Ta$_{21}$Te$_{13}$ Structure: A21B13_hP136_183_abc3d6e2f_2ab3d5e-001
| Prototype | Ta$_{21}$Te$_{13}$ |
| AFLOW prototype label | A21B13_hP136_183_abc3d6e2f_2ab3d5e-001 |
| ICSD | 91811 |
| Pearson symbol | hP136 |
| Space group number | 183 |
| Space group symbol | $P6mm$ |
| AFLOW prototype command |
aflow --proto=A21B13_hP136_183_abc3d6e2f_2ab3d5e-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak z_{18}, \allowbreak x_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak z_{20}, \allowbreak x_{21}, \allowbreak z_{21}, \allowbreak x_{22}, \allowbreak z_{22}, \allowbreak x_{23}, \allowbreak z_{23}, \allowbreak x_{24}, \allowbreak y_{24}, \allowbreak z_{24}, \allowbreak x_{25}, \allowbreak y_{25}, \allowbreak z_{25}$ |
- This is a hexagonal approximate of the quasicrystal dodecagonal tantalum telluride (dd-Ta$_{1.6}$Te) structure. It may be useful as a starting point for first-principles calculations.
- Space group $P6mm$ #183 does not specify the origin of the $z$-axis. We use the values of (Conrad, 2000). (Villars, 2006) sets $z_{2} = 0$ for the Te-I site.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (1a) | Ta I |
| $\mathbf{B_{2}}$ | = | $z_{2} \, \mathbf{a}_{3}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (1a) | Te I |
| $\mathbf{B_{3}}$ | = | $z_{3} \, \mathbf{a}_{3}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (1a) | Te II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2b) | Ta II |
| $\mathbf{B_{5}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2b) | Ta II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (2b) | Te III |
| $\mathbf{B_{7}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (2b) | Te III |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (3c) | Ta III |
| $\mathbf{B_{9}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (3c) | Ta III |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{6} \,\mathbf{\hat{z}}$ | (3c) | Ta III |
| $\mathbf{B_{11}}$ | = | $x_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{7} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (6d) | Ta IV |
| $\mathbf{B_{12}}$ | = | $x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{7} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (6d) | Ta IV |
| $\mathbf{B_{13}}$ | = | $- x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+c z_{7} \,\mathbf{\hat{z}}$ | (6d) | Ta IV |
| $\mathbf{B_{14}}$ | = | $- x_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{7} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (6d) | Ta IV |
| $\mathbf{B_{15}}$ | = | $- x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{7} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (6d) | Ta IV |
| $\mathbf{B_{16}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+c z_{7} \,\mathbf{\hat{z}}$ | (6d) | Ta IV |
| $\mathbf{B_{17}}$ | = | $x_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{8} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (6d) | Ta V |
| $\mathbf{B_{18}}$ | = | $x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{8} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (6d) | Ta V |
| $\mathbf{B_{19}}$ | = | $- x_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+c z_{8} \,\mathbf{\hat{z}}$ | (6d) | Ta V |
| $\mathbf{B_{20}}$ | = | $- x_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{8} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (6d) | Ta V |
| $\mathbf{B_{21}}$ | = | $- x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{8} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (6d) | Ta V |
| $\mathbf{B_{22}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+c z_{8} \,\mathbf{\hat{z}}$ | (6d) | Ta V |
| $\mathbf{B_{23}}$ | = | $x_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{9} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (6d) | Ta VI |
| $\mathbf{B_{24}}$ | = | $x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{9} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (6d) | Ta VI |
| $\mathbf{B_{25}}$ | = | $- x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+c z_{9} \,\mathbf{\hat{z}}$ | (6d) | Ta VI |
| $\mathbf{B_{26}}$ | = | $- x_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{9} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (6d) | Ta VI |
| $\mathbf{B_{27}}$ | = | $- x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{9} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (6d) | Ta VI |
| $\mathbf{B_{28}}$ | = | $x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+c z_{9} \,\mathbf{\hat{z}}$ | (6d) | Ta VI |
| $\mathbf{B_{29}}$ | = | $x_{10} \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{10} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (6d) | Te IV |
| $\mathbf{B_{30}}$ | = | $x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{10} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (6d) | Te IV |
| $\mathbf{B_{31}}$ | = | $- x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+c z_{10} \,\mathbf{\hat{z}}$ | (6d) | Te IV |
