\mathbf{\hat{z}}$ | (1a) | Al IX |
| $\mathbf{B_{10}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\left(a x_{10} + b y_{10} \cos{\gamma} + c_{x} z_{10}\right) \,\mathbf{\hat{x}}+\left(b y_{10} \sin{\gamma} + c_{y} z_{10}\right) \,\mathbf{\hat{y}}+c_{z} z_{10} \,\mathbf{\hat{z}}$ | (1a) | Al X |
| $\mathbf{B_{11}}$ | = | $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\left(a x_{11} + b y_{11} \cos{\gamma} + c_{x} z_{11}\right) \,\mathbf{\hat{x}}+\left(b y_{11} \sin{\gamma} + c_{y} z_{11}\right) \,\mathbf{\hat{y}}+c_{z} z_{11} \,\mathbf{\hat{z}}$ | (1a) | Al XI |
| $\mathbf{B_{12}}$ | = | $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\left(a x_{12} + b y_{12} \cos{\gamma} + c_{x} z_{12}\right) \,\mathbf{\hat{x}}+\left(b y_{12} \sin{\gamma} + c_{y} z_{12}\right) \,\mathbf{\hat{y}}+c_{z} z_{12} \,\mathbf{\hat{z}}$ | (1a) | Al XII |
| $\mathbf{B_{13}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\left(a x_{13} + b y_{13} \cos{\gamma} + c_{x} z_{13}\right) \,\mathbf{\hat{x}}+\left(b y_{13} \sin{\gamma} + c_{y} z_{13}\right) \,\mathbf{\hat{y}}+c_{z} z_{13} \,\mathbf{\hat{z}}$ | (1a) | Al XIII |
| $\mathbf{B_{14}}$ | = | $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\left(a x_{14} + b y_{14} \cos{\gamma} + c_{x} z_{14}\right) \,\mathbf{\hat{x}}+\left(b y_{14} \sin{\gamma} + c_{y} z_{14}\right) \,\mathbf{\hat{y}}+c_{z} z_{14} \,\mathbf{\hat{z}}$ | (1a) | Al XIV |
| $\mathbf{B_{15}}$ | = | $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\left(a x_{15} + b y_{15} \cos{\gamma} + c_{x} z_{15}\right) \,\mathbf{\hat{x}}+\left(b y_{15} \sin{\gamma} + c_{y} z_{15}\right) \,\mathbf{\hat{y}}+c_{z} z_{15} \,\mathbf{\hat{z}}$ | (1a) | Al XV |
| $\mathbf{B_{16}}$ | = | $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\left(a x_{16} + b y_{16} \cos{\gamma} + c_{x} z_{16}\right) \,\mathbf{\hat{x}}+\left(b y_{16} \sin{\gamma} + c_{y} z_{16}\right) \,\mathbf{\hat{y}}+c_{z} z_{16} \,\mathbf{\hat{z}}$ | (1a) | Al XVI |
| $\mathbf{B_{17}}$ | = | $x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\left(a x_{17} + b y_{17} \cos{\gamma} + c_{x} z_{17}\right) \,\mathbf{\hat{x}}+\left(b y_{17} \sin{\gamma} + c_{y} z_{17}\right) \,\mathbf{\hat{y}}+c_{z} z_{17} \,\mathbf{\hat{z}}$ | (1a) | Al XVII |
| $\mathbf{B_{18}}$ | = | $x_{18} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $\left(a x_{18} + b y_{18} \cos{\gamma} + c_{x} z_{18}\right) \,\mathbf{\hat{x}}+\left(b y_{18} \sin{\gamma} + c_{y} z_{18}\right) \,\mathbf{\hat{y}}+c_{z} z_{18} \,\mathbf{\hat{z}}$ | (1a) | Al XVIII |
| $\mathbf{B_{19}}$ | = | $x_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $\left(a x_{19} + b y_{19} \cos{\gamma} + c_{x} z_{19}\right) \,\mathbf{\hat{x}}+\left(b y_{19} \sin{\gamma} + c_{y} z_{19}\right) \,\mathbf{\hat{y}}+c_{z} z_{19} \,\mathbf{\hat{z}}$ | (1a) | Al XIX |
| $\mathbf{B_{20}}$ | = | $x_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $\left(a x_{20} + b y_{20} \cos{\gamma} + c_{x} z_{20}\right) \,\mathbf{\hat{x}}+\left(b y_{20} \sin{\gamma} + c_{y} z_{20}\right) \,\mathbf{\hat{y}}+c_{z} z_{20} \,\mathbf{\hat{z}}$ | (1a) | Al XX |
| $\mathbf{B_{21}}$ | = | $x_{21} \, \mathbf{a}_{1}+y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $\left(a x_{21} + b y_{21} \cos{\gamma} + c_{x} z_{21}\right) \,\mathbf{\hat{x}}+\left(b y_{21} \sin{\gamma} + c_{y} z_{21}\right) \,\mathbf{\hat{y}}+c_{z} z_{21} \,\mathbf{\hat{z}}$ | (1a) | Al XXI |
| $\mathbf{B_{22}}$ | = | $x_{22} \, \mathbf{a}_{1}+y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $\left(a x_{22} + b y_{22} \cos{\gamma} + c_{x} z_{22}\right) \,\mathbf{\hat{x}}+\left(b y_{22} \sin{\gamma} + c_{y} z_{22}\right) \,\mathbf{\hat{y}}+c_{z} z_{22} \,\mathbf{\hat{z}}$ | (1a) | Al XXII |
| $\mathbf{B_{23}}$ | = | $x_{23} \, \mathbf{a}_{1}+y_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $\left(a x_{23} + b y_{23} \cos{\gamma} + c_{x} z_{23}\right) \,\mathbf{\hat{x}}+\left(b y_{23} \sin{\gamma} + c_{y} z_{23}\right) \,\mathbf{\hat{y}}+c_{z} z_{23} \,\mathbf{\hat{z}}$ | (1a) | Al XXIII |
| $\mathbf{B_{24}}$ | = | $x_{24} \, \mathbf{a}_{1}+y_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $\left(a x_{24} + b y_{24} \cos{\gamma} + c_{x} z_{24}\right) \,\mathbf{\hat{x}}+\left(b y_{24} \sin{\gamma} + c_{y} z_{24}\right) \,\mathbf{\hat{y}}+c_{z} z_{24} \,\mathbf{\hat{z}}$ | (1a) | Al XXIV |
| $\mathbf{B_{25}}$ | = | $x_{25} \, \mathbf{a}_{1}+y_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $\left(a x_{25} + b y_{25} \cos{\gamma} + c_{x} z_{25}\right) \,\mathbf{\hat{x}}+\left(b y_{25} \sin{\gamma} + c_{y} z_{25}\right) \,\mathbf{\hat{y}}+c_{z} z_{25} \,\mathbf{\hat{z}}$ | (1a) | Al XXV |
| $\mathbf{B_{26}}$ | = | $x_{26} \, \mathbf{a}_{1}+y_{26} \, \mathbf{a}_{2}+z_{26} \, \mathbf{a}_{3}$ | = | $\left(a x_{26} + b y_{26} \cos{\gamma} + c_{x} z_{26}\right) \,\mathbf{\hat{x}}+\left(b y_{26} \sin{\gamma} + c_{y} z_{26}\right) \,\mathbf{\hat{y}}+c_{z} z_{26} \,\mathbf{\hat{z}}$ | (1a) | Al XXVI |
| $\mathbf{B_{27}}$ | = | $x_{27} \, \mathbf{a}_{1}+y_{27} \, \mathbf{a}_{2}+z_{27} \, \mathbf{a}_{3}$ | = | $\left(a x_{27} + b y_{27} \cos{\gamma} + c_{x} z_{27}\right) \,\mathbf{\hat{x}}+\left(b y_{27} \sin{\gamma} + c_{y} z_{27}\right) \,\mathbf{\hat{y}}+c_{z} z_{27} \,\mathbf{\hat{z}}$ | (1a) | Al XXVII |
| $\mathbf{B_{28}}$ | = | $x_{28} \, \mathbf{a}_{1}+y_{28} \, \mathbf{a}_{2}+z_{28} \, \mathbf{a}_{3}$ | = | $\left(a x_{28} + b y_{28} \cos{\gamma} + c_{x} z_{28}\right) \,\mathbf{\hat{x}}+\left(b y_{28} \sin{\gamma} + c_{y} z_{28}\right) \,\mathbf{\hat{y}}+c_{z} z_{28} \,\mathbf{\hat{z}}$ | (1a) | Al XXVIII |
| $\mathbf{B_{29}}$ | = | $x_{29} \, \mathbf{a}_{1}+y_{29} \, \mathbf{a}_{2}+z_{29} \, \mathbf{a}_{3}$ | = | $\left(a x_{29} + b y_{29} \cos{\gamma} + c_{x} z_{29}\right) \,\mathbf{\hat{x}}+\left(b y_{29} \sin{\gamma} + c_{y} z_{29}\right) \,\mathbf{\hat{y}}+c_{z} z_{29} \,\mathbf{\hat{z}}$ | (1a) | Al XXIX |
| $\mathbf{B_{30}}$ | = | $x_{30} \, \mathbf{a}_{1}+y_{30} \, \mathbf{a}_{2}+z_{30} \, \mathbf{a}_{3}$ | = | $\left(a x_{30} + b y_{30} \cos{\gamma} + c_{x} z_{30}\right) \,\mathbf{\hat{x}}+\left(b y_{30} \sin{\gamma} + c_{y} z_{30}\right) \,\mathbf{\hat{y}}+c_{z} z_{30} \,\mathbf{\hat{z}}$ | (1a) | Al XXX |
| $\mathbf{B_{31}}$ | = | $x_{31} \, \mathbf{a}_{1}+y_{31} \, \mathbf{a}_{2}+z_{31} \, \mathbf{a}_{3}$ | = | $\left(a x_{31} + b y_{31} \cos{\gamma} + c_{x} z_{31}\right) \,\mathbf{\hat{x}}+\left(b y_{31} \sin{\gamma} + c_{y} z_{31}\right) \,\mathbf{\hat{y}}+c_{z} z_{31} \,\mathbf{\hat{z}}$ | (1a) | Al XXXI |
| $\mathbf{B_{32}}$ | = | $x_{32} \, \mathbf{a}_{1}+y_{32} \, \mathbf{a}_{2}+z_{32} \, \mathbf{a}_{3}$ | = | $\left(a x_{32} + b y_{32} \cos{\gamma} + c_{x} z_{32}\right) \,\mathbf{\hat{x}}+\left(b y_{32} \sin{\gamma} + c_{y} z_{32}\right) \,\mathbf{\hat{y}}+c_{z} z_{32} \,\mathbf{\hat{z}}$ | (1a) | Al XXXII |
| $\mathbf{B_{33}}$ | = | $x_{33} \, \mathbf{a}_{1}+y_{33} \, \mathbf{a}_{2}+z_{33} \, \mathbf{a}_{3}$ | = | $\left(a x_{33} + b y_{33} \cos{\gamma} + c_{x} z_{33}\right) \,\mathbf{\hat{x}}+\left(b y_{33} \sin{\gamma} + c_{y} z_{33}\right) \,\mathbf{\hat{y}}+c_{z} z_{33} \,\mathbf{\hat{z}}$ | (1a) | Al XXXIII |
| $\mathbf{B_{34}}$ | = | $x_{34} \, \mathbf{a}_{1}+y_{34} \, \mathbf{a}_{2}+z_{34} \, \mathbf{a}_{3}$ | = | $\left(a x_{34} + b y_{34} \cos{\gamma} + c_{x} z_{34}\right) \,\mathbf{\hat{x}}+\left(b y_{34} \sin{\gamma} + c_{y} z_{34}\right) \,\mathbf{\hat{y}}+c_{z} z_{34} \,\mathbf{\hat{z}}$ | (1a) | Al XXXIV |
| $\mathbf{B_{35}}$ | = | $x_{35} \, \mathbf{a}_{1}+y_{35} \, \mathbf{a}_{2}+z_{35} \, \mathbf{a}_{3}$ | = | $\left(a x_{35} + b y_{35} \cos{\gamma} + c_{x} z_{35}\right) \,\mathbf{\hat{x}}+\left(b y_{35} \sin{\gamma} + c_{y} z_{35}\right) \,\mathbf{\hat{y}}+c_{z} z_{35} \,\mathbf{\hat{z}}$ | (1a) | Al XXXV |
| $\mathbf{B_{36}}$ | = | $x_{36} \, \mathbf{a}_{1}+y_{36} \, \mathbf{a}_{2}+z_{36} \, \mathbf{a}_{3}$ | = | $\left(a x_{36} + b y_{36} \cos{\gamma} + c_{x} z_{36}\right) \,\mathbf{\hat{x}}+\left(b y_{36} \sin{\gamma} + c_{y} z_{36}\right) \,\mathbf{\hat{y}}+c_{z} z_{36} \,\mathbf{\hat{z}}$ | (1a) | Al XXXVI |
| $\mathbf{B_{37}}$ | = | $x_{37} \, \mathbf{a}_{1}+y_{37} \, \mathbf{a}_{2}+z_{37} \, \mathbf{a}_{3}$ | = | $\left(a x_{37} + b y_{37} \cos{\gamma} + c_{x} z_{37}\right) \,\mathbf{\hat{x}}+\left(b y_{37} \sin{\gamma} + c_{y} z_{37}\right) \,\mathbf{\hat{y}}+c_{z} z_{37} \,\mathbf{\hat{z}}$ | (1a) | Al XXXVII |
| $\mathbf{B_{38}}$ | = | $x_{38} \, \mathbf{a}_{1}+y_{38} \, \mathbf{a}_{2}+z_{38} \, \mathbf{a}_{3}$ | = | $\left(a x_{38} + b y_{38} \cos{\gamma} + c_{x} z_{38}\right) \,\mathbf{\hat{x}}+\left(b y_{38} \sin{\gamma} + c_{y} z_{38}\right) \,\mathbf{\hat{y}}+c_{z} z_{38} \,\mathbf{\hat{z}}$ | (1a) | Al XXXVIII |
| $\mathbf{B_{39}}$ | = | $x_{39} \, \mathbf{a}_{1}+y_{39} \, \mathbf{a}_{2}+z_{39} \, \mathbf{a}_{3}$ | = | $\left(a x_{39} + b y_{39} \cos{\gamma} + c_{x} z_{39}\right) \,\mathbf{\hat{x}}+\left(b y_{39} \sin{\gamma} + c_{y} z_{39}\right) \,\mathbf{\hat{y}}+c_{z} z_{39} \,\mathbf{\hat{z}}$ | (1a) | Al XXXIX |
