Zr$_{6}$Cl$_{15}$ (Zr$_{2}$Cl$_{5}$) Structure: A5B2_cI336_230_g2h_h-001
| Prototype | Cl$_{5}$Zr$_{2}$ |
| AFLOW prototype label | A5B2_cI336_230_g2h_h-001 |
| ICSD | 36425 |
| CCDC | 1608156 |
| Pearson symbol | cI336 |
| Space group number | 230 |
| Space group symbol | $Ia\overline{3}d$ |
| AFLOW prototype command |
aflow --proto=A5B2_cI336_230_g2h_h-001
--params=$a, \allowbreak y_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
Ta$_{6}$Br$_{15}$, Ta$_{6}$Cl$_{15}$, Ta$_{6}$Zr$_{15}$
- This is a body-centered cubic ordering of Zr$_{6}$Cl$_{15}$ molecules.
- This structure was first determined by (Corbett, 1978) and reprinted in (Corbett, 1982). The ICSD entry lists the earlier paper as the reference.
- The ICSD using Ta$_{6}$Cl$_{15}$ as the prototype.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(y_{1} - \frac{3}{8}\right) \, \mathbf{a}_{2}+\left(y_{1} + \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a y_{1} \,\mathbf{\hat{y}}- a \left(y_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{2}}$ | = | $- \left(2 y_{1} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(y_{1} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(y_{1} - \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \,\mathbf{\hat{x}}- a \left(y_{1} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{3}}$ | = | $\left(2 y_{1} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{1} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(y_{1} + \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \,\mathbf{\hat{x}}+a \left(y_{1} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(y_{1} + \frac{3}{8}\right) \, \mathbf{a}_{2}- \left(y_{1} - \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}- a y_{1} \,\mathbf{\hat{y}}+a \left(y_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{5}}$ | = | $\left(y_{1} + \frac{1}{8}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(y_{1} - \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{1} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a y_{1} \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{6}}$ | = | $- \left(y_{1} - \frac{3}{8}\right) \, \mathbf{a}_{1}- \left(2 y_{1} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(y_{1} - \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{1} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{8}a \,\mathbf{\hat{y}}- a \left(y_{1} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{7}}$ | = | $\left(y_{1} + \frac{3}{8}\right) \, \mathbf{a}_{1}+\left(2 y_{1} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(y_{1} + \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{1} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{8}a \,\mathbf{\hat{y}}+a \left(y_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{8}}$ | = | $- \left(y_{1} - \frac{1}{8}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\left(y_{1} + \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{1} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}- a y_{1} \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{9}}$ | = | $- \left(y_{1} - \frac{3}{8}\right) \, \mathbf{a}_{1}+\left(y_{1} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a y_{1} \,\mathbf{\hat{x}}- a \left(y_{1} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{10}}$ | = | $- \left(y_{1} - \frac{1}{8}\right) \, \mathbf{a}_{1}- \left(y_{1} - \frac{3}{8}\right) \, \mathbf{a}_{2}- \left(2 y_{1} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{1} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}a \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{11}}$ | = | $\left(y_{1} + \frac{1}{8}\right) \, \mathbf{a}_{1}+\left(y_{1} + \frac{3}{8}\right) \, \mathbf{a}_{2}+\left(2 y_{1} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}a \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{12}}$ | = | $\left(y_{1} + \frac{3}{8}\right) \, \mathbf{a}_{1}- \left(y_{1} - \frac{1}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a y_{1} \,\mathbf{\hat{x}}+a \left(y_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{13}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(y_{1} + \frac{5}{8}\right) \, \mathbf{a}_{2}- \left(y_{1} - \frac{7}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}- a \left(y_{1} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{14}}$ | = | $\left(2 y_{1} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{1} + \frac{7}{8}\right) \, \mathbf{a}_{2}+\left(y_{1} + \frac{5}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}+a y_{1} \,\mathbf{\hat{y}}+a \left(y_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{15}}$ | = | $- \left(2 y_{1} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(y_{1} - \frac{7}{8}\right) \, \mathbf{a}_{2}- \left(y_{1} - \frac{5}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}- a y_{1} \,\mathbf{\hat{y}}- a \left(y_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{16}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(y_{1} - \frac{5}{8}\right) \, \mathbf{a}_{2}+\left(y_{1} + \frac{7}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+a \left(y_{1} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{17}}$ | = | $- \left(y_{1} - \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(y_{1} + \frac{5}{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{1} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}- a \left(y_{1} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{18}}$ | = | $\left(y_{1} + \frac{5}{8}\right) \, \mathbf{a}_{1}+\left(2 y_{1} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(y_{1} + \frac{7}{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{1} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}+a y_{1} \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{19}}$ | = | $- \left(y_{1} - \frac{5}{8}\right) \, \mathbf{a}_{1}- \left(2 y_{1} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(y_{1} - \frac{7}{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{1} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}- a y_{1} \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{20}}$ | = | $\left(y_{1} + \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- \left(y_{1} - \frac{5}{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{1} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+a \left(y_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{21}}$ | = | $\left(y_{1} + \frac{5}{8}\right) \, \mathbf{a}_{1}- \left(y_{1} - \frac{7}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a \left(y_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{22}}$ | = | $\left(y_{1} + \frac{7}{8}\right) \, \mathbf{a}_{1}+\left(y_{1} + \frac{5}{8}\right) \, \mathbf{a}_{2}+\left(2 y_{1} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{1} \,\mathbf{\hat{x}}+a \left(y_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{23}}$ | = | $- \left(y_{1} - \frac{7}{8}\right) \, \mathbf{a}_{1}- \left(y_{1} - \frac{5}{8}\right) \, \mathbf{a}_{2}- \left(2 y_{1} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{1} \,\mathbf{\hat{x}}- a \left(y_{1} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{24}}$ | = | $- \left(y_{1} - \frac{5}{8}\right) \, \mathbf{a}_{1}+\left(y_{1} + \frac{7}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a \left(y_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{1} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48g) | Cl I |
| $\mathbf{B_{25}}$ | = | $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{26}}$ | = | $\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{27}}$ | = | $\left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{28}}$ | = | $- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}- a \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{29}}$ | = | $\left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{30}}$ | = | $- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{31}}$ | = | $\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{32}}$ | = | $\left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{33}}$ | = | $\left(x_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{34}}$ | = | $- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{35}}$ | = | $- \left(x_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{36}}$ | = | $\left(x_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{37}}$ | = | $\left(x_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{38}}$ | = | $- \left(x_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{39}}$ | = | $- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{40}}$ | = | $\left(x_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{41}}$ | = | $\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{42}}$ | = | $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{43}}$ | = | $- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{44}}$ | = | $\left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{45}}$ | = | $\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{46}}$ | = | $\left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{47}}$ | = | $\left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{48}}$ | = | $- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{49}}$ | = | $- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{50}}$ | = | $\left(y_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{51}}$ | = | $- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{52}}$ | = | $\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+a \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{53}}$ | = | $- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{54}}$ | = | $\left(x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{55}}$ | = | $\left(x_{2} - y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{56}}$ | = | $- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{57}}$ | = | $- \left(x_{2} + z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{58}}$ | = | $\left(x_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{59}}$ | = | $\left(x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{60}}$ | = | $\left(- x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{61}}$ | = | $\left(- x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{62}}$ | = | $\left(x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{63}}$ | = | $\left(x_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{64}}$ | = | $- \left(x_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(y_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{65}}$ | = | $\left(y_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{66}}$ | = | $- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{67}}$ | = | $\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{68}}$ | = | $- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{69}}$ | = | $\left(x_{2} - y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{70}}$ | = | $- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{71}}$ | = | $- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{72}}$ | = | $\left(x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl II |
| $\mathbf{B_{73}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{74}}$ | = | $\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{75}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{76}}$ | = | $- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{77}}$ | = | $\left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{78}}$ | = | $- \left(x_{3} + y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{79}}$ | = | $\left(- x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{80}}$ | = | $\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{81}}$ | = | $\left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{82}}$ | = | $- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{83}}$ | = | $- \left(x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{84}}$ | = | $\left(x_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{85}}$ | = | $\left(x_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{86}}$ | = | $- \left(x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{87}}$ | = | $- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{88}}$ | = | $\left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{89}}$ | = | $\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{90}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{91}}$ | = | $- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{92}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{93}}$ | = | $\left(- x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{94}}$ | = | $\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{95}}$ | = | $\left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{96}}$ | = | $- \left(x_{3} + y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{97}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{98}}$ | = | $\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{99}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{100}}$ | = | $\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{101}}$ | = | $- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{102}}$ | = | $\left(x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{103}}$ | = | $\left(x_{3} - y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{104}}$ | = | $- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{105}}$ | = | $- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{106}}$ | = | $\left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{107}}$ | = | $\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{108}}$ | = | $\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{109}}$ | = | $\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{110}}$ | = | $\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{111}}$ | = | $\left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{112}}$ | = | $- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{113}}$ | = | $\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{114}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{115}}$ | = | $\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{116}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{117}}$ | = | $\left(x_{3} - y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{118}}$ | = | $- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{119}}$ | = | $- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{120}}$ | = | $\left(x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Cl III |
| $\mathbf{B_{121}}$ | = | $\left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{122}}$ | = | $\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{123}}$ | = | $\left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{124}}$ | = | $- \left(y_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{125}}$ | = | $\left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{126}}$ | = | $- \left(x_{4} + y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{127}}$ | = | $\left(- x_{4} + y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{128}}$ | = | $\left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}- \left(y_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{129}}$ | = | $\left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{2}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{130}}$ | = | $- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{131}}$ | = | $- \left(x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{132}}$ | = | $\left(x_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}- \left(y_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{133}}$ | = | $\left(x_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{134}}$ | = | $- \left(x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{135}}$ | = | $- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{136}}$ | = | $\left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{137}}$ | = | $\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{138}}$ | = | $\left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{139}}$ | = | $- \left(y_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{140}}$ | = | $\left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{141}}$ | = | $\left(- x_{4} + y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{142}}$ | = | $\left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{143}}$ | = | $\left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{144}}$ | = | $- \left(x_{4} + y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{145}}$ | = | $- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{146}}$ | = | $\left(y_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{147}}$ | = | $- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{148}}$ | = | $\left(y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{149}}$ | = | $- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{150}}$ | = | $\left(x_{4} + y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{151}}$ | = | $\left(x_{4} - y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{152}}$ | = | $- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}+\left(y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{153}}$ | = | $- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{2}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{154}}$ | = | $\left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{155}}$ | = | $\left(x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{156}}$ | = | $\left(- x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+\left(y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{157}}$ | = | $\left(- x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{158}}$ | = | $\left(x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{159}}$ | = | $\left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{160}}$ | = | $- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(y_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{161}}$ | = | $\left(y_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{162}}$ | = | $- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{163}}$ | = | $\left(y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{164}}$ | = | $- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{2}+\left(- x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{165}}$ | = | $\left(x_{4} - y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{166}}$ | = | $- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(y_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{167}}$ | = | $- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
| $\mathbf{B_{168}}$ | = | $\left(x_{4} + y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Zr I |
References
- J. D. Corbett, K. R. Poeppelmeier, and R. L. Daake, Synthesis and structures of Sc$_{7}$Cl$_{12}$ and Zr$_{6}$Cl$_{15}$, Z. Anorganische und Allgemeine Chemie 491, 51–59 (1982), doi:10.1002/zaac.19824910108.
- J. D. Corbett, R. L. Daake, K. R. Poeppelmeier, and D. H. Guthrie, Metal-metal bonded clusters in transition metal Groups 3 and 4. Synthesis and structure of three M$_{6}$X$_{12}$-type clusters for scandium and zirconium, J. Am. Chem. Soc. 100, 652–654 (1978), doi:10.1021/ja00470a062.
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=A5B2_cI336_230_g2h_h --params=$a,y_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4}$