| $\mathbf{B_{32}}$ | = | $- x_{10} \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{10} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (6d) | Te IV |
| $\mathbf{B_{33}}$ | = | $- x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{10} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (6d) | Te IV |
| $\mathbf{B_{34}}$ | = | $x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+c z_{10} \,\mathbf{\hat{z}}$ | (6d) | Te IV |
| $\mathbf{B_{35}}$ | = | $x_{11} \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{11} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (6d) | Te V |
| $\mathbf{B_{36}}$ | = | $x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{11} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (6d) | Te V |
| $\mathbf{B_{37}}$ | = | $- x_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+c z_{11} \,\mathbf{\hat{z}}$ | (6d) | Te V |
| $\mathbf{B_{38}}$ | = | $- x_{11} \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{11} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (6d) | Te V |
| $\mathbf{B_{39}}$ | = | $- x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{11} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (6d) | Te V |
| $\mathbf{B_{40}}$ | = | $x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+c z_{11} \,\mathbf{\hat{z}}$ | (6d) | Te V |
| $\mathbf{B_{41}}$ | = | $x_{12} \, \mathbf{a}_{1}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{12} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (6d) | Te VI |
| $\mathbf{B_{42}}$ | = | $x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{12} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (6d) | Te VI |
| $\mathbf{B_{43}}$ | = | $- x_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}+c z_{12} \,\mathbf{\hat{z}}$ | (6d) | Te VI |
| $\mathbf{B_{44}}$ | = | $- x_{12} \, \mathbf{a}_{1}+z_{12} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{12} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (6d) | Te VI |
| $\mathbf{B_{45}}$ | = | $- x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{12} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (6d) | Te VI |
| $\mathbf{B_{46}}$ | = | $x_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+c z_{12} \,\mathbf{\hat{z}}$ | (6d) | Te VI |
| $\mathbf{B_{47}}$ | = | $x_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (6e) | Ta VII |
| $\mathbf{B_{48}}$ | = | $x_{13} \, \mathbf{a}_{1}+2 x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{13} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (6e) | Ta VII |
| $\mathbf{B_{49}}$ | = | $- 2 x_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{13} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (6e) | Ta VII |
| $\mathbf{B_{50}}$ | = | $- x_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (6e) | Ta VII |
| $\mathbf{B_{51}}$ | = | $- x_{13} \, \mathbf{a}_{1}- 2 x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{13} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (6e) | Ta VII |
| $\mathbf{B_{52}}$ | = | $2 x_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{13} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (6e) | Ta VII |
| $\mathbf{B_{53}}$ | = | $x_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (6e) | Ta VIII |
| $\mathbf{B_{54}}$ | = | $x_{14} \, \mathbf{a}_{1}+2 x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{14} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (6e) | Ta VIII |
| $\mathbf{B_{55}}$ | = | $- 2 x_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{14} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (6e) | Ta VIII |
| $\mathbf{B_{56}}$ | = | $- x_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (6e) | Ta VIII |
| $\mathbf{B_{57}}$ | = | $- x_{14} \, \mathbf{a}_{1}- 2 x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{14} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (6e) | Ta VIII |
| $\mathbf{B_{58}}$ | = | $2 x_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{14} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (6e) | Ta VIII |
| $\mathbf{B_{59}}$ | = | $x_{15} \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (6e) | Ta IX |
| $\mathbf{B_{60}}$ | = | $x_{15} \, \mathbf{a}_{1}+2 x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{15} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (6e) | Ta IX |
| $\mathbf{B_{61}}$ | = | $- 2 x_{15} \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{15} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (6e) | Ta IX |
| $\mathbf{B_{62}}$ | = | $- x_{15} \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (6e) | Ta IX |
| $\mathbf{B_{63}}$ | = | $- x_{15} \, \mathbf{a}_{1}- 2 x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{15} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (6e) | Ta IX |
| $\mathbf{B_{64}}$ | = | $2 x_{15} \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{15} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (6e) | Ta IX |