| $\mathbf{B_{40}}$ | = | $x_{40} \, \mathbf{a}_{1}+y_{40} \, \mathbf{a}_{2}+z_{40} \, \mathbf{a}_{3}$ | = | $\left(a x_{40} + b y_{40} \cos{\gamma} + c_{x} z_{40}\right) \,\mathbf{\hat{x}}+\left(b y_{40} \sin{\gamma} + c_{y} z_{40}\right) \,\mathbf{\hat{y}}+c_{z} z_{40} \,\mathbf{\hat{z}}$ | (1a) | Al XL |
| $\mathbf{B_{41}}$ | = | $x_{41} \, \mathbf{a}_{1}+y_{41} \, \mathbf{a}_{2}+z_{41} \, \mathbf{a}_{3}$ | = | $\left(a x_{41} + b y_{41} \cos{\gamma} + c_{x} z_{41}\right) \,\mathbf{\hat{x}}+\left(b y_{41} \sin{\gamma} + c_{y} z_{41}\right) \,\mathbf{\hat{y}}+c_{z} z_{41} \,\mathbf{\hat{z}}$ | (1a) | O I |
| $\mathbf{B_{42}}$ | = | $x_{42} \, \mathbf{a}_{1}+y_{42} \, \mathbf{a}_{2}+z_{42} \, \mathbf{a}_{3}$ | = | $\left(a x_{42} + b y_{42} \cos{\gamma} + c_{x} z_{42}\right) \,\mathbf{\hat{x}}+\left(b y_{42} \sin{\gamma} + c_{y} z_{42}\right) \,\mathbf{\hat{y}}+c_{z} z_{42} \,\mathbf{\hat{z}}$ | (1a) | O II |
| $\mathbf{B_{43}}$ | = | $x_{43} \, \mathbf{a}_{1}+y_{43} \, \mathbf{a}_{2}+z_{43} \, \mathbf{a}_{3}$ | = | $\left(a x_{43} + b y_{43} \cos{\gamma} + c_{x} z_{43}\right) \,\mathbf{\hat{x}}+\left(b y_{43} \sin{\gamma} + c_{y} z_{43}\right) \,\mathbf{\hat{y}}+c_{z} z_{43} \,\mathbf{\hat{z}}$ | (1a) | O III |
| $\mathbf{B_{44}}$ | = | $x_{44} \, \mathbf{a}_{1}+y_{44} \, \mathbf{a}_{2}+z_{44} \, \mathbf{a}_{3}$ | = | $\left(a x_{44} + b y_{44} \cos{\gamma} + c_{x} z_{44}\right) \,\mathbf{\hat{x}}+\left(b y_{44} \sin{\gamma} + c_{y} z_{44}\right) \,\mathbf{\hat{y}}+c_{z} z_{44} \,\mathbf{\hat{z}}$ | (1a) | O IV |
| $\mathbf{B_{45}}$ | = | $x_{45} \, \mathbf{a}_{1}+y_{45} \, \mathbf{a}_{2}+z_{45} \, \mathbf{a}_{3}$ | = | $\left(a x_{45} + b y_{45} \cos{\gamma} + c_{x} z_{45}\right) \,\mathbf{\hat{x}}+\left(b y_{45} \sin{\gamma} + c_{y} z_{45}\right) \,\mathbf{\hat{y}}+c_{z} z_{45} \,\mathbf{\hat{z}}$ | (1a) | O V |
| $\mathbf{B_{46}}$ | = | $x_{46} \, \mathbf{a}_{1}+y_{46} \, \mathbf{a}_{2}+z_{46} \, \mathbf{a}_{3}$ | = | $\left(a x_{46} + b y_{46} \cos{\gamma} + c_{x} z_{46}\right) \,\mathbf{\hat{x}}+\left(b y_{46} \sin{\gamma} + c_{y} z_{46}\right) \,\mathbf{\hat{y}}+c_{z} z_{46} \,\mathbf{\hat{z}}$ | (1a) | O VI |
| $\mathbf{B_{47}}$ | = | $x_{47} \, \mathbf{a}_{1}+y_{47} \, \mathbf{a}_{2}+z_{47} \, \mathbf{a}_{3}$ | = | $\left(a x_{47} + b y_{47} \cos{\gamma} + c_{x} z_{47}\right) \,\mathbf{\hat{x}}+\left(b y_{47} \sin{\gamma} + c_{y} z_{47}\right) \,\mathbf{\hat{y}}+c_{z} z_{47} \,\mathbf{\hat{z}}$ | (1a) | O VII |
| $\mathbf{B_{48}}$ | = | $x_{48} \, \mathbf{a}_{1}+y_{48} \, \mathbf{a}_{2}+z_{48} \, \mathbf{a}_{3}$ | = | $\left(a x_{48} + b y_{48} \cos{\gamma} + c_{x} z_{48}\right) \,\mathbf{\hat{x}}+\left(b y_{48} \sin{\gamma} + c_{y} z_{48}\right) \,\mathbf{\hat{y}}+c_{z} z_{48} \,\mathbf{\hat{z}}$ | (1a) | O VIII |
| $\mathbf{B_{49}}$ | = | $x_{49} \, \mathbf{a}_{1}+y_{49} \, \mathbf{a}_{2}+z_{49} \, \mathbf{a}_{3}$ | = | $\left(a x_{49} + b y_{49} \cos{\gamma} + c_{x} z_{49}\right) \,\mathbf{\hat{x}}+\left(b y_{49} \sin{\gamma} + c_{y} z_{49}\right) \,\mathbf{\hat{y}}+c_{z} z_{49} \,\mathbf{\hat{z}}$ | (1a) | O IX |
| $\mathbf{B_{50}}$ | = | $x_{50} \, \mathbf{a}_{1}+y_{50} \, \mathbf{a}_{2}+z_{50} \, \mathbf{a}_{3}$ | = | $\left(a x_{50} + b y_{50} \cos{\gamma} + c_{x} z_{50}\right) \,\mathbf{\hat{x}}+\left(b y_{50} \sin{\gamma} + c_{y} z_{50}\right) \,\mathbf{\hat{y}}+c_{z} z_{50} \,\mathbf{\hat{z}}$ | (1a) | O X |
| $\mathbf{B_{51}}$ | = | $x_{51} \, \mathbf{a}_{1}+y_{51} \, \mathbf{a}_{2}+z_{51} \, \mathbf{a}_{3}$ | = | $\left(a x_{51} + b y_{51} \cos{\gamma} + c_{x} z_{51}\right) \,\mathbf{\hat{x}}+\left(b y_{51} \sin{\gamma} + c_{y} z_{51}\right) \,\mathbf{\hat{y}}+c_{z} z_{51} \,\mathbf{\hat{z}}$ | (1a) | O XI |
| $\mathbf{B_{52}}$ | = | $x_{52} \, \mathbf{a}_{1}+y_{52} \, \mathbf{a}_{2}+z_{52} \, \mathbf{a}_{3}$ | = | $\left(a x_{52} + b y_{52} \cos{\gamma} + c_{x} z_{52}\right) \,\mathbf{\hat{x}}+\left(b y_{52} \sin{\gamma} + c_{y} z_{52}\right) \,\mathbf{\hat{y}}+c_{z} z_{52} \,\mathbf{\hat{z}}$ | (1a) | O XII |
| $\mathbf{B_{53}}$ | = | $x_{53} \, \mathbf{a}_{1}+y_{53} \, \mathbf{a}_{2}+z_{53} \, \mathbf{a}_{3}$ | = | $\left(a x_{53} + b y_{53} \cos{\gamma} + c_{x} z_{53}\right) \,\mathbf{\hat{x}}+\left(b y_{53} \sin{\gamma} + c_{y} z_{53}\right) \,\mathbf{\hat{y}}+c_{z} z_{53} \,\mathbf{\hat{z}}$ | (1a) | O XIII |
| $\mathbf{B_{54}}$ | = | $x_{54} \, \mathbf{a}_{1}+y_{54} \, \mathbf{a}_{2}+z_{54} \, \mathbf{a}_{3}$ | = | $\left(a x_{54} + b y_{54} \cos{\gamma} + c_{x} z_{54}\right) \,\mathbf{\hat{x}}+\left(b y_{54} \sin{\gamma} + c_{y} z_{54}\right) \,\mathbf{\hat{y}}+c_{z} z_{54} \,\mathbf{\hat{z}}$ | (1a) | O XIV |
| $\mathbf{B_{55}}$ | = | $x_{55} \, \mathbf{a}_{1}+y_{55} \, \mathbf{a}_{2}+z_{55} \, \mathbf{a}_{3}$ | = | $\left(a x_{55} + b y_{55} \cos{\gamma} + c_{x} z_{55}\right) \,\mathbf{\hat{x}}+\left(b y_{55} \sin{\gamma} + c_{y} z_{55}\right) \,\mathbf{\hat{y}}+c_{z} z_{55} \,\mathbf{\hat{z}}$ | (1a) | O XV |
| $\mathbf{B_{56}}$ | = | $x_{56} \, \mathbf{a}_{1}+y_{56} \, \mathbf{a}_{2}+z_{56} \, \mathbf{a}_{3}$ | = | $\left(a x_{56} + b y_{56} \cos{\gamma} + c_{x} z_{56}\right) \,\mathbf{\hat{x}}+\left(b y_{56} \sin{\gamma} + c_{y} z_{56}\right) \,\mathbf{\hat{y}}+c_{z} z_{56} \,\mathbf{\hat{z}}$ | (1a) | O XVI |
| $\mathbf{B_{57}}$ | = | $x_{57} \, \mathbf{a}_{1}+y_{57} \, \mathbf{a}_{2}+z_{57} \, \mathbf{a}_{3}$ | = | $\left(a x_{57} + b y_{57} \cos{\gamma} + c_{x} z_{57}\right) \,\mathbf{\hat{x}}+\left(b y_{57} \sin{\gamma} + c_{y} z_{57}\right) \,\mathbf{\hat{y}}+c_{z} z_{57} \,\mathbf{\hat{z}}$ | (1a) | O XVII |
| $\mathbf{B_{58}}$ | = | $x_{58} \, \mathbf{a}_{1}+y_{58} \, \mathbf{a}_{2}+z_{58} \, \mathbf{a}_{3}$ | = | $\left(a x_{58} + b y_{58} \cos{\gamma} + c_{x} z_{58}\right) \,\mathbf{\hat{x}}+\left(b y_{58} \sin{\gamma} + c_{y} z_{58}\right) \,\mathbf{\hat{y}}+c_{z} z_{58} \,\mathbf{\hat{z}}$ | (1a) | O XVIII |
| $\mathbf{B_{59}}$ | = | $x_{59} \, \mathbf{a}_{1}+y_{59} \, \mathbf{a}_{2}+z_{59} \, \mathbf{a}_{3}$ | = | $\left(a x_{59} + b y_{59} \cos{\gamma} + c_{x} z_{59}\right) \,\mathbf{\hat{x}}+\left(b y_{59} \sin{\gamma} + c_{y} z_{59}\right) \,\mathbf{\hat{y}}+c_{z} z_{59} \,\mathbf{\hat{z}}$ | (1a) | O XIX |
| $\mathbf{B_{60}}$ | = | $x_{60} \, \mathbf{a}_{1}+y_{60} \, \mathbf{a}_{2}+z_{60} \, \mathbf{a}_{3}$ | = | $\left(a x_{60} + b y_{60} \cos{\gamma} + c_{x} z_{60}\right) \,\mathbf{\hat{x}}+\left(b y_{60} \sin{\gamma} + c_{y} z_{60}\right) \,\mathbf{\hat{y}}+c_{z} z_{60} \,\mathbf{\hat{z}}$ | (1a) | O XX |
| $\mathbf{B_{61}}$ | = | $x_{61} \, \mathbf{a}_{1}+y_{61} \, \mathbf{a}_{2}+z_{61} \, \mathbf{a}_{3}$ | = | $\left(a x_{61} + b y_{61} \cos{\gamma} + c_{x} z_{61}\right) \,\mathbf{\hat{x}}+\left(b y_{61} \sin{\gamma} + c_{y} z_{61}\right) \,\mathbf{\hat{y}}+c_{z} z_{61} \,\mathbf{\hat{z}}$ | (1a) | O XXI |
| $\mathbf{B_{62}}$ | = | $x_{62} \, \mathbf{a}_{1}+y_{62} \, \mathbf{a}_{2}+z_{62} \, \mathbf{a}_{3}$ | = | $\left(a x_{62} + b y_{62} \cos{\gamma} + c_{x} z_{62}\right) \,\mathbf{\hat{x}}+\left(b y_{62} \sin{\gamma} + c_{y} z_{62}\right) \,\mathbf{\hat{y}}+c_{z} z_{62} \,\mathbf{\hat{z}}$ | (1a) | O XXII |
| $\mathbf{B_{63}}$ | = | $x_{63} \, \mathbf{a}_{1}+y_{63} \, \mathbf{a}_{2}+z_{63} \, \mathbf{a}_{3}$ | = | $\left(a x_{63} + b y_{63} \cos{\gamma} + c_{x} z_{63}\right) \,\mathbf{\hat{x}}+\left(b y_{63} \sin{\gamma} + c_{y} z_{63}\right) \,\mathbf{\hat{y}}+c_{z} z_{63} \,\mathbf{\hat{z}}$ | (1a) | O XXIII |
| $\mathbf{B_{64}}$ | = | $x_{64} \, \mathbf{a}_{1}+y_{64} \, \mathbf{a}_{2}+z_{64} \, \mathbf{a}_{3}$ | = | $\left(a x_{64} + b y_{64} \cos{\gamma} + c_{x} z_{64}\right) \,\mathbf{\hat{x}}+\left(b y_{64} \sin{\gamma} + c_{y} z_{64}\right) \,\mathbf{\hat{y}}+c_{z} z_{64} \,\mathbf{\hat{z}}$ | (1a) | O XXIV |
| $\mathbf{B_{65}}$ | = | $x_{65} \, \mathbf{a}_{1}+y_{65} \, \mathbf{a}_{2}+z_{65} \, \mathbf{a}_{3}$ | = | $\left(a x_{65} + b y_{65} \cos{\gamma} + c_{x} z_{65}\right) \,\mathbf{\hat{x}}+\left(b y_{65} \sin{\gamma} + c_{y} z_{65}\right) \,\mathbf{\hat{y}}+c_{z} z_{65} \,\mathbf{\hat{z}}$ | (1a) | O XXV |
| $\mathbf{B_{66}}$ | = | $x_{66} \, \mathbf{a}_{1}+y_{66} \, \mathbf{a}_{2}+z_{66} \, \mathbf{a}_{3}$ | = | $\left(a x_{66} + b y_{66} \cos{\gamma} + c_{x} z_{66}\right) \,\mathbf{\hat{x}}+\left(b y_{66} \sin{\gamma} + c_{y} z_{66}\right) \,\mathbf{\hat{y}}+c_{z} z_{66} \,\mathbf{\hat{z}}$ | (1a) | O XXVI |
| $\mathbf{B_{67}}$ | = | $x_{67} \, \mathbf{a}_{1}+y_{67} \, \mathbf{a}_{2}+z_{67} \, \mathbf{a}_{3}$ | = | $\left(a x_{67} + b y_{67} \cos{\gamma} + c_{x} z_{67}\right) \,\mathbf{\hat{x}}+\left(b y_{67} \sin{\gamma} + c_{y} z_{67}\right) \,\mathbf{\hat{y}}+c_{z} z_{67} \,\mathbf{\hat{z}}$ | (1a) | O XXVII |
| $\mathbf{B_{68}}$ | = | $x_{68} \, \mathbf{a}_{1}+y_{68} \, \mathbf{a}_{2}+z_{68} \, \mathbf{a}_{3}$ | = | $\left(a x_{68} + b y_{68} \cos{\gamma} + c_{x} z_{68}\right) \,\mathbf{\hat{x}}+\left(b y_{68} \sin{\gamma} + c_{y} z_{68}\right) \,\mathbf{\hat{y}}+c_{z} z_{68} \,\mathbf{\hat{z}}$ | (1a) | O XXVIII |
| $\mathbf{B_{69}}$ | = | $x_{69} \, \mathbf{a}_{1}+y_{69} \, \mathbf{a}_{2}+z_{69} \, \mathbf{a}_{3}$ | = | $\left(a x_{69} + b y_{69} \cos{\gamma} + c_{x} z_{69}\right) \,\mathbf{\hat{x}}+\left(b y_{69} \sin{\gamma} + c_{y} z_{69}\right) \,\mathbf{\hat{y}}+c_{z} z_{69} \,\mathbf{\hat{z}}$ | (1a) | O XXIX |
