AlPO$_{4}$-54 Structure: AB2_hP108_193_kl_fg2ijl-001
| Prototype | AlO$_{4}$P |
| AFLOW prototype label | AB2_hP108_193_kl_fg2ijl-001 |
| ICSD | 40272 |
| CCDC | 1610141 |
| Pearson symbol | hP108 |
| Space group number | 193 |
| Space group symbol | $P6_3/mcm$ |
| AFLOW prototype command |
aflow --proto=AB2_hP108_193_kl_fg2ijl-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}$ |
- We take the label AlPO$_{4}$-54 from (Withers, 2005).
- Related structures can be found on the silica and aluminum phosphate page.
- The (12k) and (24l) sites are a 50-50 mixture of aluminium and phosphorous. We arbitarily label them as aluminum.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}$ | (6f) | O I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}$ | (6f) | O I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (6f) | O I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (6f) | O I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (6f) | O I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (6f) | O I |
| $\mathbf{B_{7}}$ | = | $x_{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{2} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6g) | O II |
| $\mathbf{B_{8}}$ | = | $x_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{2} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6g) | O II |
| $\mathbf{B_{9}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6g) | O II |
| $\mathbf{B_{10}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{2} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6g) | O II |
| $\mathbf{B_{11}}$ | = | $- x_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{2} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6g) | O II |
| $\mathbf{B_{12}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6g) | O II |
| $\mathbf{B_{13}}$ | = | $x_{3} \, \mathbf{a}_{1}+2 x_{3} \, \mathbf{a}_{2}$ | = | $\frac{3}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}$ | (12i) | O III |
| $\mathbf{B_{14}}$ | = | $- 2 x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $- \frac{3}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}$ | (12i) | O III |
| $\mathbf{B_{15}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $- \sqrt{3}a x_{3} \,\mathbf{\hat{y}}$ | (12i) | O III |
| $\mathbf{B_{16}}$ | = | $- x_{3} \, \mathbf{a}_{1}- 2 x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{17}}$ | = | $2 x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{18}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{19}}$ | = | $- x_{3} \, \mathbf{a}_{1}- 2 x_{3} \, \mathbf{a}_{2}$ | = | $- \frac{3}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}$ | (12i) | O III |
| $\mathbf{B_{20}}$ | = | $2 x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}$ | = | $\frac{3}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}$ | (12i) | O III |
| $\mathbf{B_{21}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}$ | = | $\sqrt{3}a x_{3} \,\mathbf{\hat{y}}$ | (12i) | O III |
| $\mathbf{B_{22}}$ | = | $x_{3} \, \mathbf{a}_{1}+2 x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{23}}$ | = | $- 2 x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{24}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{25}}$ | = | $x_{4} \, \mathbf{a}_{1}+2 x_{4} \, \mathbf{a}_{2}$ | = | $\frac{3}{2}a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}$ | (12i) | O IV |
| $\mathbf{B_{26}}$ | = | $- 2 x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}$ | = | $- \frac{3}{2}a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}$ | (12i) | O IV |
| $\mathbf{B_{27}}$ | = | $x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}$ | = | $- \sqrt{3}a x_{4} \,\mathbf{\hat{y}}$ | (12i) | O IV |
| $\mathbf{B_{28}}$ | = | $- x_{4} \, \mathbf{a}_{1}- 2 x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{4} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{29}}$ | = | $2 x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{4} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{30}}$ | = | $- x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{31}}$ | = | $- x_{4} \, \mathbf{a}_{1}- 2 x_{4} \, \mathbf{a}_{2}$ | = | $- \frac{3}{2}a x_{4} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}$ | (12i) | O IV |
| $\mathbf{B_{32}}$ | = | $2 x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}$ | = | $\frac{3}{2}a x_{4} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}$ | (12i) | O IV |
| $\mathbf{B_{33}}$ | = | $- x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}$ | = | $\sqrt{3}a x_{4} \,\mathbf{\hat{y}}$ | (12i) | O IV |
| $\mathbf{B_{34}}$ | = | $x_{4} \, \mathbf{a}_{1}+2 x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{35}}$ | = | $- 2 x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{36}}$ | = | $x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{37}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} + y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{5} - y_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (12j) | O V |
| $\mathbf{B_{38}}$ | = | $- y_{5} \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} - 2 y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (12j) | O V |
| $\mathbf{B_{39}}$ | = | $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{5} - y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (12j) | O V |
| $\mathbf{B_{40}}$ | = | $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{5} + y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{5} - y_{5}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (12j) | O V |
| $\mathbf{B_{41}}$ | = | $y_{5} \, \mathbf{a}_{1}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{5} + 2 y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (12j) | O V |
| $\mathbf{B_{42}}$ | = | $\left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{5} - y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (12j) | O V |
| $\mathbf{B_{43}}$ | = | $y_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} + y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{5} - y_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (12j) | O V |
| $\mathbf{B_{44}}$ | = | $\left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} - 2 y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (12j) | O V |
| $\mathbf{B_{45}}$ | = | $- x_{5} \, \mathbf{a}_{1}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{5} - y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (12j) | O V |
| $\mathbf{B_{46}}$ | = | $- y_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{5} + y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{5} - y_{5}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (12j) | O V |