| $\mathbf{B_{65}}$ | = | $x_{16} \, \mathbf{a}_{1}- x_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (6e) | Ta X |
| $\mathbf{B_{66}}$ | = | $x_{16} \, \mathbf{a}_{1}+2 x_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{16} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (6e) | Ta X |
| $\mathbf{B_{67}}$ | = | $- 2 x_{16} \, \mathbf{a}_{1}- x_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{16} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (6e) | Ta X |
| $\mathbf{B_{68}}$ | = | $- x_{16} \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (6e) | Ta X |
| $\mathbf{B_{69}}$ | = | $- x_{16} \, \mathbf{a}_{1}- 2 x_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{16} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (6e) | Ta X |
| $\mathbf{B_{70}}$ | = | $2 x_{16} \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{16} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (6e) | Ta X |
| $\mathbf{B_{71}}$ | = | $x_{17} \, \mathbf{a}_{1}- x_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (6e) | Ta XI |
| $\mathbf{B_{72}}$ | = | $x_{17} \, \mathbf{a}_{1}+2 x_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{17} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (6e) | Ta XI |
| $\mathbf{B_{73}}$ | = | $- 2 x_{17} \, \mathbf{a}_{1}- x_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{17} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (6e) | Ta XI |
| $\mathbf{B_{74}}$ | = | $- x_{17} \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (6e) | Ta XI |
| $\mathbf{B_{75}}$ | = | $- x_{17} \, \mathbf{a}_{1}- 2 x_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{17} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (6e) | Ta XI |
| $\mathbf{B_{76}}$ | = | $2 x_{17} \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{17} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (6e) | Ta XI |
| $\mathbf{B_{77}}$ | = | $x_{18} \, \mathbf{a}_{1}- x_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (6e) | Ta XII |
| $\mathbf{B_{78}}$ | = | $x_{18} \, \mathbf{a}_{1}+2 x_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{18} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (6e) | Ta XII |
| $\mathbf{B_{79}}$ | = | $- 2 x_{18} \, \mathbf{a}_{1}- x_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{18} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (6e) | Ta XII |
| $\mathbf{B_{80}}$ | = | $- x_{18} \, \mathbf{a}_{1}+x_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (6e) | Ta XII |
| $\mathbf{B_{81}}$ | = | $- x_{18} \, \mathbf{a}_{1}- 2 x_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{18} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (6e) | Ta XII |
| $\mathbf{B_{82}}$ | = | $2 x_{18} \, \mathbf{a}_{1}+x_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{18} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (6e) | Ta XII |
| $\mathbf{B_{83}}$ | = | $x_{19} \, \mathbf{a}_{1}- x_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (6e) | Te VII |
| $\mathbf{B_{84}}$ | = | $x_{19} \, \mathbf{a}_{1}+2 x_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{19} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (6e) | Te VII |
| $\mathbf{B_{85}}$ | = | $- 2 x_{19} \, \mathbf{a}_{1}- x_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{19} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (6e) | Te VII |
| $\mathbf{B_{86}}$ | = | $- x_{19} \, \mathbf{a}_{1}+x_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (6e) | Te VII |
| $\mathbf{B_{87}}$ | = | $- x_{19} \, \mathbf{a}_{1}- 2 x_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{19} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (6e) | Te VII |
| $\mathbf{B_{88}}$ | = | $2 x_{19} \, \mathbf{a}_{1}+x_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{19} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (6e) | Te VII |
| $\mathbf{B_{89}}$ | = | $x_{20} \, \mathbf{a}_{1}- x_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (6e) | Te VIII |
| $\mathbf{B_{90}}$ | = | $x_{20} \, \mathbf{a}_{1}+2 x_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{20} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (6e) | Te VIII |
| $\mathbf{B_{91}}$ | = | $- 2 x_{20} \, \mathbf{a}_{1}- x_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{20} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (6e) | Te VIII |
| $\mathbf{B_{92}}$ | = | $- x_{20} \, \mathbf{a}_{1}+x_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (6e) | Te VIII |
| $\mathbf{B_{93}}$ | = | $- x_{20} \, \mathbf{a}_{1}- 2 x_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{20} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (6e) | Te VIII |
| $\mathbf{B_{94}}$ | = | $2 x_{20} \, \mathbf{a}_{1}+x_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{20} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (6e) | Te VIII |
| $\mathbf{B_{95}}$ | = | $x_{21} \, \mathbf{a}_{1}- x_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ | (6e) | Te IX |