| $\mathbf{B_{70}}$ | = | $x_{70} \, \mathbf{a}_{1}+y_{70} \, \mathbf{a}_{2}+z_{70} \, \mathbf{a}_{3}$ | = | $\left(a x_{70} + b y_{70} \cos{\gamma} + c_{x} z_{70}\right) \,\mathbf{\hat{x}}+\left(b y_{70} \sin{\gamma} + c_{y} z_{70}\right) \,\mathbf{\hat{y}}+c_{z} z_{70} \,\mathbf{\hat{z}}$ | (1a) | O XXX |
| $\mathbf{B_{71}}$ | = | $x_{71} \, \mathbf{a}_{1}+y_{71} \, \mathbf{a}_{2}+z_{71} \, \mathbf{a}_{3}$ | = | $\left(a x_{71} + b y_{71} \cos{\gamma} + c_{x} z_{71}\right) \,\mathbf{\hat{x}}+\left(b y_{71} \sin{\gamma} + c_{y} z_{71}\right) \,\mathbf{\hat{y}}+c_{z} z_{71} \,\mathbf{\hat{z}}$ | (1a) | O XXXI |
| $\mathbf{B_{72}}$ | = | $x_{72} \, \mathbf{a}_{1}+y_{72} \, \mathbf{a}_{2}+z_{72} \, \mathbf{a}_{3}$ | = | $\left(a x_{72} + b y_{72} \cos{\gamma} + c_{x} z_{72}\right) \,\mathbf{\hat{x}}+\left(b y_{72} \sin{\gamma} + c_{y} z_{72}\right) \,\mathbf{\hat{y}}+c_{z} z_{72} \,\mathbf{\hat{z}}$ | (1a) | O XXXII |
| $\mathbf{B_{73}}$ | = | $x_{73} \, \mathbf{a}_{1}+y_{73} \, \mathbf{a}_{2}+z_{73} \, \mathbf{a}_{3}$ | = | $\left(a x_{73} + b y_{73} \cos{\gamma} + c_{x} z_{73}\right) \,\mathbf{\hat{x}}+\left(b y_{73} \sin{\gamma} + c_{y} z_{73}\right) \,\mathbf{\hat{y}}+c_{z} z_{73} \,\mathbf{\hat{z}}$ | (1a) | O XXXIII |
| $\mathbf{B_{74}}$ | = | $x_{74} \, \mathbf{a}_{1}+y_{74} \, \mathbf{a}_{2}+z_{74} \, \mathbf{a}_{3}$ | = | $\left(a x_{74} + b y_{74} \cos{\gamma} + c_{x} z_{74}\right) \,\mathbf{\hat{x}}+\left(b y_{74} \sin{\gamma} + c_{y} z_{74}\right) \,\mathbf{\hat{y}}+c_{z} z_{74} \,\mathbf{\hat{z}}$ | (1a) | O XXXIV |
| $\mathbf{B_{75}}$ | = | $x_{75} \, \mathbf{a}_{1}+y_{75} \, \mathbf{a}_{2}+z_{75} \, \mathbf{a}_{3}$ | = | $\left(a x_{75} + b y_{75} \cos{\gamma} + c_{x} z_{75}\right) \,\mathbf{\hat{x}}+\left(b y_{75} \sin{\gamma} + c_{y} z_{75}\right) \,\mathbf{\hat{y}}+c_{z} z_{75} \,\mathbf{\hat{z}}$ | (1a) | O XXXV |
| $\mathbf{B_{76}}$ | = | $x_{76} \, \mathbf{a}_{1}+y_{76} \, \mathbf{a}_{2}+z_{76} \, \mathbf{a}_{3}$ | = | $\left(a x_{76} + b y_{76} \cos{\gamma} + c_{x} z_{76}\right) \,\mathbf{\hat{x}}+\left(b y_{76} \sin{\gamma} + c_{y} z_{76}\right) \,\mathbf{\hat{y}}+c_{z} z_{76} \,\mathbf{\hat{z}}$ | (1a) | O XXXVI |
| $\mathbf{B_{77}}$ | = | $x_{77} \, \mathbf{a}_{1}+y_{77} \, \mathbf{a}_{2}+z_{77} \, \mathbf{a}_{3}$ | = | $\left(a x_{77} + b y_{77} \cos{\gamma} + c_{x} z_{77}\right) \,\mathbf{\hat{x}}+\left(b y_{77} \sin{\gamma} + c_{y} z_{77}\right) \,\mathbf{\hat{y}}+c_{z} z_{77} \,\mathbf{\hat{z}}$ | (1a) | O XXXVII |
| $\mathbf{B_{78}}$ | = | $x_{78} \, \mathbf{a}_{1}+y_{78} \, \mathbf{a}_{2}+z_{78} \, \mathbf{a}_{3}$ | = | $\left(a x_{78} + b y_{78} \cos{\gamma} + c_{x} z_{78}\right) \,\mathbf{\hat{x}}+\left(b y_{78} \sin{\gamma} + c_{y} z_{78}\right) \,\mathbf{\hat{y}}+c_{z} z_{78} \,\mathbf{\hat{z}}$ | (1a) | O XXXVIII |
| $\mathbf{B_{79}}$ | = | $x_{79} \, \mathbf{a}_{1}+y_{79} \, \mathbf{a}_{2}+z_{79} \, \mathbf{a}_{3}$ | = | $\left(a x_{79} + b y_{79} \cos{\gamma} + c_{x} z_{79}\right) \,\mathbf{\hat{x}}+\left(b y_{79} \sin{\gamma} + c_{y} z_{79}\right) \,\mathbf{\hat{y}}+c_{z} z_{79} \,\mathbf{\hat{z}}$ | (1a) | O XXXIX |
| $\mathbf{B_{80}}$ | = | $x_{80} \, \mathbf{a}_{1}+y_{80} \, \mathbf{a}_{2}+z_{80} \, \mathbf{a}_{3}$ | = | $\left(a x_{80} + b y_{80} \cos{\gamma} + c_{x} z_{80}\right) \,\mathbf{\hat{x}}+\left(b y_{80} \sin{\gamma} + c_{y} z_{80}\right) \,\mathbf{\hat{y}}+c_{z} z_{80} \,\mathbf{\hat{z}}$ | (1a) | O XL |
| $\mathbf{B_{81}}$ | = | $x_{81} \, \mathbf{a}_{1}+y_{81} \, \mathbf{a}_{2}+z_{81} \, \mathbf{a}_{3}$ | = | $\left(a x_{81} + b y_{81} \cos{\gamma} + c_{x} z_{81}\right) \,\mathbf{\hat{x}}+\left(b y_{81} \sin{\gamma} + c_{y} z_{81}\right) \,\mathbf{\hat{y}}+c_{z} z_{81} \,\mathbf{\hat{z}}$ | (1a) | O XLI |
| $\mathbf{B_{82}}$ | = | $x_{82} \, \mathbf{a}_{1}+y_{82} \, \mathbf{a}_{2}+z_{82} \, \mathbf{a}_{3}$ | = | $\left(a x_{82} + b y_{82} \cos{\gamma} + c_{x} z_{82}\right) \,\mathbf{\hat{x}}+\left(b y_{82} \sin{\gamma} + c_{y} z_{82}\right) \,\mathbf{\hat{y}}+c_{z} z_{82} \,\mathbf{\hat{z}}$ | (1a) | O XLII |
| $\mathbf{B_{83}}$ | = | $x_{83} \, \mathbf{a}_{1}+y_{83} \, \mathbf{a}_{2}+z_{83} \, \mathbf{a}_{3}$ | = | $\left(a x_{83} + b y_{83} \cos{\gamma} + c_{x} z_{83}\right) \,\mathbf{\hat{x}}+\left(b y_{83} \sin{\gamma} + c_{y} z_{83}\right) \,\mathbf{\hat{y}}+c_{z} z_{83} \,\mathbf{\hat{z}}$ | (1a) | O XLIII |
| $\mathbf{B_{84}}$ | = | $x_{84} \, \mathbf{a}_{1}+y_{84} \, \mathbf{a}_{2}+z_{84} \, \mathbf{a}_{3}$ | = | $\left(a x_{84} + b y_{84} \cos{\gamma} + c_{x} z_{84}\right) \,\mathbf{\hat{x}}+\left(b y_{84} \sin{\gamma} + c_{y} z_{84}\right) \,\mathbf{\hat{y}}+c_{z} z_{84} \,\mathbf{\hat{z}}$ | (1a) | O XLIV |
| $\mathbf{B_{85}}$ | = | $x_{85} \, \mathbf{a}_{1}+y_{85} \, \mathbf{a}_{2}+z_{85} \, \mathbf{a}_{3}$ | = | $\left(a x_{85} + b y_{85} \cos{\gamma} + c_{x} z_{85}\right) \,\mathbf{\hat{x}}+\left(b y_{85} \sin{\gamma} + c_{y} z_{85}\right) \,\mathbf{\hat{y}}+c_{z} z_{85} \,\mathbf{\hat{z}}$ | (1a) | O XLV |
| $\mathbf{B_{86}}$ | = | $x_{86} \, \mathbf{a}_{1}+y_{86} \, \mathbf{a}_{2}+z_{86} \, \mathbf{a}_{3}$ | = | $\left(a x_{86} + b y_{86} \cos{\gamma} + c_{x} z_{86}\right) \,\mathbf{\hat{x}}+\left(b y_{86} \sin{\gamma} + c_{y} z_{86}\right) \,\mathbf{\hat{y}}+c_{z} z_{86} \,\mathbf{\hat{z}}$ | (1a) | O XLVI |
| $\mathbf{B_{87}}$ | = | $x_{87} \, \mathbf{a}_{1}+y_{87} \, \mathbf{a}_{2}+z_{87} \, \mathbf{a}_{3}$ | = | $\left(a x_{87} + b y_{87} \cos{\gamma} + c_{x} z_{87}\right) \,\mathbf{\hat{x}}+\left(b y_{87} \sin{\gamma} + c_{y} z_{87}\right) \,\mathbf{\hat{y}}+c_{z} z_{87} \,\mathbf{\hat{z}}$ | (1a) | O XLVII |
| $\mathbf{B_{88}}$ | = | $x_{88} \, \mathbf{a}_{1}+y_{88} \, \mathbf{a}_{2}+z_{88} \, \mathbf{a}_{3}$ | = | $\left(a x_{88} + b y_{88} \cos{\gamma} + c_{x} z_{88}\right) \,\mathbf{\hat{x}}+\left(b y_{88} \sin{\gamma} + c_{y} z_{88}\right) \,\mathbf{\hat{y}}+c_{z} z_{88} \,\mathbf{\hat{z}}$ | (1a) | O XLVIII |
| $\mathbf{B_{89}}$ | = | $x_{89} \, \mathbf{a}_{1}+y_{89} \, \mathbf{a}_{2}+z_{89} \, \mathbf{a}_{3}$ | = | $\left(a x_{89} + b y_{89} \cos{\gamma} + c_{x} z_{89}\right) \,\mathbf{\hat{x}}+\left(b y_{89} \sin{\gamma} + c_{y} z_{89}\right) \,\mathbf{\hat{y}}+c_{z} z_{89} \,\mathbf{\hat{z}}$ | (1a) | O XLIX |
| $\mathbf{B_{90}}$ | = | $x_{90} \, \mathbf{a}_{1}+y_{90} \, \mathbf{a}_{2}+z_{90} \, \mathbf{a}_{3}$ | = | $\left(a x_{90} + b y_{90} \cos{\gamma} + c_{x} z_{90}\right) \,\mathbf{\hat{x}}+\left(b y_{90} \sin{\gamma} + c_{y} z_{90}\right) \,\mathbf{\hat{y}}+c_{z} z_{90} \,\mathbf{\hat{z}}$ | (1a) | O L |
| $\mathbf{B_{91}}$ | = | $x_{91} \, \mathbf{a}_{1}+y_{91} \, \mathbf{a}_{2}+z_{91} \, \mathbf{a}_{3}$ | = | $\left(a x_{91} + b y_{91} \cos{\gamma} + c_{x} z_{91}\right) \,\mathbf{\hat{x}}+\left(b y_{91} \sin{\gamma} + c_{y} z_{91}\right) \,\mathbf{\hat{y}}+c_{z} z_{91} \,\mathbf{\hat{z}}$ | (1a) | O LI |
| $\mathbf{B_{92}}$ | = | $x_{92} \, \mathbf{a}_{1}+y_{92} \, \mathbf{a}_{2}+z_{92} \, \mathbf{a}_{3}$ | = | $\left(a x_{92} + b y_{92} \cos{\gamma} + c_{x} z_{92}\right) \,\mathbf{\hat{x}}+\left(b y_{92} \sin{\gamma} + c_{y} z_{92}\right) \,\mathbf{\hat{y}}+c_{z} z_{92} \,\mathbf{\hat{z}}$ | (1a) | O LII |
| $\mathbf{B_{93}}$ | = | $x_{93} \, \mathbf{a}_{1}+y_{93} \, \mathbf{a}_{2}+z_{93} \, \mathbf{a}_{3}$ | = | $\left(a x_{93} + b y_{93} \cos{\gamma} + c_{x} z_{93}\right) \,\mathbf{\hat{x}}+\left(b y_{93} \sin{\gamma} + c_{y} z_{93}\right) \,\mathbf{\hat{y}}+c_{z} z_{93} \,\mathbf{\hat{z}}$ | (1a) | O LIII |
| $\mathbf{B_{94}}$ | = | $x_{94} \, \mathbf{a}_{1}+y_{94} \, \mathbf{a}_{2}+z_{94} \, \mathbf{a}_{3}$ | = | $\left(a x_{94} + b y_{94} \cos{\gamma} + c_{x} z_{94}\right) \,\mathbf{\hat{x}}+\left(b y_{94} \sin{\gamma} + c_{y} z_{94}\right) \,\mathbf{\hat{y}}+c_{z} z_{94} \,\mathbf{\hat{z}}$ | (1a) | O LIV |
| $\mathbf{B_{95}}$ | = | $x_{95} \, \mathbf{a}_{1}+y_{95} \, \mathbf{a}_{2}+z_{95} \, \mathbf{a}_{3}$ | = | $\left(a x_{95} + b y_{95} \cos{\gamma} + c_{x} z_{95}\right) \,\mathbf{\hat{x}}+\left(b y_{95} \sin{\gamma} + c_{y} z_{95}\right) \,\mathbf{\hat{y}}+c_{z} z_{95} \,\mathbf{\hat{z}}$ | (1a) | O LV |
| $\mathbf{B_{96}}$ | = | $x_{96} \, \mathbf{a}_{1}+y_{96} \, \mathbf{a}_{2}+z_{96} \, \mathbf{a}_{3}$ | = | $\left(a x_{96} + b y_{96} \cos{\gamma} + c_{x} z_{96}\right) \,\mathbf{\hat{x}}+\left(b y_{96} \sin{\gamma} + c_{y} z_{96}\right) \,\mathbf{\hat{y}}+c_{z} z_{96} \,\mathbf{\hat{z}}$ | (1a) | O LVI |
| $\mathbf{B_{97}}$ | = | $x_{97} \, \mathbf{a}_{1}+y_{97} \, \mathbf{a}_{2}+z_{97} \, \mathbf{a}_{3}$ | = | $\left(a x_{97} + b y_{97} \cos{\gamma} + c_{x} z_{97}\right) \,\mathbf{\hat{x}}+\left(b y_{97} \sin{\gamma} + c_{y} z_{97}\right) \,\mathbf{\hat{y}}+c_{z} z_{97} \,\mathbf{\hat{z}}$ | (1a) | O LVII |
| $\mathbf{B_{98}}$ | = | $x_{98} \, \mathbf{a}_{1}+y_{98} \, \mathbf{a}_{2}+z_{98} \, \mathbf{a}_{3}$ | = | $\left(a x_{98} + b y_{98} \cos{\gamma} + c_{x} z_{98}\right) \,\mathbf{\hat{x}}+\left(b y_{98} \sin{\gamma} + c_{y} z_{98}\right) \,\mathbf{\hat{y}}+c_{z} z_{98} \,\mathbf{\hat{z}}$ | (1a) | O LVIII |
