Te[OH]$_{6}$ Structure: A12B6C_cF608_210_4h_2h_e-001
| Prototype | H$_{6}$O$_{6}$Te |
| AFLOW prototype label | A12B6C_cF608_210_4h_2h_e-001 |
| ICSD | 16435 |
| Pearson symbol | cF608 |
| Space group number | 210 |
| Space group symbol | $F4_132$ |
| AFLOW prototype command |
aflow --proto=A12B6C_cF608_210_4h_2h_e-001
--params=$a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}$ |
- The hydrogen sites are only half occupied. Presumably this means that there is only one hydrogen atom bound to each oxygen.
- (Kirkpatrick, 1926) originally concluded that Te[OH]$_{6}$ was in space group $Fd\overline{3}c$ #228, but the did not find the positions of the hydrogen atoms. The current structure appears to be the correct one.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (32e) | Te I |
| $\mathbf{B_{2}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}- 3 x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (32e) | Te I |
| $\mathbf{B_{3}}$ | = | $x_{1} \, \mathbf{a}_{1}- 3 x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ | (32e) | Te I |
| $\mathbf{B_{4}}$ | = | $- 3 x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ | (32e) | Te I |
| $\mathbf{B_{5}}$ | = | $- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(3 x_{1} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | Te I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | Te I |
| $\mathbf{B_{7}}$ | = | $- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(3 x_{1} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | Te I |
| $\mathbf{B_{8}}$ | = | $\left(3 x_{1} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | Te I |
| $\mathbf{B_{9}}$ | = | $\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{10}}$ | = | $\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{11}}$ | = | $\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{12}}$ | = | $- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{13}}$ | = | $\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{14}}$ | = | $- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{15}}$ | = | $\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{16}}$ | = | $\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{17}}$ | = | $\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{18}}$ | = | $\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{19}}$ | = | $- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{20}}$ | = | $\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{21}}$ | = | $\left(x_{2} - y_{2} - z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} - y_{2} + z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{22}}$ | = | $- \left(x_{2} - y_{2} + z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} - z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} - z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{23}}$ | = | $- \left(x_{2} + y_{2} - z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2} + z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{24}}$ | = | $\left(x_{2} + y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} - z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} - z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{25}}$ | = | $- \left(x_{2} + y_{2} - z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} - z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{26}}$ | = | $\left(x_{2} + y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} - y_{2} + z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} - z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{27}}$ | = | $\left(x_{2} - y_{2} - z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} - z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2} + z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{28}}$ | = | $- \left(x_{2} - y_{2} + z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} - z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{29}}$ | = | $- \left(x_{2} - y_{2} + z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} - z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{30}}$ | = | $\left(x_{2} - y_{2} - z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} - z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{31}}$ | = | $\left(x_{2} + y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} - z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2} + z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{32}}$ | = | $- \left(x_{2} + y_{2} - z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} - y_{2} + z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} - z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H I |
| $\mathbf{B_{33}}$ | = | $\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{34}}$ | = | $\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{35}}$ | = | $\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{36}}$ | = | $- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{37}}$ | = | $\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{38}}$ | = | $- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{39}}$ | = | $\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{40}}$ | = | $\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{41}}$ | = | $\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{42}}$ | = | $\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{43}}$ | = | $- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{44}}$ | = | $\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{45}}$ | = | $\left(x_{3} - y_{3} - z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3} + z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{46}}$ | = | $- \left(x_{3} - y_{3} + z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} - z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{47}}$ | = | $- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3} + z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{48}}$ | = | $\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} - z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{49}}$ | = | $- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} - z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{50}}$ | = | $\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3} + z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{51}}$ | = | $\left(x_{3} - y_{3} - z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3} + z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{52}}$ | = | $- \left(x_{3} - y_{3} + z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} - z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{53}}$ | = | $- \left(x_{3} - y_{3} + z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{54}}$ | = | $\left(x_{3} - y_{3} - z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{55}}$ | = | $\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} - z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3} + z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{56}}$ | = | $- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3} + z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} - z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H II |
| $\mathbf{B_{57}}$ | = | $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{58}}$ | = | $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{59}}$ | = | $\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{60}}$ | = | $- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{61}}$ | = | $\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{62}}$ | = | $- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{63}}$ | = | $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{64}}$ | = | $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{65}}$ | = | $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{66}}$ | = | $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{67}}$ | = | $- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{68}}$ | = | $\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{69}}$ | = | $\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{70}}$ | = | $- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{71}}$ | = | $- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{72}}$ | = | $\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{73}}$ | = | $- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{74}}$ | = | $\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{75}}$ | = | $\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{76}}$ | = | $- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{77}}$ | = | $- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{78}}$ | = | $\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{79}}$ | = | $\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{80}}$ | = | $- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H III |
| $\mathbf{B_{81}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{82}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{83}}$ | = | $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{84}}$ | = | $- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{85}}$ | = | $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{86}}$ | = | $- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{87}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{88}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{89}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{90}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{91}}$ | = | $- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{92}}$ | = | $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{93}}$ | = | $\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{94}}$ | = | $- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{95}}$ | = | $- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{96}}$ | = | $\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{97}}$ | = | $- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{98}}$ | = | $\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{99}}$ | = | $\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{100}}$ | = | $- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{101}}$ | = | $- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{102}}$ | = | $\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{103}}$ | = | $\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{104}}$ | = | $- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | H IV |
| $\mathbf{B_{105}}$ | = | $\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{106}}$ | = | $\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{107}}$ | = | $\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{108}}$ | = | $- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{109}}$ | = | $\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{1}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{110}}$ | = | $- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{111}}$ | = | $\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{112}}$ | = | $\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{113}}$ | = | $\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{114}}$ | = | $\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{115}}$ | = | $- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{116}}$ | = | $\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{117}}$ | = | $\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{118}}$ | = | $- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{119}}$ | = | $- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{120}}$ | = | $\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{121}}$ | = | $- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{122}}$ | = | $\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{123}}$ | = | $\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{124}}$ | = | $- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{125}}$ | = | $- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{126}}$ | = | $\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{127}}$ | = | $\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{128}}$ | = | $- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O I |
| $\mathbf{B_{129}}$ | = | $\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{130}}$ | = | $\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{131}}$ | = | $\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{132}}$ | = | $- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{133}}$ | = | $\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+a y_{7} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{134}}$ | = | $- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- a y_{7} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{135}}$ | = | $\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a z_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+a y_{7} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{136}}$ | = | $\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a z_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- a y_{7} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{137}}$ | = | $\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{2}+\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{138}}$ | = | $\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{139}}$ | = | $- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{140}}$ | = | $\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{141}}$ | = | $\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{142}}$ | = | $- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{143}}$ | = | $- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{144}}$ | = | $\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{145}}$ | = | $- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{146}}$ | = | $\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{147}}$ | = | $\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{148}}$ | = | $- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{149}}$ | = | $- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{150}}$ | = | $\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{151}}$ | = | $\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{152}}$ | = | $- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
References
- D. F. Mullica, J. D. Korp, W. O. Milligan, G. W. Beall, and I. Bernal, Neutron structural refinement of cubic orthotelluric acid, Acta Crystallogr. Sect. B 36, 2565–2570 (1980), doi:10.1107/S0567740880009454.
- L. M. Kirkpatrick and L. Pauling, Über die Kristallstruktur der kubischen Tellursäure, Z. Krystallogr. 63, 502–506 (1926), doi:10.1524/zkri.1926.63.1.502.
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.
Prototype Generator
aflow --proto=A12B6C_cF608_210_4h_2h_e --params=$a,x_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7}$