| $\mathbf{B_{96}}$ | = | $x_{21} \, \mathbf{a}_{1}+2 x_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{21} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ | (6e) | Te IX |
| $\mathbf{B_{97}}$ | = | $- 2 x_{21} \, \mathbf{a}_{1}- x_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{21} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ | (6e) | Te IX |
| $\mathbf{B_{98}}$ | = | $- x_{21} \, \mathbf{a}_{1}+x_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ | (6e) | Te IX |
| $\mathbf{B_{99}}$ | = | $- x_{21} \, \mathbf{a}_{1}- 2 x_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{21} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ | (6e) | Te IX |
| $\mathbf{B_{100}}$ | = | $2 x_{21} \, \mathbf{a}_{1}+x_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{21} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ | (6e) | Te IX |
| $\mathbf{B_{101}}$ | = | $x_{22} \, \mathbf{a}_{1}- x_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ | (6e) | Te X |
| $\mathbf{B_{102}}$ | = | $x_{22} \, \mathbf{a}_{1}+2 x_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{22} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ | (6e) | Te X |
| $\mathbf{B_{103}}$ | = | $- 2 x_{22} \, \mathbf{a}_{1}- x_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{22} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ | (6e) | Te X |
| $\mathbf{B_{104}}$ | = | $- x_{22} \, \mathbf{a}_{1}+x_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ | (6e) | Te X |
| $\mathbf{B_{105}}$ | = | $- x_{22} \, \mathbf{a}_{1}- 2 x_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{22} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ | (6e) | Te X |
| $\mathbf{B_{106}}$ | = | $2 x_{22} \, \mathbf{a}_{1}+x_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{22} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ | (6e) | Te X |
| $\mathbf{B_{107}}$ | = | $x_{23} \, \mathbf{a}_{1}- x_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ | (6e) | Te XI |
| $\mathbf{B_{108}}$ | = | $x_{23} \, \mathbf{a}_{1}+2 x_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{23} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ | (6e) | Te XI |
| $\mathbf{B_{109}}$ | = | $- 2 x_{23} \, \mathbf{a}_{1}- x_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{23} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ | (6e) | Te XI |
| $\mathbf{B_{110}}$ | = | $- x_{23} \, \mathbf{a}_{1}+x_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ | (6e) | Te XI |
| $\mathbf{B_{111}}$ | = | $- x_{23} \, \mathbf{a}_{1}- 2 x_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{23} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ | (6e) | Te XI |
| $\mathbf{B_{112}}$ | = | $2 x_{23} \, \mathbf{a}_{1}+x_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{23} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ | (6e) | Te XI |
| $\mathbf{B_{113}}$ | = | $x_{24} \, \mathbf{a}_{1}+y_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{24} + y_{24}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{24} - y_{24}\right) \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (12f) | Ta XIII |
| $\mathbf{B_{114}}$ | = | $- y_{24} \, \mathbf{a}_{1}+\left(x_{24} - y_{24}\right) \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{24} - 2 y_{24}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (12f) | Ta XIII |
| $\mathbf{B_{115}}$ | = | $- \left(x_{24} - y_{24}\right) \, \mathbf{a}_{1}- x_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{24} - y_{24}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (12f) | Ta XIII |
| $\mathbf{B_{116}}$ | = | $- x_{24} \, \mathbf{a}_{1}- y_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{24} + y_{24}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{24} - y_{24}\right) \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (12f) | Ta XIII |
| $\mathbf{B_{117}}$ | = | $y_{24} \, \mathbf{a}_{1}- \left(x_{24} - y_{24}\right) \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{24} + 2 y_{24}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (12f) | Ta XIII |
| $\mathbf{B_{118}}$ | = | $\left(x_{24} - y_{24}\right) \, \mathbf{a}_{1}+x_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{24} - y_{24}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (12f) | Ta XIII |
| $\mathbf{B_{119}}$ | = | $- y_{24} \, \mathbf{a}_{1}- x_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{24} + y_{24}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{24} - y_{24}\right) \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (12f) | Ta XIII |
| $\mathbf{B_{120}}$ | = | $- \left(x_{24} - y_{24}\right) \, \mathbf{a}_{1}+y_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{24} + 2 y_{24}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (12f) | Ta XIII |
| $\mathbf{B_{121}}$ | = | $x_{24} \, \mathbf{a}_{1}+\left(x_{24} - y_{24}\right) \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{24} - y_{24}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (12f) | Ta XIII |