| $\mathbf{B_{99}}$ | = | $x_{99} \, \mathbf{a}_{1}+y_{99} \, \mathbf{a}_{2}+z_{99} \, \mathbf{a}_{3}$ | = | $\left(a x_{99} + b y_{99} \cos{\gamma} + c_{x} z_{99}\right) \,\mathbf{\hat{x}}+\left(b y_{99} \sin{\gamma} + c_{y} z_{99}\right) \,\mathbf{\hat{y}}+c_{z} z_{99} \,\mathbf{\hat{z}}$ | (1a) | O LIX |
| $\mathbf{B_{100}}$ | = | $x_{100} \, \mathbf{a}_{1}+y_{100} \, \mathbf{a}_{2}+z_{100} \, \mathbf{a}_{3}$ | = | $\left(a x_{100} + b y_{100} \cos{\gamma} + c_{x} z_{100}\right) \,\mathbf{\hat{x}}+\left(b y_{100} \sin{\gamma} + c_{y} z_{100}\right) \,\mathbf{\hat{y}}+c_{z} z_{100} \,\mathbf{\hat{z}}$ | (1a) | O LX |
| $\mathbf{B_{101}}$ | = | $x_{101} \, \mathbf{a}_{1}+y_{101} \, \mathbf{a}_{2}+z_{101} \, \mathbf{a}_{3}$ | = | $\left(a x_{101} + b y_{101} \cos{\gamma} + c_{x} z_{101}\right) \,\mathbf{\hat{x}}+\left(b y_{101} \sin{\gamma} + c_{y} z_{101}\right) \,\mathbf{\hat{y}}+c_{z} z_{101} \,\mathbf{\hat{z}}$ | (1a) | O LXI |
| $\mathbf{B_{102}}$ | = | $x_{102} \, \mathbf{a}_{1}+y_{102} \, \mathbf{a}_{2}+z_{102} \, \mathbf{a}_{3}$ | = | $\left(a x_{102} + b y_{102} \cos{\gamma} + c_{x} z_{102}\right) \,\mathbf{\hat{x}}+\left(b y_{102} \sin{\gamma} + c_{y} z_{102}\right) \,\mathbf{\hat{y}}+c_{z} z_{102} \,\mathbf{\hat{z}}$ | (1a) | O LXII |
| $\mathbf{B_{103}}$ | = | $x_{103} \, \mathbf{a}_{1}+y_{103} \, \mathbf{a}_{2}+z_{103} \, \mathbf{a}_{3}$ | = | $\left(a x_{103} + b y_{103} \cos{\gamma} + c_{x} z_{103}\right) \,\mathbf{\hat{x}}+\left(b y_{103} \sin{\gamma} + c_{y} z_{103}\right) \,\mathbf{\hat{y}}+c_{z} z_{103} \,\mathbf{\hat{z}}$ | (1a) | O LXIII |
| $\mathbf{B_{104}}$ | = | $x_{104} \, \mathbf{a}_{1}+y_{104} \, \mathbf{a}_{2}+z_{104} \, \mathbf{a}_{3}$ | = | $\left(a x_{104} + b y_{104} \cos{\gamma} + c_{x} z_{104}\right) \,\mathbf{\hat{x}}+\left(b y_{104} \sin{\gamma} + c_{y} z_{104}\right) \,\mathbf{\hat{y}}+c_{z} z_{104} \,\mathbf{\hat{z}}$ | (1a) | O LXIV |
| $\mathbf{B_{105}}$ | = | $x_{105} \, \mathbf{a}_{1}+y_{105} \, \mathbf{a}_{2}+z_{105} \, \mathbf{a}_{3}$ | = | $\left(a x_{105} + b y_{105} \cos{\gamma} + c_{x} z_{105}\right) \,\mathbf{\hat{x}}+\left(b y_{105} \sin{\gamma} + c_{y} z_{105}\right) \,\mathbf{\hat{y}}+c_{z} z_{105} \,\mathbf{\hat{z}}$ | (1a) | O LXV |
| $\mathbf{B_{106}}$ | = | $x_{106} \, \mathbf{a}_{1}+y_{106} \, \mathbf{a}_{2}+z_{106} \, \mathbf{a}_{3}$ | = | $\left(a x_{106} + b y_{106} \cos{\gamma} + c_{x} z_{106}\right) \,\mathbf{\hat{x}}+\left(b y_{106} \sin{\gamma} + c_{y} z_{106}\right) \,\mathbf{\hat{y}}+c_{z} z_{106} \,\mathbf{\hat{z}}$ | (1a) | O LXVI |
| $\mathbf{B_{107}}$ | = | $x_{107} \, \mathbf{a}_{1}+y_{107} \, \mathbf{a}_{2}+z_{107} \, \mathbf{a}_{3}$ | = | $\left(a x_{107} + b y_{107} \cos{\gamma} + c_{x} z_{107}\right) \,\mathbf{\hat{x}}+\left(b y_{107} \sin{\gamma} + c_{y} z_{107}\right) \,\mathbf{\hat{y}}+c_{z} z_{107} \,\mathbf{\hat{z}}$ | (1a) | O LXVII |
| $\mathbf{B_{108}}$ | = | $x_{108} \, \mathbf{a}_{1}+y_{108} \, \mathbf{a}_{2}+z_{108} \, \mathbf{a}_{3}$ | = | $\left(a x_{108} + b y_{108} \cos{\gamma} + c_{x} z_{108}\right) \,\mathbf{\hat{x}}+\left(b y_{108} \sin{\gamma} + c_{y} z_{108}\right) \,\mathbf{\hat{y}}+c_{z} z_{108} \,\mathbf{\hat{z}}$ | (1a) | O LXVIII |
| $\mathbf{B_{109}}$ | = | $x_{109} \, \mathbf{a}_{1}+y_{109} \, \mathbf{a}_{2}+z_{109} \, \mathbf{a}_{3}$ | = | $\left(a x_{109} + b y_{109} \cos{\gamma} + c_{x} z_{109}\right) \,\mathbf{\hat{x}}+\left(b y_{109} \sin{\gamma} + c_{y} z_{109}\right) \,\mathbf{\hat{y}}+c_{z} z_{109} \,\mathbf{\hat{z}}$ | (1a) | O LXIX |
| $\mathbf{B_{110}}$ | = | $x_{110} \, \mathbf{a}_{1}+y_{110} \, \mathbf{a}_{2}+z_{110} \, \mathbf{a}_{3}$ | = | $\left(a x_{110} + b y_{110} \cos{\gamma} + c_{x} z_{110}\right) \,\mathbf{\hat{x}}+\left(b y_{110} \sin{\gamma} + c_{y} z_{110}\right) \,\mathbf{\hat{y}}+c_{z} z_{110} \,\mathbf{\hat{z}}$ | (1a) | O LXX |
| $\mathbf{B_{111}}$ | = | $x_{111} \, \mathbf{a}_{1}+y_{111} \, \mathbf{a}_{2}+z_{111} \, \mathbf{a}_{3}$ | = | $\left(a x_{111} + b y_{111} \cos{\gamma} + c_{x} z_{111}\right) \,\mathbf{\hat{x}}+\left(b y_{111} \sin{\gamma} + c_{y} z_{111}\right) \,\mathbf{\hat{y}}+c_{z} z_{111} \,\mathbf{\hat{z}}$ | (1a) | O LXXI |
| $\mathbf{B_{112}}$ | = | $x_{112} \, \mathbf{a}_{1}+y_{112} \, \mathbf{a}_{2}+z_{112} \, \mathbf{a}_{3}$ | = | $\left(a x_{112} + b y_{112} \cos{\gamma} + c_{x} z_{112}\right) \,\mathbf{\hat{x}}+\left(b y_{112} \sin{\gamma} + c_{y} z_{112}\right) \,\mathbf{\hat{y}}+c_{z} z_{112} \,\mathbf{\hat{z}}$ | (1a) | O LXXII |
| $\mathbf{B_{113}}$ | = | $x_{113} \, \mathbf{a}_{1}+y_{113} \, \mathbf{a}_{2}+z_{113} \, \mathbf{a}_{3}$ | = | $\left(a x_{113} + b y_{113} \cos{\gamma} + c_{x} z_{113}\right) \,\mathbf{\hat{x}}+\left(b y_{113} \sin{\gamma} + c_{y} z_{113}\right) \,\mathbf{\hat{y}}+c_{z} z_{113} \,\mathbf{\hat{z}}$ | (1a) | O LXXIII |
| $\mathbf{B_{114}}$ | = | $x_{114} \, \mathbf{a}_{1}+y_{114} \, \mathbf{a}_{2}+z_{114} \, \mathbf{a}_{3}$ | = | $\left(a x_{114} + b y_{114} \cos{\gamma} + c_{x} z_{114}\right) \,\mathbf{\hat{x}}+\left(b y_{114} \sin{\gamma} + c_{y} z_{114}\right) \,\mathbf{\hat{y}}+c_{z} z_{114} \,\mathbf{\hat{z}}$ | (1a) | O LXXIV |
| $\mathbf{B_{115}}$ | = | $x_{115} \, \mathbf{a}_{1}+y_{115} \, \mathbf{a}_{2}+z_{115} \, \mathbf{a}_{3}$ | = | $\left(a x_{115} + b y_{115} \cos{\gamma} + c_{x} z_{115}\right) \,\mathbf{\hat{x}}+\left(b y_{115} \sin{\gamma} + c_{y} z_{115}\right) \,\mathbf{\hat{y}}+c_{z} z_{115} \,\mathbf{\hat{z}}$ | (1a) | O LXXV |
| $\mathbf{B_{116}}$ | = | $x_{116} \, \mathbf{a}_{1}+y_{116} \, \mathbf{a}_{2}+z_{116} \, \mathbf{a}_{3}$ | = | $\left(a x_{116} + b y_{116} \cos{\gamma} + c_{x} z_{116}\right) \,\mathbf{\hat{x}}+\left(b y_{116} \sin{\gamma} + c_{y} z_{116}\right) \,\mathbf{\hat{y}}+c_{z} z_{116} \,\mathbf{\hat{z}}$ | (1a) | O LXXVI |
| $\mathbf{B_{117}}$ | = | $x_{117} \, \mathbf{a}_{1}+y_{117} \, \mathbf{a}_{2}+z_{117} \, \mathbf{a}_{3}$ | = | $\left(a x_{117} + b y_{117} \cos{\gamma} + c_{x} z_{117}\right) \,\mathbf{\hat{x}}+\left(b y_{117} \sin{\gamma} + c_{y} z_{117}\right) \,\mathbf{\hat{y}}+c_{z} z_{117} \,\mathbf{\hat{z}}$ | (1a) | O LXXVII |
| $\mathbf{B_{118}}$ | = | $x_{118} \, \mathbf{a}_{1}+y_{118} \, \mathbf{a}_{2}+z_{118} \, \mathbf{a}_{3}$ | = | $\left(a x_{118} + b y_{118} \cos{\gamma} + c_{x} z_{118}\right) \,\mathbf{\hat{x}}+\left(b y_{118} \sin{\gamma} + c_{y} z_{118}\right) \,\mathbf{\hat{y}}+c_{z} z_{118} \,\mathbf{\hat{z}}$ | (1a) | O LXXVIII |
| $\mathbf{B_{119}}$ | = | $x_{119} \, \mathbf{a}_{1}+y_{119} \, \mathbf{a}_{2}+z_{119} \, \mathbf{a}_{3}$ | = | $\left(a x_{119} + b y_{119} \cos{\gamma} + c_{x} z_{119}\right) \,\mathbf{\hat{x}}+\left(b y_{119} \sin{\gamma} + c_{y} z_{119}\right) \,\mathbf{\hat{y}}+c_{z} z_{119} \,\mathbf{\hat{z}}$ | (1a) | O LXXIX |
| $\mathbf{B_{120}}$ | = | $x_{120} \, \mathbf{a}_{1}+y_{120} \, \mathbf{a}_{2}+z_{120} \, \mathbf{a}_{3}$ | = | $\left(a x_{120} + b y_{120} \cos{\gamma} + c_{x} z_{120}\right) \,\mathbf{\hat{x}}+\left(b y_{120} \sin{\gamma} + c_{y} z_{120}\right) \,\mathbf{\hat{y}}+c_{z} z_{120} \,\mathbf{\hat{z}}$ | (1a) | O LXXX |
| $\mathbf{B_{121}}$ | = | $x_{121} \, \mathbf{a}_{1}+y_{121} \, \mathbf{a}_{2}+z_{121} \, \mathbf{a}_{3}$ | = | $\left(a x_{121} + b y_{121} \cos{\gamma} + c_{x} z_{121}\right) \,\mathbf{\hat{x}}+\left(b y_{121} \sin{\gamma} + c_{y} z_{121}\right) \,\mathbf{\hat{y}}+c_{z} z_{121} \,\mathbf{\hat{z}}$ | (1a) | O LXXXI |
| $\mathbf{B_{122}}$ | = | $x_{122} \, \mathbf{a}_{1}+y_{122} \, \mathbf{a}_{2}+z_{122} \, \mathbf{a}_{3}$ | = | $\left(a x_{122} + b y_{122} \cos{\gamma} + c_{x} z_{122}\right) \,\mathbf{\hat{x}}+\left(b y_{122} \sin{\gamma} + c_{y} z_{122}\right) \,\mathbf{\hat{y}}+c_{z} z_{122} \,\mathbf{\hat{z}}$ | (1a) | O LXXXII |
| $\mathbf{B_{123}}$ | = | $x_{123} \, \mathbf{a}_{1}+y_{123} \, \mathbf{a}_{2}+z_{123} \, \mathbf{a}_{3}$ | = | $\left(a x_{123} + b y_{123} \cos{\gamma} + c_{x} z_{123}\right) \,\mathbf{\hat{x}}+\left(b y_{123} \sin{\gamma} + c_{y} z_{123}\right) \,\mathbf{\hat{y}}+c_{z} z_{123} \,\mathbf{\hat{z}}$ | (1a) | O LXXXIII |
| $\mathbf{B_{124}}$ | = | $x_{124} \, \mathbf{a}_{1}+y_{124} \, \mathbf{a}_{2}+z_{124} \, \mathbf{a}_{3}$ | = | $\left(a x_{124} + b y_{124} \cos{\gamma} + c_{x} z_{124}\right) \,\mathbf{\hat{x}}+\left(b y_{124} \sin{\gamma} + c_{y} z_{124}\right) \,\mathbf{\hat{y}}+c_{z} z_{124} \,\mathbf{\hat{z}}$ | (1a) | O LXXXIV |
| $\mathbf{B_{125}}$ | = | $x_{125} \, \mathbf{a}_{1}+y_{125} \, \mathbf{a}_{2}+z_{125} \, \mathbf{a}_{3}$ | = | $\left(a x_{125} + b y_{125} \cos{\gamma} + c_{x} z_{125}\right) \,\mathbf{\hat{x}}+\left(b y_{125} \sin{\gamma} + c_{y} z_{125}\right) \,\mathbf{\hat{y}}+c_{z} z_{125} \,\mathbf{\hat{z}}$ | (1a) | O LXXXV |
| $\mathbf{B_{126}}$ | = | $x_{126} \, \mathbf{a}_{1}+y_{126} \, \mathbf{a}_{2}+z_{126} \, \mathbf{a}_{3}$ | = | $\left(a x_{126} + b y_{126} \cos{\gamma} + c_{x} z_{126}\right) \,\mathbf{\hat{x}}+\left(b y_{126} \sin{\gamma} + c_{y} z_{126}\right) \,\mathbf{\hat{y}}+c_{z} z_{126} \,\mathbf{\hat{z}}$ | (1a) | O LXXXVI |
| $\mathbf{B_{127}}$ | = | $x_{127} \, \mathbf{a}_{1}+y_{127} \, \mathbf{a}_{2}+z_{127} \, \mathbf{a}_{3}$ | = | $\left(a x_{127} + b y_{127} \cos{\gamma} + c_{x} z_{127}\right) \,\mathbf{\hat{x}}+\left(b y_{127} \sin{\gamma} + c_{y} z_{127}\right) \,\mathbf{\hat{y}}+c_{z} z_{127} \,\mathbf{\hat{z}}$ | (1a) | O LXXXVII |
