SrCuTe$_{2}$O$_{6}$ Structure: AB6CD2_cP120_213_d_3e_ac_e-001
| Prototype | CuO$_{6}$SrTe$_{2}$ |
| AFLOW prototype label | AB6CD2_cP120_213_d_3e_ac_e-001 |
| ICSD | 32364 |
| Pearson symbol | cP120 |
| Space group number | 213 |
| Space group symbol | $P4_132$ |
| AFLOW prototype command |
aflow --proto=AB6CD2_cP120_213_d_3e_ac_e-001
--params=$a, \allowbreak x_{2}, \allowbreak y_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}$ |
Other compounds with this structure
BaCuTe$_{2}$O$_{6}$, PbCuTe$_{2}$O$_{6}$
- We have shifted the origin so that the Sr-I atoms, located on the (4b) (7/8 7/8 7/8) Wyckoff positions by (Chillal, 2020) are now on the (4a) (3/8 3/8 3/8) sites.
- This structure can also be expressed in the enantiomorphic space group $P4_{3}32$ #212.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (4a) | Sr I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}+\frac{7}{8}a \,\mathbf{\hat{z}}$ | (4a) | Sr I |
| $\mathbf{B_{3}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}+\frac{7}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (4a) | Sr I |
| $\mathbf{B_{4}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (4a) | Sr I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{6}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{8}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{9}}$ | = | $\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{10}}$ | = | $- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{11}}$ | = | $\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{12}}$ | = | $- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{13}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (12d) | Cu I |
| $\mathbf{B_{14}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (12d) | Cu I |
| $\mathbf{B_{15}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (12d) | Cu I |
| $\mathbf{B_{16}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (12d) | Cu I |
| $\mathbf{B_{17}}$ | = | $\left(y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (12d) | Cu I |
| $\mathbf{B_{18}}$ | = | $\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (12d) | Cu I |
| $\mathbf{B_{19}}$ | = | $- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{7}{8}a \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | Cu I |
| $\mathbf{B_{20}}$ | = | $- \left(y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | Cu I |
| $\mathbf{B_{21}}$ | = | $y_{3} \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (12d) | Cu I |
| $\mathbf{B_{22}}$ | = | $- y_{3} \, \mathbf{a}_{1}+\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (12d) | Cu I |
| $\mathbf{B_{23}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{7}{8}a \,\mathbf{\hat{z}}$ | (12d) | Cu I |
| $\mathbf{B_{24}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (12d) | Cu I |
| $\mathbf{B_{25}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{26}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{27}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{28}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{29}}$ | = | $z_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{30}}$ | = | $\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{31}}$ | = | $- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{32}}$ | = | $- z_{4} \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{33}}$ | = | $y_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{34}}$ | = | $- y_{4} \, \mathbf{a}_{1}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{35}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{36}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{37}}$ | = | $\left(y_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{38}}$ | = | $- \left(y_{4} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{39}}$ | = | $\left(y_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{40}}$ | = | $- \left(y_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{41}}$ | = | $\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{42}}$ | = | $- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(z_{4} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{43}}$ | = | $- \left(x_{4} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(z_{4} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{44}}$ | = | $\left(x_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(y_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{45}}$ | = | $\left(z_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{46}}$ | = | $\left(z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{47}}$ | = | $- \left(z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{48}}$ | = | $- \left(z_{4} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O I |
| $\mathbf{B_{49}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{50}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{51}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{52}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{53}}$ | = | $z_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{54}}$ | = | $\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ | = | $a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{55}}$ | = | $- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{56}}$ | = | $- z_{5} \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{57}}$ | = | $y_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{58}}$ | = | $- y_{5} \, \mathbf{a}_{1}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{59}}$ | = | $\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{60}}$ | = | $- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{61}}$ | = | $\left(y_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{62}}$ | = | $- \left(y_{5} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(z_{5} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{63}}$ | = | $\left(y_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{64}}$ | = | $- \left(y_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{65}}$ | = | $\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{66}}$ | = | $- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(z_{5} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{67}}$ | = | $- \left(x_{5} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(z_{5} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(y_{5} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{68}}$ | = | $\left(x_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(y_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{69}}$ | = | $\left(z_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{5} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{70}}$ | = | $\left(z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{71}}$ | = | $- \left(z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{5} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{72}}$ | = | $- \left(z_{5} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(y_{5} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{5} - \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O II |
| $\mathbf{B_{73}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{74}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{75}}$ | = | $- x_{6} \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{76}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{77}}$ | = | $z_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{78}}$ | = | $\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{79}}$ | = | $- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{80}}$ | = | $- z_{6} \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{81}}$ | = | $y_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{82}}$ | = | $- y_{6} \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{83}}$ | = | $\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{84}}$ | = | $- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{85}}$ | = | $\left(y_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{86}}$ | = | $- \left(y_{6} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{87}}$ | = | $\left(y_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{88}}$ | = | $- \left(y_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{89}}$ | = | $\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{90}}$ | = | $- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{91}}$ | = | $- \left(x_{6} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(z_{6} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(y_{6} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{92}}$ | = | $\left(x_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(y_{6} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{93}}$ | = | $\left(z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{94}}$ | = | $\left(z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{95}}$ | = | $- \left(z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{6} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{96}}$ | = | $- \left(z_{6} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | O III |
| $\mathbf{B_{97}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{98}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{99}}$ | = | $- x_{7} \, \mathbf{a}_{1}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{100}}$ | = | $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{101}}$ | = | $z_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+a y_{7} \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{102}}$ | = | $\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{7} \, \mathbf{a}_{3}$ | = | $a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{7} \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{103}}$ | = | $- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{104}}$ | = | $- z_{7} \, \mathbf{a}_{1}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{7} \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{105}}$ | = | $y_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{106}}$ | = | $- y_{7} \, \mathbf{a}_{1}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{107}}$ | = | $\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{108}}$ | = | $- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{109}}$ | = | $\left(y_{7} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{110}}$ | = | $- \left(y_{7} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{111}}$ | = | $\left(y_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{112}}$ | = | $- \left(y_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{113}}$ | = | $\left(x_{7} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(y_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{114}}$ | = | $- \left(x_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(z_{7} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(y_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{115}}$ | = | $- \left(x_{7} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(z_{7} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(y_{7} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{7} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{116}}$ | = | $\left(x_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(y_{7} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{7} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{117}}$ | = | $\left(z_{7} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{7} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{118}}$ | = | $\left(z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{119}}$ | = | $- \left(z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{7} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
| $\mathbf{B_{120}}$ | = | $- \left(z_{7} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(y_{7} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{7} - \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (24e) | Te I |
References
- S. Chillal, A. T. M. N. Islam, H. Luetkens, E. Canévet, Y. Skourski, D. Khalyavin, and B. Lake, Magnetic structure of the quantum magnet SrCuTe$_{2}$O$_{6}$, Phys. Rev. B 102, 224424 (2020), doi:10.1103/PhysRevB.102.224424.
Found in
- P. Bag, N. Ahmed, V. Singh, M. Sahoo, A. A. Tsirlin, and R. Nath, Low-dimensional magnetism of BaCuTe$_{2}$O$_{6}$, Phys. Rev. B 103, 134410 (2021), doi:10.1103/PhysRevB.103.134410.
Prototype Generator
aflow --proto=AB6CD2_cP120_213_d_3e_ac_e --params=$a,x_{2},y_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7}$