| $\mathbf{B_{122}}$ | = | $y_{24} \, \mathbf{a}_{1}+x_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{24} + y_{24}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{24} - y_{24}\right) \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (12f) | Ta XIII |
| $\mathbf{B_{123}}$ | = | $\left(x_{24} - y_{24}\right) \, \mathbf{a}_{1}- y_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{24} - 2 y_{24}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (12f) | Ta XIII |
| $\mathbf{B_{124}}$ | = | $- x_{24} \, \mathbf{a}_{1}- \left(x_{24} - y_{24}\right) \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{24} - y_{24}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (12f) | Ta XIII |
| $\mathbf{B_{125}}$ | = | $x_{25} \, \mathbf{a}_{1}+y_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{25} + y_{25}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{25} - y_{25}\right) \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (12f) | Ta XIV |
| $\mathbf{B_{126}}$ | = | $- y_{25} \, \mathbf{a}_{1}+\left(x_{25} - y_{25}\right) \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{25} - 2 y_{25}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{25} \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (12f) | Ta XIV |
| $\mathbf{B_{127}}$ | = | $- \left(x_{25} - y_{25}\right) \, \mathbf{a}_{1}- x_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{25} - y_{25}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{25} \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (12f) | Ta XIV |
| $\mathbf{B_{128}}$ | = | $- x_{25} \, \mathbf{a}_{1}- y_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{25} + y_{25}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{25} - y_{25}\right) \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (12f) | Ta XIV |
| $\mathbf{B_{129}}$ | = | $y_{25} \, \mathbf{a}_{1}- \left(x_{25} - y_{25}\right) \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{25} + 2 y_{25}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{25} \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (12f) | Ta XIV |
| $\mathbf{B_{130}}$ | = | $\left(x_{25} - y_{25}\right) \, \mathbf{a}_{1}+x_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{25} - y_{25}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{25} \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (12f) | Ta XIV |
| $\mathbf{B_{131}}$ | = | $- y_{25} \, \mathbf{a}_{1}- x_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{25} + y_{25}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{25} - y_{25}\right) \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (12f) | Ta XIV |
| $\mathbf{B_{132}}$ | = | $- \left(x_{25} - y_{25}\right) \, \mathbf{a}_{1}+y_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{25} + 2 y_{25}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{25} \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (12f) | Ta XIV |
| $\mathbf{B_{133}}$ | = | $x_{25} \, \mathbf{a}_{1}+\left(x_{25} - y_{25}\right) \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{25} - y_{25}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{25} \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (12f) | Ta XIV |
| $\mathbf{B_{134}}$ | = | $y_{25} \, \mathbf{a}_{1}+x_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{25} + y_{25}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{25} - y_{25}\right) \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (12f) | Ta XIV |
| $\mathbf{B_{135}}$ | = | $\left(x_{25} - y_{25}\right) \, \mathbf{a}_{1}- y_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{25} - 2 y_{25}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{25} \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (12f) | Ta XIV |
| $\mathbf{B_{136}}$ | = | $- x_{25} \, \mathbf{a}_{1}- \left(x_{25} - y_{25}\right) \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{25} - y_{25}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{25} \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (12f) | Ta XIV |
References
- M. Conrad, F. Krumeich, C. Reich, and B. Harbrecht, Hexagonal approximants of a dodecagonal tantalum telluride – the crystal structure of Ta$_{21}$Te$_{13}$}, msea \textbf{294-296, 37–40 (2000), doi:10.1016/S0921-5093(00)01150-3.
Found in
- P. Villars, K. Cenzual, J. Daams, R. Gladyshevskii, O. Shcherban, V. Dubenskyy, N. Melnichenko-Koblyuk, O. Pavlyuk, I. Savesyuk, S. Stoiko, and L. Sysa, Landolt-Börnstein - Group III Condensed Matter 43A4 (Springer-Verlag, Berlin Heidelberg, 2006), chap. Structure Types. Part 4: Space Groups (189) P-62m - (174) P-6. Ta$_2$$_1$Te$_1$$_3$, doi:10.1007/10920527_353.
Prototype Generator
aflow --proto=A21B13_hP136_183_abc3d6e2f_2ab3d5e --params=$a,c/a,z_{1},z_{2},z_{3},z_{4},z_{5},z_{6},x_{7},z_{7},x_{8},z_{8},x_{9},z_{9},x_{10},z_{10},x_{11},z_{11},x_{12},z_{12},x_{13},z_{13},x_{14},z_{14},x_{15},z_{15},x_{16},z_{16},x_{17},z_{17},x_{18},z_{18},x_{19},z_{19},x_{20},z_{20},x_{21},z_{21},x_{22},z_{22},x_{23},z_{23},x_{24},y_{24},z_{24},x_{25},y_{25},z_{25}$