| $\mathbf{B_{128}}$ | = | $x_{128} \, \mathbf{a}_{1}+y_{128} \, \mathbf{a}_{2}+z_{128} \, \mathbf{a}_{3}$ | = | $\left(a x_{128} + b y_{128} \cos{\gamma} + c_{x} z_{128}\right) \,\mathbf{\hat{x}}+\left(b y_{128} \sin{\gamma} + c_{y} z_{128}\right) \,\mathbf{\hat{y}}+c_{z} z_{128} \,\mathbf{\hat{z}}$ | (1a) | O LXXXVIII |
| $\mathbf{B_{129}}$ | = | $x_{129} \, \mathbf{a}_{1}+y_{129} \, \mathbf{a}_{2}+z_{129} \, \mathbf{a}_{3}$ | = | $\left(a x_{129} + b y_{129} \cos{\gamma} + c_{x} z_{129}\right) \,\mathbf{\hat{x}}+\left(b y_{129} \sin{\gamma} + c_{y} z_{129}\right) \,\mathbf{\hat{y}}+c_{z} z_{129} \,\mathbf{\hat{z}}$ | (1a) | O LXXXIX |
| $\mathbf{B_{130}}$ | = | $x_{130} \, \mathbf{a}_{1}+y_{130} \, \mathbf{a}_{2}+z_{130} \, \mathbf{a}_{3}$ | = | $\left(a x_{130} + b y_{130} \cos{\gamma} + c_{x} z_{130}\right) \,\mathbf{\hat{x}}+\left(b y_{130} \sin{\gamma} + c_{y} z_{130}\right) \,\mathbf{\hat{y}}+c_{z} z_{130} \,\mathbf{\hat{z}}$ | (1a) | O XC |
| $\mathbf{B_{131}}$ | = | $x_{131} \, \mathbf{a}_{1}+y_{131} \, \mathbf{a}_{2}+z_{131} \, \mathbf{a}_{3}$ | = | $\left(a x_{131} + b y_{131} \cos{\gamma} + c_{x} z_{131}\right) \,\mathbf{\hat{x}}+\left(b y_{131} \sin{\gamma} + c_{y} z_{131}\right) \,\mathbf{\hat{y}}+c_{z} z_{131} \,\mathbf{\hat{z}}$ | (1a) | O XCI |
| $\mathbf{B_{132}}$ | = | $x_{132} \, \mathbf{a}_{1}+y_{132} \, \mathbf{a}_{2}+z_{132} \, \mathbf{a}_{3}$ | = | $\left(a x_{132} + b y_{132} \cos{\gamma} + c_{x} z_{132}\right) \,\mathbf{\hat{x}}+\left(b y_{132} \sin{\gamma} + c_{y} z_{132}\right) \,\mathbf{\hat{y}}+c_{z} z_{132} \,\mathbf{\hat{z}}$ | (1a) | O XCII |
| $\mathbf{B_{133}}$ | = | $x_{133} \, \mathbf{a}_{1}+y_{133} \, \mathbf{a}_{2}+z_{133} \, \mathbf{a}_{3}$ | = | $\left(a x_{133} + b y_{133} \cos{\gamma} + c_{x} z_{133}\right) \,\mathbf{\hat{x}}+\left(b y_{133} \sin{\gamma} + c_{y} z_{133}\right) \,\mathbf{\hat{y}}+c_{z} z_{133} \,\mathbf{\hat{z}}$ | (1a) | O XCIII |
| $\mathbf{B_{134}}$ | = | $x_{134} \, \mathbf{a}_{1}+y_{134} \, \mathbf{a}_{2}+z_{134} \, \mathbf{a}_{3}$ | = | $\left(a x_{134} + b y_{134} \cos{\gamma} + c_{x} z_{134}\right) \,\mathbf{\hat{x}}+\left(b y_{134} \sin{\gamma} + c_{y} z_{134}\right) \,\mathbf{\hat{y}}+c_{z} z_{134} \,\mathbf{\hat{z}}$ | (1a) | O XCIV |
| $\mathbf{B_{135}}$ | = | $x_{135} \, \mathbf{a}_{1}+y_{135} \, \mathbf{a}_{2}+z_{135} \, \mathbf{a}_{3}$ | = | $\left(a x_{135} + b y_{135} \cos{\gamma} + c_{x} z_{135}\right) \,\mathbf{\hat{x}}+\left(b y_{135} \sin{\gamma} + c_{y} z_{135}\right) \,\mathbf{\hat{y}}+c_{z} z_{135} \,\mathbf{\hat{z}}$ | (1a) | O XCV |
| $\mathbf{B_{136}}$ | = | $x_{136} \, \mathbf{a}_{1}+y_{136} \, \mathbf{a}_{2}+z_{136} \, \mathbf{a}_{3}$ | = | $\left(a x_{136} + b y_{136} \cos{\gamma} + c_{x} z_{136}\right) \,\mathbf{\hat{x}}+\left(b y_{136} \sin{\gamma} + c_{y} z_{136}\right) \,\mathbf{\hat{y}}+c_{z} z_{136} \,\mathbf{\hat{z}}$ | (1a) | O XCVI |
| $\mathbf{B_{137}}$ | = | $x_{137} \, \mathbf{a}_{1}+y_{137} \, \mathbf{a}_{2}+z_{137} \, \mathbf{a}_{3}$ | = | $\left(a x_{137} + b y_{137} \cos{\gamma} + c_{x} z_{137}\right) \,\mathbf{\hat{x}}+\left(b y_{137} \sin{\gamma} + c_{y} z_{137}\right) \,\mathbf{\hat{y}}+c_{z} z_{137} \,\mathbf{\hat{z}}$ | (1a) | O XCVII |
| $\mathbf{B_{138}}$ | = | $x_{138} \, \mathbf{a}_{1}+y_{138} \, \mathbf{a}_{2}+z_{138} \, \mathbf{a}_{3}$ | = | $\left(a x_{138} + b y_{138} \cos{\gamma} + c_{x} z_{138}\right) \,\mathbf{\hat{x}}+\left(b y_{138} \sin{\gamma} + c_{y} z_{138}\right) \,\mathbf{\hat{y}}+c_{z} z_{138} \,\mathbf{\hat{z}}$ | (1a) | O XCVIII |
| $\mathbf{B_{139}}$ | = | $x_{139} \, \mathbf{a}_{1}+y_{139} \, \mathbf{a}_{2}+z_{139} \, \mathbf{a}_{3}$ | = | $\left(a x_{139} + b y_{139} \cos{\gamma} + c_{x} z_{139}\right) \,\mathbf{\hat{x}}+\left(b y_{139} \sin{\gamma} + c_{y} z_{139}\right) \,\mathbf{\hat{y}}+c_{z} z_{139} \,\mathbf{\hat{z}}$ | (1a) | O XCIX |
| $\mathbf{B_{140}}$ | = | $x_{140} \, \mathbf{a}_{1}+y_{140} \, \mathbf{a}_{2}+z_{140} \, \mathbf{a}_{3}$ | = | $\left(a x_{140} + b y_{140} \cos{\gamma} + c_{x} z_{140}\right) \,\mathbf{\hat{x}}+\left(b y_{140} \sin{\gamma} + c_{y} z_{140}\right) \,\mathbf{\hat{y}}+c_{z} z_{140} \,\mathbf{\hat{z}}$ | (1a) | O C |
| $\mathbf{B_{141}}$ | = | $x_{141} \, \mathbf{a}_{1}+y_{141} \, \mathbf{a}_{2}+z_{141} \, \mathbf{a}_{3}$ | = | $\left(a x_{141} + b y_{141} \cos{\gamma} + c_{x} z_{141}\right) \,\mathbf{\hat{x}}+\left(b y_{141} \sin{\gamma} + c_{y} z_{141}\right) \,\mathbf{\hat{y}}+c_{z} z_{141} \,\mathbf{\hat{z}}$ | (1a) | O CI |
| $\mathbf{B_{142}}$ | = | $x_{142} \, \mathbf{a}_{1}+y_{142} \, \mathbf{a}_{2}+z_{142} \, \mathbf{a}_{3}$ | = | $\left(a x_{142} + b y_{142} \cos{\gamma} + c_{x} z_{142}\right) \,\mathbf{\hat{x}}+\left(b y_{142} \sin{\gamma} + c_{y} z_{142}\right) \,\mathbf{\hat{y}}+c_{z} z_{142} \,\mathbf{\hat{z}}$ | (1a) | O CII |
| $\mathbf{B_{143}}$ | = | $x_{143} \, \mathbf{a}_{1}+y_{143} \, \mathbf{a}_{2}+z_{143} \, \mathbf{a}_{3}$ | = | $\left(a x_{143} + b y_{143} \cos{\gamma} + c_{x} z_{143}\right) \,\mathbf{\hat{x}}+\left(b y_{143} \sin{\gamma} + c_{y} z_{143}\right) \,\mathbf{\hat{y}}+c_{z} z_{143} \,\mathbf{\hat{z}}$ | (1a) | O CIII |
| $\mathbf{B_{144}}$ | = | $x_{144} \, \mathbf{a}_{1}+y_{144} \, \mathbf{a}_{2}+z_{144} \, \mathbf{a}_{3}$ | = | $\left(a x_{144} + b y_{144} \cos{\gamma} + c_{x} z_{144}\right) \,\mathbf{\hat{x}}+\left(b y_{144} \sin{\gamma} + c_{y} z_{144}\right) \,\mathbf{\hat{y}}+c_{z} z_{144} \,\mathbf{\hat{z}}$ | (1a) | O CIV |
| $\mathbf{B_{145}}$ | = | $x_{145} \, \mathbf{a}_{1}+y_{145} \, \mathbf{a}_{2}+z_{145} \, \mathbf{a}_{3}$ | = | $\left(a x_{145} + b y_{145} \cos{\gamma} + c_{x} z_{145}\right) \,\mathbf{\hat{x}}+\left(b y_{145} \sin{\gamma} + c_{y} z_{145}\right) \,\mathbf{\hat{y}}+c_{z} z_{145} \,\mathbf{\hat{z}}$ | (1a) | O CV |
| $\mathbf{B_{146}}$ | = | $x_{146} \, \mathbf{a}_{1}+y_{146} \, \mathbf{a}_{2}+z_{146} \, \mathbf{a}_{3}$ | = | $\left(a x_{146} + b y_{146} \cos{\gamma} + c_{x} z_{146}\right) \,\mathbf{\hat{x}}+\left(b y_{146} \sin{\gamma} + c_{y} z_{146}\right) \,\mathbf{\hat{y}}+c_{z} z_{146} \,\mathbf{\hat{z}}$ | (1a) | O CVI |
| $\mathbf{B_{147}}$ | = | $x_{147} \, \mathbf{a}_{1}+y_{147} \, \mathbf{a}_{2}+z_{147} \, \mathbf{a}_{3}$ | = | $\left(a x_{147} + b y_{147} \cos{\gamma} + c_{x} z_{147}\right) \,\mathbf{\hat{x}}+\left(b y_{147} \sin{\gamma} + c_{y} z_{147}\right) \,\mathbf{\hat{y}}+c_{z} z_{147} \,\mathbf{\hat{z}}$ | (1a) | O CVII |
| $\mathbf{B_{148}}$ | = | $x_{148} \, \mathbf{a}_{1}+y_{148} \, \mathbf{a}_{2}+z_{148} \, \mathbf{a}_{3}$ | = | $\left(a x_{148} + b y_{148} \cos{\gamma} + c_{x} z_{148}\right) \,\mathbf{\hat{x}}+\left(b y_{148} \sin{\gamma} + c_{y} z_{148}\right) \,\mathbf{\hat{y}}+c_{z} z_{148} \,\mathbf{\hat{z}}$ | (1a) | O CVIII |
| $\mathbf{B_{149}}$ | = | $x_{149} \, \mathbf{a}_{1}+y_{149} \, \mathbf{a}_{2}+z_{149} \, \mathbf{a}_{3}$ | = | $\left(a x_{149} + b y_{149} \cos{\gamma} + c_{x} z_{149}\right) \,\mathbf{\hat{x}}+\left(b y_{149} \sin{\gamma} + c_{y} z_{149}\right) \,\mathbf{\hat{y}}+c_{z} z_{149} \,\mathbf{\hat{z}}$ | (1a) | O CIX |
| $\mathbf{B_{150}}$ | = | $x_{150} \, \mathbf{a}_{1}+y_{150} \, \mathbf{a}_{2}+z_{150} \, \mathbf{a}_{3}$ | = | $\left(a x_{150} + b y_{150} \cos{\gamma} + c_{x} z_{150}\right) \,\mathbf{\hat{x}}+\left(b y_{150} \sin{\gamma} + c_{y} z_{150}\right) \,\mathbf{\hat{y}}+c_{z} z_{150} \,\mathbf{\hat{z}}$ | (1a) | O CX |
| $\mathbf{B_{151}}$ | = | $x_{151} \, \mathbf{a}_{1}+y_{151} \, \mathbf{a}_{2}+z_{151} \, \mathbf{a}_{3}$ | = | $\left(a x_{151} + b y_{151} \cos{\gamma} + c_{x} z_{151}\right) \,\mathbf{\hat{x}}+\left(b y_{151} \sin{\gamma} + c_{y} z_{151}\right) \,\mathbf{\hat{y}}+c_{z} z_{151} \,\mathbf{\hat{z}}$ | (1a) | O CXI |
| $\mathbf{B_{152}}$ | = | $x_{152} \, \mathbf{a}_{1}+y_{152} \, \mathbf{a}_{2}+z_{152} \, \mathbf{a}_{3}$ | = | $\left(a x_{152} + b y_{152} \cos{\gamma} + c_{x} z_{152}\right) \,\mathbf{\hat{x}}+\left(b y_{152} \sin{\gamma} + c_{y} z_{152}\right) \,\mathbf{\hat{y}}+c_{z} z_{152} \,\mathbf{\hat{z}}$ | (1a) | O CXII |
| $\mathbf{B_{153}}$ | = | $x_{153} \, \mathbf{a}_{1}+y_{153} \, \mathbf{a}_{2}+z_{153} \, \mathbf{a}_{3}$ | = | $\left(a x_{153} + b y_{153} \cos{\gamma} + c_{x} z_{153}\right) \,\mathbf{\hat{x}}+\left(b y_{153} \sin{\gamma} + c_{y} z_{153}\right) \,\mathbf{\hat{y}}+c_{z} z_{153} \,\mathbf{\hat{z}}$ | (1a) | O CXIII |
| $\mathbf{B_{154}}$ | = | $x_{154} \, \mathbf{a}_{1}+y_{154} \, \mathbf{a}_{2}+z_{154} \, \mathbf{a}_{3}$ | = | $\left(a x_{154} + b y_{154} \cos{\gamma} + c_{x} z_{154}\right) \,\mathbf{\hat{x}}+\left(b y_{154} \sin{\gamma} + c_{y} z_{154}\right) \,\mathbf{\hat{y}}+c_{z} z_{154} \,\mathbf{\hat{z}}$ | (1a) | O CXIV |
| $\mathbf{B_{155}}$ | = | $x_{155} \, \mathbf{a}_{1}+y_{155} \, \mathbf{a}_{2}+z_{155} \, \mathbf{a}_{3}$ | = | $\left(a x_{155} + b y_{155} \cos{\gamma} + c_{x} z_{155}\right) \,\mathbf{\hat{x}}+\left(b y_{155} \sin{\gamma} + c_{y} z_{155}\right) \,\mathbf{\hat{y}}+c_{z} z_{155} \,\mathbf{\hat{z}}$ | (1a) | O CXV |