| $\mathbf{B_{47}}$ | = | $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{5} + 2 y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (12j) | O V |
| $\mathbf{B_{48}}$ | = | $x_{5} \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{5} - y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (12j) | O V |
| $\mathbf{B_{49}}$ | = | $x_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (12k) | Al I |
| $\mathbf{B_{50}}$ | = | $x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (12k) | Al I |
| $\mathbf{B_{51}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+c z_{6} \,\mathbf{\hat{z}}$ | (12k) | Al I |
| $\mathbf{B_{52}}$ | = | $- x_{6} \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | Al I |
| $\mathbf{B_{53}}$ | = | $- x_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | Al I |
| $\mathbf{B_{54}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | Al I |
| $\mathbf{B_{55}}$ | = | $x_{6} \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | Al I |
| $\mathbf{B_{56}}$ | = | $x_{6} \, \mathbf{a}_{1}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | Al I |
| $\mathbf{B_{57}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | Al I |
| $\mathbf{B_{58}}$ | = | $- x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (12k) | Al I |
| $\mathbf{B_{59}}$ | = | $- x_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (12k) | Al I |
| $\mathbf{B_{60}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- c z_{6} \,\mathbf{\hat{z}}$ | (12k) | Al I |
| $\mathbf{B_{61}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{62}}$ | = | $- y_{7} \, \mathbf{a}_{1}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - 2 y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{63}}$ | = | $- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{64}}$ | = | $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{65}}$ | = | $y_{7} \, \mathbf{a}_{1}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{7} + 2 y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{66}}$ | = | $\left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{67}}$ | = | $y_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{68}}$ | = | $\left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - 2 y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{69}}$ | = | $- x_{7} \, \mathbf{a}_{1}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{70}}$ | = | $- y_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{71}}$ | = | $- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{7} + 2 y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{72}}$ | = | $x_{7} \, \mathbf{a}_{1}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{73}}$ | = | $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{74}}$ | = | $y_{7} \, \mathbf{a}_{1}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{7} + 2 y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{75}}$ | = | $\left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{76}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{77}}$ | = | $- y_{7} \, \mathbf{a}_{1}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - 2 y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{78}}$ | = | $- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{79}}$ | = | $- y_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{80}}$ | = | $- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{7} + 2 y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{81}}$ | = | $x_{7} \, \mathbf{a}_{1}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{82}}$ | = | $y_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{83}}$ | = | $\left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - 2 y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{84}}$ | = | $- x_{7} \, \mathbf{a}_{1}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (24l) | Al II |
| $\mathbf{B_{85}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{86}}$ | = | $- y_{8} \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - 2 y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{87}}$ | = | $- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{88}}$ | = | $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{89}}$ | = | $y_{8} \, \mathbf{a}_{1}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{8} + 2 y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{90}}$ | = | $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{91}}$ | = | $y_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{92}}$ | = | $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - 2 y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{93}}$ | = | $- x_{8} \, \mathbf{a}_{1}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{94}}$ | = | $- y_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{95}}$ | = | $- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{8} + 2 y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{96}}$ | = | $x_{8} \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{97}}$ | = | $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{98}}$ | = | $y_{8} \, \mathbf{a}_{1}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{8} + 2 y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{99}}$ | = | $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{100}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{101}}$ | = | $- y_{8} \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - 2 y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{102}}$ | = | $- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{103}}$ | = | $- y_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{104}}$ | = | $- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{8} + 2 y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{105}}$ | = | $x_{8} \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{106}}$ | = | $y_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{107}}$ | = | $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - 2 y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (24l) | O VI |
| $\mathbf{B_{108}}$ | = | $- x_{8} \, \mathbf{a}_{1}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (24l) | O VI |
References
- J. W. R. Jr., J. V. Smith, and J. J. Pluth, Theoretical nets with 18-ring channels: enumeration, geometrical modeling, and neutron diffraction study of aluminophosphate 54, J. Phys. Chem. 93, 8212–8219 (1989), doi:10.1021/j100362a014.
Found in
- R. L. Withers and Y. Lin, A coupled electron diffraction and rigid unit mode (RUM) study of the crystal chemistry of some zeotypic AlPO$_{4}$ compounds, J. Solid State Chem. 178, 2647–2657 (2005), doi:10.1016/j.jssc.2005.06.003.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=AB2_hP108_193_kl_fg2ijl --params=$a,c/a,x_{2},x_{3},x_{4},x_{5},y_{5},x_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8}$