| $\mathbf{B_{156}}$ | = | $x_{156} \, \mathbf{a}_{1}+y_{156} \, \mathbf{a}_{2}+z_{156} \, \mathbf{a}_{3}$ | = | $\left(a x_{156} + b y_{156} \cos{\gamma} + c_{x} z_{156}\right) \,\mathbf{\hat{x}}+\left(b y_{156} \sin{\gamma} + c_{y} z_{156}\right) \,\mathbf{\hat{y}}+c_{z} z_{156} \,\mathbf{\hat{z}}$ | (1a) | O CXVI |
| $\mathbf{B_{157}}$ | = | $x_{157} \, \mathbf{a}_{1}+y_{157} \, \mathbf{a}_{2}+z_{157} \, \mathbf{a}_{3}$ | = | $\left(a x_{157} + b y_{157} \cos{\gamma} + c_{x} z_{157}\right) \,\mathbf{\hat{x}}+\left(b y_{157} \sin{\gamma} + c_{y} z_{157}\right) \,\mathbf{\hat{y}}+c_{z} z_{157} \,\mathbf{\hat{z}}$ | (1a) | O CXVII |
| $\mathbf{B_{158}}$ | = | $x_{158} \, \mathbf{a}_{1}+y_{158} \, \mathbf{a}_{2}+z_{158} \, \mathbf{a}_{3}$ | = | $\left(a x_{158} + b y_{158} \cos{\gamma} + c_{x} z_{158}\right) \,\mathbf{\hat{x}}+\left(b y_{158} \sin{\gamma} + c_{y} z_{158}\right) \,\mathbf{\hat{y}}+c_{z} z_{158} \,\mathbf{\hat{z}}$ | (1a) | O CXVIII |
| $\mathbf{B_{159}}$ | = | $x_{159} \, \mathbf{a}_{1}+y_{159} \, \mathbf{a}_{2}+z_{159} \, \mathbf{a}_{3}$ | = | $\left(a x_{159} + b y_{159} \cos{\gamma} + c_{x} z_{159}\right) \,\mathbf{\hat{x}}+\left(b y_{159} \sin{\gamma} + c_{y} z_{159}\right) \,\mathbf{\hat{y}}+c_{z} z_{159} \,\mathbf{\hat{z}}$ | (1a) | O CXIX |
| $\mathbf{B_{160}}$ | = | $x_{160} \, \mathbf{a}_{1}+y_{160} \, \mathbf{a}_{2}+z_{160} \, \mathbf{a}_{3}$ | = | $\left(a x_{160} + b y_{160} \cos{\gamma} + c_{x} z_{160}\right) \,\mathbf{\hat{x}}+\left(b y_{160} \sin{\gamma} + c_{y} z_{160}\right) \,\mathbf{\hat{y}}+c_{z} z_{160} \,\mathbf{\hat{z}}$ | (1a) | O CXX |
| $\mathbf{B_{161}}$ | = | $x_{161} \, \mathbf{a}_{1}+y_{161} \, \mathbf{a}_{2}+z_{161} \, \mathbf{a}_{3}$ | = | $\left(a x_{161} + b y_{161} \cos{\gamma} + c_{x} z_{161}\right) \,\mathbf{\hat{x}}+\left(b y_{161} \sin{\gamma} + c_{y} z_{161}\right) \,\mathbf{\hat{y}}+c_{z} z_{161} \,\mathbf{\hat{z}}$ | (1a) | O CXXI |
| $\mathbf{B_{162}}$ | = | $x_{162} \, \mathbf{a}_{1}+y_{162} \, \mathbf{a}_{2}+z_{162} \, \mathbf{a}_{3}$ | = | $\left(a x_{162} + b y_{162} \cos{\gamma} + c_{x} z_{162}\right) \,\mathbf{\hat{x}}+\left(b y_{162} \sin{\gamma} + c_{y} z_{162}\right) \,\mathbf{\hat{y}}+c_{z} z_{162} \,\mathbf{\hat{z}}$ | (1a) | O CXXII |
| $\mathbf{B_{163}}$ | = | $x_{163} \, \mathbf{a}_{1}+y_{163} \, \mathbf{a}_{2}+z_{163} \, \mathbf{a}_{3}$ | = | $\left(a x_{163} + b y_{163} \cos{\gamma} + c_{x} z_{163}\right) \,\mathbf{\hat{x}}+\left(b y_{163} \sin{\gamma} + c_{y} z_{163}\right) \,\mathbf{\hat{y}}+c_{z} z_{163} \,\mathbf{\hat{z}}$ | (1a) | O CXXIII |
| $\mathbf{B_{164}}$ | = | $x_{164} \, \mathbf{a}_{1}+y_{164} \, \mathbf{a}_{2}+z_{164} \, \mathbf{a}_{3}$ | = | $\left(a x_{164} + b y_{164} \cos{\gamma} + c_{x} z_{164}\right) \,\mathbf{\hat{x}}+\left(b y_{164} \sin{\gamma} + c_{y} z_{164}\right) \,\mathbf{\hat{y}}+c_{z} z_{164} \,\mathbf{\hat{z}}$ | (1a) | O CXXIV |
| $\mathbf{B_{165}}$ | = | $x_{165} \, \mathbf{a}_{1}+y_{165} \, \mathbf{a}_{2}+z_{165} \, \mathbf{a}_{3}$ | = | $\left(a x_{165} + b y_{165} \cos{\gamma} + c_{x} z_{165}\right) \,\mathbf{\hat{x}}+\left(b y_{165} \sin{\gamma} + c_{y} z_{165}\right) \,\mathbf{\hat{y}}+c_{z} z_{165} \,\mathbf{\hat{z}}$ | (1a) | O CXXV |
| $\mathbf{B_{166}}$ | = | $x_{166} \, \mathbf{a}_{1}+y_{166} \, \mathbf{a}_{2}+z_{166} \, \mathbf{a}_{3}$ | = | $\left(a x_{166} + b y_{166} \cos{\gamma} + c_{x} z_{166}\right) \,\mathbf{\hat{x}}+\left(b y_{166} \sin{\gamma} + c_{y} z_{166}\right) \,\mathbf{\hat{y}}+c_{z} z_{166} \,\mathbf{\hat{z}}$ | (1a) | O CXXVI |
| $\mathbf{B_{167}}$ | = | $x_{167} \, \mathbf{a}_{1}+y_{167} \, \mathbf{a}_{2}+z_{167} \, \mathbf{a}_{3}$ | = | $\left(a x_{167} + b y_{167} \cos{\gamma} + c_{x} z_{167}\right) \,\mathbf{\hat{x}}+\left(b y_{167} \sin{\gamma} + c_{y} z_{167}\right) \,\mathbf{\hat{y}}+c_{z} z_{167} \,\mathbf{\hat{z}}$ | (1a) | O CXXVII |
| $\mathbf{B_{168}}$ | = | $x_{168} \, \mathbf{a}_{1}+y_{168} \, \mathbf{a}_{2}+z_{168} \, \mathbf{a}_{3}$ | = | $\left(a x_{168} + b y_{168} \cos{\gamma} + c_{x} z_{168}\right) \,\mathbf{\hat{x}}+\left(b y_{168} \sin{\gamma} + c_{y} z_{168}\right) \,\mathbf{\hat{y}}+c_{z} z_{168} \,\mathbf{\hat{z}}$ | (1a) | O CXXVIII |
| $\mathbf{B_{169}}$ | = | $x_{169} \, \mathbf{a}_{1}+y_{169} \, \mathbf{a}_{2}+z_{169} \, \mathbf{a}_{3}$ | = | $\left(a x_{169} + b y_{169} \cos{\gamma} + c_{x} z_{169}\right) \,\mathbf{\hat{x}}+\left(b y_{169} \sin{\gamma} + c_{y} z_{169}\right) \,\mathbf{\hat{y}}+c_{z} z_{169} \,\mathbf{\hat{z}}$ | (1a) | O CXXIX |
| $\mathbf{B_{170}}$ | = | $x_{170} \, \mathbf{a}_{1}+y_{170} \, \mathbf{a}_{2}+z_{170} \, \mathbf{a}_{3}$ | = | $\left(a x_{170} + b y_{170} \cos{\gamma} + c_{x} z_{170}\right) \,\mathbf{\hat{x}}+\left(b y_{170} \sin{\gamma} + c_{y} z_{170}\right) \,\mathbf{\hat{y}}+c_{z} z_{170} \,\mathbf{\hat{z}}$ | (1a) | O CXXX |
| $\mathbf{B_{171}}$ | = | $x_{171} \, \mathbf{a}_{1}+y_{171} \, \mathbf{a}_{2}+z_{171} \, \mathbf{a}_{3}$ | = | $\left(a x_{171} + b y_{171} \cos{\gamma} + c_{x} z_{171}\right) \,\mathbf{\hat{x}}+\left(b y_{171} \sin{\gamma} + c_{y} z_{171}\right) \,\mathbf{\hat{y}}+c_{z} z_{171} \,\mathbf{\hat{z}}$ | (1a) | O CXXXI |
| $\mathbf{B_{172}}$ | = | $x_{172} \, \mathbf{a}_{1}+y_{172} \, \mathbf{a}_{2}+z_{172} \, \mathbf{a}_{3}$ | = | $\left(a x_{172} + b y_{172} \cos{\gamma} + c_{x} z_{172}\right) \,\mathbf{\hat{x}}+\left(b y_{172} \sin{\gamma} + c_{y} z_{172}\right) \,\mathbf{\hat{y}}+c_{z} z_{172} \,\mathbf{\hat{z}}$ | (1a) | O CXXXII |
| $\mathbf{B_{173}}$ | = | $x_{173} \, \mathbf{a}_{1}+y_{173} \, \mathbf{a}_{2}+z_{173} \, \mathbf{a}_{3}$ | = | $\left(a x_{173} + b y_{173} \cos{\gamma} + c_{x} z_{173}\right) \,\mathbf{\hat{x}}+\left(b y_{173} \sin{\gamma} + c_{y} z_{173}\right) \,\mathbf{\hat{y}}+c_{z} z_{173} \,\mathbf{\hat{z}}$ | (1a) | O CXXXIII |
| $\mathbf{B_{174}}$ | = | $x_{174} \, \mathbf{a}_{1}+y_{174} \, \mathbf{a}_{2}+z_{174} \, \mathbf{a}_{3}$ | = | $\left(a x_{174} + b y_{174} \cos{\gamma} + c_{x} z_{174}\right) \,\mathbf{\hat{x}}+\left(b y_{174} \sin{\gamma} + c_{y} z_{174}\right) \,\mathbf{\hat{y}}+c_{z} z_{174} \,\mathbf{\hat{z}}$ | (1a) | O CXXXIV |
| $\mathbf{B_{175}}$ | = | $x_{175} \, \mathbf{a}_{1}+y_{175} \, \mathbf{a}_{2}+z_{175} \, \mathbf{a}_{3}$ | = | $\left(a x_{175} + b y_{175} \cos{\gamma} + c_{x} z_{175}\right) \,\mathbf{\hat{x}}+\left(b y_{175} \sin{\gamma} + c_{y} z_{175}\right) \,\mathbf{\hat{y}}+c_{z} z_{175} \,\mathbf{\hat{z}}$ | (1a) | O CXXXV |
| $\mathbf{B_{176}}$ | = | $x_{176} \, \mathbf{a}_{1}+y_{176} \, \mathbf{a}_{2}+z_{176} \, \mathbf{a}_{3}$ | = | $\left(a x_{176} + b y_{176} \cos{\gamma} + c_{x} z_{176}\right) \,\mathbf{\hat{x}}+\left(b y_{176} \sin{\gamma} + c_{y} z_{176}\right) \,\mathbf{\hat{y}}+c_{z} z_{176} \,\mathbf{\hat{z}}$ | (1a) | O CXXXVI |
| $\mathbf{B_{177}}$ | = | $x_{177} \, \mathbf{a}_{1}+y_{177} \, \mathbf{a}_{2}+z_{177} \, \mathbf{a}_{3}$ | = | $\left(a x_{177} + b y_{177} \cos{\gamma} + c_{x} z_{177}\right) \,\mathbf{\hat{x}}+\left(b y_{177} \sin{\gamma} + c_{y} z_{177}\right) \,\mathbf{\hat{y}}+c_{z} z_{177} \,\mathbf{\hat{z}}$ | (1a) | O CXXXVII |
| $\mathbf{B_{178}}$ | = | $x_{178} \, \mathbf{a}_{1}+y_{178} \, \mathbf{a}_{2}+z_{178} \, \mathbf{a}_{3}$ | = | $\left(a x_{178} + b y_{178} \cos{\gamma} + c_{x} z_{178}\right) \,\mathbf{\hat{x}}+\left(b y_{178} \sin{\gamma} + c_{y} z_{178}\right) \,\mathbf{\hat{y}}+c_{z} z_{178} \,\mathbf{\hat{z}}$ | (1a) | O CXXXVIII |
| $\mathbf{B_{179}}$ | = | $x_{179} \, \mathbf{a}_{1}+y_{179} \, \mathbf{a}_{2}+z_{179} \, \mathbf{a}_{3}$ | = | $\left(a x_{179} + b y_{179} \cos{\gamma} + c_{x} z_{179}\right) \,\mathbf{\hat{x}}+\left(b y_{179} \sin{\gamma} + c_{y} z_{179}\right) \,\mathbf{\hat{y}}+c_{z} z_{179} \,\mathbf{\hat{z}}$ | (1a) | O CXXXIX |
| $\mathbf{B_{180}}$ | = | $x_{180} \, \mathbf{a}_{1}+y_{180} \, \mathbf{a}_{2}+z_{180} \, \mathbf{a}_{3}$ | = | $\left(a x_{180} + b y_{180} \cos{\gamma} + c_{x} z_{180}\right) \,\mathbf{\hat{x}}+\left(b y_{180} \sin{\gamma} + c_{y} z_{180}\right) \,\mathbf{\hat{y}}+c_{z} z_{180} \,\mathbf{\hat{z}}$ | (1a) | O CXL |
| $\mathbf{B_{181}}$ | = | $x_{181} \, \mathbf{a}_{1}+y_{181} \, \mathbf{a}_{2}+z_{181} \, \mathbf{a}_{3}$ | = | $\left(a x_{181} + b y_{181} \cos{\gamma} + c_{x} z_{181}\right) \,\mathbf{\hat{x}}+\left(b y_{181} \sin{\gamma} + c_{y} z_{181}\right) \,\mathbf{\hat{y}}+c_{z} z_{181} \,\mathbf{\hat{z}}$ | (1a) | O CXLI |
| $\mathbf{B_{182}}$ | = | $x_{182} \, \mathbf{a}_{1}+y_{182} \, \mathbf{a}_{2}+z_{182} \, \mathbf{a}_{3}$ | = | $\left(a x_{182} + b y_{182} \cos{\gamma} + c_{x} z_{182}\right) \,\mathbf{\hat{x}}+\left(b y_{182} \sin{\gamma} + c_{y} z_{182}\right) \,\mathbf{\hat{y}}+c_{z} z_{182} \,\mathbf{\hat{z}}$ | (1a) | O CXLII |
| $\mathbf{B_{183}}$ | = | $x_{183} \, \mathbf{a}_{1}+y_{183} \, \mathbf{a}_{2}+z_{183} \, \mathbf{a}_{3}$ | = | $\left(a x_{183} + b y_{183} \cos{\gamma} + c_{x} z_{183}\right) \,\mathbf{\hat{x}}+\left(b y_{183} \sin{\gamma} + c_{y} z_{183}\right) \,\mathbf{\hat{y}}+c_{z} z_{183} \,\mathbf{\hat{z}}$ | (1a) | O CXLIII |
| $\mathbf{B_{184}}$ | = | $x_{184} \, \mathbf{a}_{1}+y_{184} \, \mathbf{a}_{2}+z_{184} \, \mathbf{a}_{3}$ | = | $\left(a x_{184} + b y_{184} \cos{\gamma} + c_{x} z_{184}\right) \,\mathbf{\hat{x}}+\left(b y_{184} \sin{\gamma} + c_{y} z_{184}\right) \,\mathbf{\hat{y}}+c_{z} z_{184} \,\mathbf{\hat{z}}$ | (1a) | O CXLIV |
| $\mathbf{B_{185}}$ | = | $x_{185} \, \mathbf{a}_{1}+y_{185} \, \mathbf{a}_{2}+z_{185} \, \mathbf{a}_{3}$ | = | $\left(a x_{185} + b y_{185} \cos{\gamma} + c_{x} z_{185}\right) \,\mathbf{\hat{x}}+\left(b y_{185} \sin{\gamma} + c_{y} z_{185}\right) \,\mathbf{\hat{y}}+c_{z} z_{185} \,\mathbf{\hat{z}}$ | (1a) | O CXLV |
| $\mathbf{B_{186}}$ | = | $x_{186} \, \mathbf{a}_{1}+y_{186} \, \mathbf{a}_{2}+z_{186} \, \mathbf{a}_{3}$ | = | $\left(a x_{186} + b y_{186} \cos{\gamma} + c_{x} z_{186}\right) \,\mathbf{\hat{x}}+\left(b y_{186} \sin{\gamma} + c_{y} z_{186}\right) \,\mathbf{\hat{y}}+c_{z} z_{186} \,\mathbf{\hat{z}}$ | (1a) | O CXLVI |
| $\mathbf{B_{187}}$ | = | $x_{187} \, \mathbf{a}_{1}+y_{187} \, \mathbf{a}_{2}+z_{187} \, \mathbf{a}_{3}$ | = | $\left(a x_{187} + b y_{187} \cos{\gamma} + c_{x} z_{187}\right) \,\mathbf{\hat{x}}+\left(b y_{187} \sin{\gamma} + c_{y} z_{187}\right) \,\mathbf{\hat{y}}+c_{z} z_{187} \,\mathbf{\hat{z}}$ | (1a) | O CXLVII |
| $\mathbf{B_{188}}$ | = | $x_{188} \, \mathbf{a}_{1}+y_{188} \, \mathbf{a}_{2}+z_{188} \, \mathbf{a}_{3}$ | = | $\left(a x_{188} + b y_{188} \cos{\gamma} + c_{x} z_{188}\right) \,\mathbf{\hat{x}}+\left(b y_{188} \sin{\gamma} + c_{y} z_{188}\right) \,\mathbf{\hat{y}}+c_{z} z_{188} \,\mathbf{\hat{z}}$ | (1a) | O CXLVIII |
| $\mathbf{B_{189}}$ | = | $x_{189} \, \mathbf{a}_{1}+y_{189} \, \mathbf{a}_{2}+z_{189} \, \mathbf{a}_{3}$ | = | $\left(a x_{189} + b y_{189} \cos{\gamma} + c_{x} z_{189}\right) \,\mathbf{\hat{x}}+\left(b y_{189} \sin{\gamma} + c_{y} z_{189}\right) \,\mathbf{\hat{y}}+c_{z} z_{189} \,\mathbf{\hat{z}}$ | (1a) | O CXLIX |
| $\mathbf{B_{190}}$ | = | $x_{190} \, \mathbf{a}_{1}+y_{190} \, \mathbf{a}_{2}+z_{190} \, \mathbf{a}_{3}$ | = | $\left(a x_{190} + b y_{190} \cos{\gamma} + c_{x} z_{190}\right) \,\mathbf{\hat{x}}+\left(b y_{190} \sin{\gamma} + c_{y} z_{190}\right) \,\mathbf{\hat{y}}+c_{z} z_{190} \,\mathbf{\hat{z}}$ | (1a) | O CL |
| $\mathbf{B_{191}}$ | = | $x_{191} \, \mathbf{a}_{1}+y_{191} \, \mathbf{a}_{2}+z_{191} \, \mathbf{a}_{3}$ | = | $\left(a x_{191} + b y_{191} \cos{\gamma} + c_{x} z_{191}\right) \,\mathbf{\hat{x}}+\left(b y_{191} \sin{\gamma} + c_{y} z_{191}\right) \,\mathbf{\hat{y}}+c_{z} z_{191} \,\mathbf{\hat{z}}$ | (1a) | O CLI |
| $\mathbf{B_{192}}$ | = | $x_{192} \, \mathbf{a}_{1}+y_{192} \, \mathbf{a}_{2}+z_{192} \, \mathbf{a}_{3}$ | = | $\left(a x_{192} + b y_{192} \cos{\gamma} + c_{x} z_{192}\right) \,\mathbf{\hat{x}}+\left(b y_{192} \sin{\gamma} + c_{y} z_{192}\right) \,\mathbf{\hat{y}}+c_{z} z_{192} \,\mathbf{\hat{z}}$ | (1a) | O CLII |
| $\mathbf{B_{193}}$ | = | $x_{193} \, \mathbf{a}_{1}+y_{193} \, \mathbf{a}_{2}+z_{193} \, \mathbf{a}_{3}$ | = | $\left(a x_{193} + b y_{193} \cos{\gamma} + c_{x} z_{193}\right) \,\mathbf{\hat{x}}+\left(b y_{193} \sin{\gamma} + c_{y} z_{193}\right) \,\mathbf{\hat{y}}+c_{z} z_{193} \,\mathbf{\hat{z}}$ | (1a) | O CLIII |
| $\mathbf{B_{194}}$ | = | $x_{194} \, \mathbf{a}_{1}+y_{194} \, \mathbf{a}_{2}+z_{194} \, \mathbf{a}_{3}$ | = | $\left(a x_{194} + b y_{194} \cos{\gamma} + c_{x} z_{194}\right) \,\mathbf{\hat{x}}+\left(b y_{194} \sin{\gamma} + c_{y} z_{194}\right) \,\mathbf{\hat{y}}+c_{z} z_{194} \,\mathbf{\hat{z}}$ | (1a) | O CLIV |
| $\mathbf{B_{195}}$ | = | $x_{195} \, \mathbf{a}_{1}+y_{195} \, \mathbf{a}_{2}+z_{195} \, \mathbf{a}_{3}$ | = | $\left(a x_{195} + b y_{195} \cos{\gamma} + c_{x} z_{195}\right) \,\mathbf{\hat{x}}+\left(b y_{195} \sin{\gamma} + c_{y} z_{195}\right) \,\mathbf{\hat{y}}+c_{z} z_{195} \,\mathbf{\hat{z}}$ | (1a) | O CLV |
| $\mathbf{B_{196}}$ | = | $x_{196} \, \mathbf{a}_{1}+y_{196} \, \mathbf{a}_{2}+z_{196} \, \mathbf{a}_{3}$ | = | $\left(a x_{196} + b y_{196} \cos{\gamma} + c_{x} z_{196}\right) \,\mathbf{\hat{x}}+\left(b y_{196} \sin{\gamma} + c_{y} z_{196}\right) \,\mathbf{\hat{y}}+c_{z} z_{196} \,\mathbf{\hat{z}}$ | (1a) | O CLVI |
| $\mathbf{B_{197}}$ | = | $x_{197} \, \mathbf{a}_{1}+y_{197} \, \mathbf{a}_{2}+z_{197} \, \mathbf{a}_{3}$ | = | $\left(a x_{197} + b y_{197} \cos{\gamma} + c_{x} z_{197}\right) \,\mathbf{\hat{x}}+\left(b y_{197} \sin{\gamma} + c_{y} z_{197}\right) \,\mathbf{\hat{y}}+c_{z} z_{197} \,\mathbf{\hat{z}}$ | (1a) | O CLVII |
| $\mathbf{B_{198}}$ | = | $x_{198} \, \mathbf{a}_{1}+y_{198} \, \mathbf{a}_{2}+z_{198} \, \mathbf{a}_{3}$ | = | $\left(a x_{198} + b y_{198} \cos{\gamma} + c_{x} z_{198}\right) \,\mathbf{\hat{x}}+\left(b y_{198} \sin{\gamma} + c_{y} z_{198}\right) \,\mathbf{\hat{y}}+c_{z} z_{198} \,\mathbf{\hat{z}}$ | (1a) | O CLVIII |
| $\mathbf{B_{199}}$ | = | $x_{199} \, \mathbf{a}_{1}+y_{199} \, \mathbf{a}_{2}+z_{199} \, \mathbf{a}_{3}$ | = | $\left(a x_{199} + b y_{199} \cos{\gamma} + c_{x} z_{199}\right) \,\mathbf{\hat{x}}+\left(b y_{199} \sin{\gamma} + c_{y} z_{199}\right) \,\mathbf{\hat{y}}+c_{z} z_{199} \,\mathbf{\hat{z}}$ | (1a) | O CLIX |
| $\mathbf{B_{200}}$ | = | $x_{200} \, \mathbf{a}_{1}+y_{200} \, \mathbf{a}_{2}+z_{200} \, \mathbf{a}_{3}$ | = | $\left(a x_{200} + b y_{200} \cos{\gamma} + c_{x} z_{200}\right) \,\mathbf{\hat{x}}+\left(b y_{200} \sin{\gamma} + c_{y} z_{200}\right) \,\mathbf{\hat{y}}+c_{z} z_{200} \,\mathbf{\hat{z}}$ | (1a) | O CLX |
| $\mathbf{B_{201}}$ | = | $x_{201} \, \mathbf{a}_{1}+y_{201} \, \mathbf{a}_{2}+z_{201} \, \mathbf{a}_{3}$ | = | $\left(a x_{201} + b y_{201} \cos{\gamma} + c_{x} z_{201}\right) \,\mathbf{\hat{x}}+\left(b y_{201} \sin{\gamma} + c_{y} z_{201}\right) \,\mathbf{\hat{y}}+c_{z} z_{201} \,\mathbf{\hat{z}}$ | (1a) | P I |
| $\mathbf{B_{202}}$ | = | $x_{202} \, \mathbf{a}_{1}+y_{202} \, \mathbf{a}_{2}+z_{202} \, \mathbf{a}_{3}$ | = | $\left(a x_{202} + b y_{202} \cos{\gamma} + c_{x} z_{202}\right) \,\mathbf{\hat{x}}+\left(b y_{202} \sin{\gamma} + c_{y} z_{202}\right) \,\mathbf{\hat{y}}+c_{z} z_{202} \,\mathbf{\hat{z}}$ | (1a) | P II |
| $\mathbf{B_{203}}$ | = | $x_{203} \, \mathbf{a}_{1}+y_{203} \, \mathbf{a}_{2}+z_{203} \, \mathbf{a}_{3}$ | = | $\left(a x_{203} + b y_{203} \cos{\gamma} + c_{x} z_{203}\right) \,\mathbf{\hat{x}}+\left(b y_{203} \sin{\gamma} + c_{y} z_{203}\right) \,\mathbf{\hat{y}}+c_{z} z_{203} \,\mathbf{\hat{z}}$ | (1a) | P III |
| $\mathbf{B_{204}}$ | = | $x_{204} \, \mathbf{a}_{1}+y_{204} \, \mathbf{a}_{2}+z_{204} \, \mathbf{a}_{3}$ | = | $\left(a x_{204} + b y_{204} \cos{\gamma} + c_{x} z_{204}\right) \,\mathbf{\hat{x}}+\left(b y_{204} \sin{\gamma} + c_{y} z_{204}\right) \,\mathbf{\hat{y}}+c_{z} z_{204} \,\mathbf{\hat{z}}$ | (1a) | P IV |
| $\mathbf{B_{205}}$ | = | $x_{205} \, \mathbf{a}_{1}+y_{205} \, \mathbf{a}_{2}+z_{205} \, \mathbf{a}_{3}$ | = | $\left(a x_{205} + b y_{205} \cos{\gamma} + c_{x} z_{205}\right) \,\mathbf{\hat{x}}+\left(b y_{205} \sin{\gamma} + c_{y} z_{205}\right) \,\mathbf{\hat{y}}+c_{z} z_{205} \,\mathbf{\hat{z}}$ | (1a) | P V |
| $\mathbf{B_{206}}$ | = | $x_{206} \, \mathbf{a}_{1}+y_{206} \, \mathbf{a}_{2}+z_{206} \, \mathbf{a}_{3}$ | = | $\left(a x_{206} + b y_{206} \cos{\gamma} + c_{x} z_{206}\right) \,\mathbf{\hat{x}}+\left(b y_{206} \sin{\gamma} + c_{y} z_{206}\right) \,\mathbf{\hat{y}}+c_{z} z_{206} \,\mathbf{\hat{z}}$ | (1a) | P VI |
| $\mathbf{B_{207}}$ | = | $x_{207} \, \mathbf{a}_{1}+y_{207} \, \mathbf{a}_{2}+z_{207} \, \mathbf{a}_{3}$ | = | $\left(a x_{207} + b y_{207} \cos{\gamma} + c_{x} z_{207}\right) \,\mathbf{\hat{x}}+\left(b y_{207} \sin{\gamma} + c_{y} z_{207}\right) \,\mathbf{\hat{y}}+c_{z} z_{207} \,\mathbf{\hat{z}}$ | (1a) | P VII |
| $\mathbf{B_{208}}$ | = | $x_{208} \, \mathbf{a}_{1}+y_{208} \, \mathbf{a}_{2}+z_{208} \, \mathbf{a}_{3}$ | = | $\left(a x_{208} + b y_{208} \cos{\gamma} + c_{x} z_{208}\right) \,\mathbf{\hat{x}}+\left(b y_{208} \sin{\gamma} + c_{y} z_{208}\right) \,\mathbf{\hat{y}}+c_{z} z_{208} \,\mathbf{\hat{z}}$ | (1a) | P VIII |
| $\mathbf{B_{209}}$ | = | $x_{209} \, \mathbf{a}_{1}+y_{209} \, \mathbf{a}_{2}+z_{209} \, \mathbf{a}_{3}$ | = | $\left(a x_{209} + b y_{209} \cos{\gamma} + c_{x} z_{209}\right) \,\mathbf{\hat{x}}+\left(b y_{209} \sin{\gamma} + c_{y} z_{209}\right) \,\mathbf{\hat{y}}+c_{z} z_{209} \,\mathbf{\hat{z}}$ | (1a) | P IX |
| $\mathbf{B_{210}}$ | = | $x_{210} \, \mathbf{a}_{1}+y_{210} \, \mathbf{a}_{2}+z_{210} \, \mathbf{a}_{3}$ | = | $\left(a x_{210} + b y_{210} \cos{\gamma} + c_{x} z_{210}\right) \,\mathbf{\hat{x}}+\left(b y_{210} \sin{\gamma} + c_{y} z_{210}\right) \,\mathbf{\hat{y}}+c_{z} z_{210} \,\mathbf{\hat{z}}$ | (1a) | P X |
| $\mathbf{B_{211}}$ | = | $x_{211} \, \mathbf{a}_{1}+y_{211} \, \mathbf{a}_{2}+z_{211} \, \mathbf{a}_{3}$ | = | $\left(a x_{211} + b y_{211} \cos{\gamma} + c_{x} z_{211}\right) \,\mathbf{\hat{x}}+\left(b y_{211} \sin{\gamma} + c_{y} z_{211}\right) \,\mathbf{\hat{y}}+c_{z} z_{211} \,\mathbf{\hat{z}}$ | (1a) | P XI |
| $\mathbf{B_{212}}$ | = | $x_{212} \, \mathbf{a}_{1}+y_{212} \, \mathbf{a}_{2}+z_{212} \, \mathbf{a}_{3}$ | = | $\left(a x_{212} + b y_{212} \cos{\gamma} + c_{x} z_{212}\right) \,\mathbf{\hat{x}}+\left(b y_{212} \sin{\gamma} + c_{y} z_{212}\right) \,\mathbf{\hat{y}}+c_{z} z_{212} \,\mathbf{\hat{z}}$ | (1a) | P XII |
| $\mathbf{B_{213}}$ | = | $x_{213} \, \mathbf{a}_{1}+y_{213} \, \mathbf{a}_{2}+z_{213} \, \mathbf{a}_{3}$ | = | $\left(a x_{213} + b y_{213} \cos{\gamma} + c_{x} z_{213}\right) \,\mathbf{\hat{x}}+\left(b y_{213} \sin{\gamma} + c_{y} z_{213}\right) \,\mathbf{\hat{y}}+c_{z} z_{213} \,\mathbf{\hat{z}}$ | (1a) | P XIII |
| $\mathbf{B_{214}}$ | = | $x_{214} \, \mathbf{a}_{1}+y_{214} \, \mathbf{a}_{2}+z_{214} \, \mathbf{a}_{3}$ | = | $\left(a x_{214} + b y_{214} \cos{\gamma} + c_{x} z_{214}\right) \,\mathbf{\hat{x}}+\left(b y_{214} \sin{\gamma} + c_{y} z_{214}\right) \,\mathbf{\hat{y}}+c_{z} z_{214} \,\mathbf{\hat{z}}$ | (1a) | P XIV |
| $\mathbf{B_{215}}$ | = | $x_{215} \, \mathbf{a}_{1}+y_{215} \, \mathbf{a}_{2}+z_{215} \, \mathbf{a}_{3}$ | = | $\left(a x_{215} + b y_{215} \cos{\gamma} + c_{x} z_{215}\right) \,\mathbf{\hat{x}}+\left(b y_{215} \sin{\gamma} + c_{y} z_{215}\right) \,\mathbf{\hat{y}}+c_{z} z_{215} \,\mathbf{\hat{z}}$ | (1a) | P XV |
| $\mathbf{B_{216}}$ | = | $x_{216} \, \mathbf{a}_{1}+y_{216} \, \mathbf{a}_{2}+z_{216} \, \mathbf{a}_{3}$ | = | $\left(a x_{216} + b y_{216} \cos{\gamma} + c_{x} z_{216}\right) \,\mathbf{\hat{x}}+\left(b y_{216} \sin{\gamma} + c_{y} z_{216}\right) \,\mathbf{\hat{y}}+c_{z} z_{216} \,\mathbf{\hat{z}}$ | (1a) | P XVI |
| $\mathbf{B_{217}}$ | = | $x_{217} \, \mathbf{a}_{1}+y_{217} \, \mathbf{a}_{2}+z_{217} \, \mathbf{a}_{3}$ | = | $\left(a x_{217} + b y_{217} \cos{\gamma} + c_{x} z_{217}\right) \,\mathbf{\hat{x}}+\left(b y_{217} \sin{\gamma} + c_{y} z_{217}\right) \,\mathbf{\hat{y}}+c_{z} z_{217} \,\mathbf{\hat{z}}$ | (1a) | P XVII |
| $\mathbf{B_{218}}$ | = | $x_{218} \, \mathbf{a}_{1}+y_{218} \, \mathbf{a}_{2}+z_{218} \, \mathbf{a}_{3}$ | = | $\left(a x_{218} + b y_{218} \cos{\gamma} + c_{x} z_{218}\right) \,\mathbf{\hat{x}}+\left(b y_{218} \sin{\gamma} + c_{y} z_{218}\right) \,\mathbf{\hat{y}}+c_{z} z_{218} \,\mathbf{\hat{z}}$ | (1a) | P XVIII |
| $\mathbf{B_{219}}$ | = | $x_{219} \, \mathbf{a}_{1}+y_{219} \, \mathbf{a}_{2}+z_{219} \, \mathbf{a}_{3}$ | = | $\left(a x_{219} + b y_{219} \cos{\gamma} + c_{x} z_{219}\right) \,\mathbf{\hat{x}}+\left(b y_{219} \sin{\gamma} + c_{y} z_{219}\right) \,\mathbf{\hat{y}}+c_{z} z_{219} \,\mathbf{\hat{z}}$ | (1a) | P XIX |
| $\mathbf{B_{220}}$ | = | $x_{220} \, \mathbf{a}_{1}+y_{220} \, \mathbf{a}_{2}+z_{220} \, \mathbf{a}_{3}$ | = | $\left(a x_{220} + b y_{220} \cos{\gamma} + c_{x} z_{220}\right) \,\mathbf{\hat{x}}+\left(b y_{220} \sin{\gamma} + c_{y} z_{220}\right) \,\mathbf{\hat{y}}+c_{z} z_{220} \,\mathbf{\hat{z}}$ | (1a) | P XX |
| $\mathbf{B_{221}}$ | = | $x_{221} \, \mathbf{a}_{1}+y_{221} \, \mathbf{a}_{2}+z_{221} \, \mathbf{a}_{3}$ | = | $\left(a x_{221} + b y_{221} \cos{\gamma} + c_{x} z_{221}\right) \,\mathbf{\hat{x}}+\left(b y_{221} \sin{\gamma} + c_{y} z_{221}\right) \,\mathbf{\hat{y}}+c_{z} z_{221} \,\mathbf{\hat{z}}$ | (1a) | P XXI |
| $\mathbf{B_{222}}$ | = | $x_{222} \, \mathbf{a}_{1}+y_{222} \, \mathbf{a}_{2}+z_{222} \, \mathbf{a}_{3}$ | = | $\left(a x_{222} + b y_{222} \cos{\gamma} + c_{x} z_{222}\right) \,\mathbf{\hat{x}}+\left(b y_{222} \sin{\gamma} + c_{y} z_{222}\right) \,\mathbf{\hat{y}}+c_{z} z_{222} \,\mathbf{\hat{z}}$ | (1a) | P XXII |
| $\mathbf{B_{223}}$ | = | $x_{223} \, \mathbf{a}_{1}+y_{223} \, \mathbf{a}_{2}+z_{223} \, \mathbf{a}_{3}$ | = | $\left(a x_{223} + b y_{223} \cos{\gamma} + c_{x} z_{223}\right) \,\mathbf{\hat{x}}+\left(b y_{223} \sin{\gamma} + c_{y} z_{223}\right) \,\mathbf{\hat{y}}+c_{z} z_{223} \,\mathbf{\hat{z}}$ | (1a) | P XXIII |
| $\mathbf{B_{224}}$ | = | $x_{224} \, \mathbf{a}_{1}+y_{224} \, \mathbf{a}_{2}+z_{224} \, \mathbf{a}_{3}$ | = | $\left(a x_{224} + b y_{224} \cos{\gamma} + c_{x} z_{224}\right) \,\mathbf{\hat{x}}+\left(b y_{224} \sin{\gamma} + c_{y} z_{224}\right) \,\mathbf{\hat{y}}+c_{z} z_{224} \,\mathbf{\hat{z}}$ | (1a) | P XXIV |
| $\mathbf{B_{225}}$ | = | $x_{225} \, \mathbf{a}_{1}+y_{225} \, \mathbf{a}_{2}+z_{225} \, \mathbf{a}_{3}$ | = | $\left(a x_{225} + b y_{225} \cos{\gamma} + c_{x} z_{225}\right) \,\mathbf{\hat{x}}+\left(b y_{225} \sin{\gamma} + c_{y} z_{225}\right) \,\mathbf{\hat{y}}+c_{z} z_{225} \,\mathbf{\hat{z}}$ | (1a) | P XXV |
| $\mathbf{B_{226}}$ | = | $x_{226} \, \mathbf{a}_{1}+y_{226} \, \mathbf{a}_{2}+z_{226} \, \mathbf{a}_{3}$ | = | $\left(a x_{226} + b y_{226} \cos{\gamma} + c_{x} z_{226}\right) \,\mathbf{\hat{x}}+\left(b y_{226} \sin{\gamma} + c_{y} z_{226}\right) \,\mathbf{\hat{y}}+c_{z} z_{226} \,\mathbf{\hat{z}}$ | (1a) | P XXVI |
| $\mathbf{B_{227}}$ | = | $x_{227} \, \mathbf{a}_{1}+y_{227} \, \mathbf{a}_{2}+z_{227} \, \mathbf{a}_{3}$ | = | $\left(a x_{227} + b y_{227} \cos{\gamma} + c_{x} z_{227}\right) \,\mathbf{\hat{x}}+\left(b y_{227} \sin{\gamma} + c_{y} z_{227}\right) \,\mathbf{\hat{y}}+c_{z} z_{227} \,\mathbf{\hat{z}}$ | (1a) | P XXVII |
| $\mathbf{B_{228}}$ | = | $x_{228} \, \mathbf{a}_{1}+y_{228} \, \mathbf{a}_{2}+z_{228} \, \mathbf{a}_{3}$ | = | $\left(a x_{228} + b y_{228} \cos{\gamma} + c_{x} z_{228}\right) \,\mathbf{\hat{x}}+\left(b y_{228} \sin{\gamma} + c_{y} z_{228}\right) \,\mathbf{\hat{y}}+c_{z} z_{228} \,\mathbf{\hat{z}}$ | (1a) | P XXVIII |
| $\mathbf{B_{229}}$ | = | $x_{229} \, \mathbf{a}_{1}+y_{229} \, \mathbf{a}_{2}+z_{229} \, \mathbf{a}_{3}$ | = | $\left(a x_{229} + b y_{229} \cos{\gamma} + c_{x} z_{229}\right) \,\mathbf{\hat{x}}+\left(b y_{229} \sin{\gamma} + c_{y} z_{229}\right) \,\mathbf{\hat{y}}+c_{z} z_{229} \,\mathbf{\hat{z}}$ | (1a) | P XXIX |
| $\mathbf{B_{230}}$ | = | $x_{230} \, \mathbf{a}_{1}+y_{230} \, \mathbf{a}_{2}+z_{230} \, \mathbf{a}_{3}$ | = | $\left(a x_{230} + b y_{230} \cos{\gamma} + c_{x} z_{230}\right) \,\mathbf{\hat{x}}+\left(b y_{230} \sin{\gamma} + c_{y} z_{230}\right) \,\mathbf{\hat{y}}+c_{z} z_{230} \,\mathbf{\hat{z}}$ | (1a) | P XXX |
| $\mathbf{B_{231}}$ | = | $x_{231} \, \mathbf{a}_{1}+y_{231} \, \mathbf{a}_{2}+z_{231} \, \mathbf{a}_{3}$ | = | $\left(a x_{231} + b y_{231} \cos{\gamma} + c_{x} z_{231}\right) \,\mathbf{\hat{x}}+\left(b y_{231} \sin{\gamma} + c_{y} z_{231}\right) \,\mathbf{\hat{y}}+c_{z} z_{231} \,\mathbf{\hat{z}}$ | (1a) | P XXXI |
| $\mathbf{B_{232}}$ | = | $x_{232} \, \mathbf{a}_{1}+y_{232} \, \mathbf{a}_{2}+z_{232} \, \mathbf{a}_{3}$ | = | $\left(a x_{232} + b y_{232} \cos{\gamma} + c_{x} z_{232}\right) \,\mathbf{\hat{x}}+\left(b y_{232} \sin{\gamma} + c_{y} z_{232}\right) \,\mathbf{\hat{y}}+c_{z} z_{232} \,\mathbf{\hat{z}}$ | (1a) | P XXXII |
| $\mathbf{B_{233}}$ | = | $x_{233} \, \mathbf{a}_{1}+y_{233} \, \mathbf{a}_{2}+z_{233} \, \mathbf{a}_{3}$ | = | $\left(a x_{233} + b y_{233} \cos{\gamma} + c_{x} z_{233}\right) \,\mathbf{\hat{x}}+\left(b y_{233} \sin{\gamma} + c_{y} z_{233}\right) \,\mathbf{\hat{y}}+c_{z} z_{233} \,\mathbf{\hat{z}}$ | (1a) | P XXXIII |
| $\mathbf{B_{234}}$ | = | $x_{234} \, \mathbf{a}_{1}+y_{234} \, \mathbf{a}_{2}+z_{234} \, \mathbf{a}_{3}$ | = | $\left(a x_{234} + b y_{234} \cos{\gamma} + c_{x} z_{234}\right) \,\mathbf{\hat{x}}+\left(b y_{234} \sin{\gamma} + c_{y} z_{234}\right) \,\mathbf{\hat{y}}+c_{z} z_{234} \,\mathbf{\hat{z}}$ | (1a) | P XXXIV |
| $\mathbf{B_{235}}$ | = | $x_{235} \, \mathbf{a}_{1}+y_{235} \, \mathbf{a}_{2}+z_{235} \, \mathbf{a}_{3}$ | = | $\left(a x_{235} + b y_{235} \cos{\gamma} + c_{x} z_{235}\right) \,\mathbf{\hat{x}}+\left(b y_{235} \sin{\gamma} + c_{y} z_{235}\right) \,\mathbf{\hat{y}}+c_{z} z_{235} \,\mathbf{\hat{z}}$ | (1a) | P XXXV |
| $\mathbf{B_{236}}$ | = | $x_{236} \, \mathbf{a}_{1}+y_{236} \, \mathbf{a}_{2}+z_{236} \, \mathbf{a}_{3}$ | = | $\left(a x_{236} + b y_{236} \cos{\gamma} + c_{x} z_{236}\right) \,\mathbf{\hat{x}}+\left(b y_{236} \sin{\gamma} + c_{y} z_{236}\right) \,\mathbf{\hat{y}}+c_{z} z_{236} \,\mathbf{\hat{z}}$ | (1a) | P XXXVI |
| $\mathbf{B_{237}}$ | = | $x_{237} \, \mathbf{a}_{1}+y_{237} \, \mathbf{a}_{2}+z_{237} \, \mathbf{a}_{3}$ | = | $\left(a x_{237} + b y_{237} \cos{\gamma} + c_{x} z_{237}\right) \,\mathbf{\hat{x}}+\left(b y_{237} \sin{\gamma} + c_{y} z_{237}\right) \,\mathbf{\hat{y}}+c_{z} z_{237} \,\mathbf{\hat{z}}$ | (1a) | P XXXVII |
| $\mathbf{B_{238}}$ | = | $x_{238} \, \mathbf{a}_{1}+y_{238} \, \mathbf{a}_{2}+z_{238} \, \mathbf{a}_{3}$ | = | $\left(a x_{238} + b y_{238} \cos{\gamma} + c_{x} z_{238}\right) \,\mathbf{\hat{x}}+\left(b y_{238} \sin{\gamma} + c_{y} z_{238}\right) \,\mathbf{\hat{y}}+c_{z} z_{238} \,\mathbf{\hat{z}}$ | (1a) | P XXXVIII |
| $\mathbf{B_{239}}$ | = | $x_{239} \, \mathbf{a}_{1}+y_{239} \, \mathbf{a}_{2}+z_{239} \, \mathbf{a}_{3}$ | = | $\left(a x_{239} + b y_{239} \cos{\gamma} + c_{x} z_{239}\right) \,\mathbf{\hat{x}}+\left(b y_{239} \sin{\gamma} + c_{y} z_{239}\right) \,\mathbf{\hat{y}}+c_{z} z_{239} \,\mathbf{\hat{z}}$ | (1a) | P XXXIX |
| $\mathbf{B_{240}}$ | = | $x_{240} \, \mathbf{a}_{1}+y_{240} \, \mathbf{a}_{2}+z_{240} \, \mathbf{a}_{3}$ | = | $\left(a x_{240} + b y_{240} \cos{\gamma} + c_{x} z_{240}\right) \,\mathbf{\hat{x}}+\left(b y_{240} \sin{\gamma} + c_{y} z_{240}\right) \,\mathbf{\hat{y}}+c_{z} z_{240} \,\mathbf{\hat{z}}$ | (1a) | P XL |
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_aP240_1_40a_160a_40a 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