AFLOW Prototype: A8B9C24D19E3_hR63_148_cf_df_4f_a3f_bc-001
If you are using this page, please cite:
H. Eckert, S. Divilov, M. J. Mehl, D. Hicks, A. C. Zettel, M. Esters. X. Campilongo and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 4. Submitted to Computational Materials Science.
Links to this page
https://aflow.org/p/GGPS
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https://aflow.org/p/A8B9C24D19E3_hR63_148_cf_df_4f_a3f_bc-001
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PDF Version
Prototype | Cl$_{3}$Cu$_{9}$H$_{19}$O$_{19}$Y$_{3}$ |
AFLOW prototype label | A8B9C24D19E3_hR63_148_cf_df_4f_a3f_bc-001 |
CCDC | 1532410 |
Pearson symbol | hR63 |
Space group number | 148 |
Space group symbol | $R\overline{3}$ |
AFLOW prototype command |
aflow --proto=A8B9C24D19E3_hR63_148_cf_df_4f_a3f_bc-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}$ |
--hex
. Basis vectors
Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
---|---|---|---|---|---|---|
$\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | O I |
$\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | Y I |
$\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Cl I |
$\mathbf{B_{4}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Cl I |
$\mathbf{B_{5}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $c x_{4} \,\mathbf{\hat{z}}$ | (2c) | Y II |
$\mathbf{B_{6}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- c x_{4} \,\mathbf{\hat{z}}$ | (2c) | Y II |
$\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3d) | Cu I |
$\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3d) | Cu I |
$\mathbf{B_{9}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3d) | Cu I |
$\mathbf{B_{10}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{6} - 2 y_{6} + z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl II |
$\mathbf{B_{11}}$ | = | $z_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{6} - y_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl II |
$\mathbf{B_{12}}$ | = | $y_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{6} + y_{6} - 2 z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl II |
$\mathbf{B_{13}}$ | = | $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} - 2 y_{6} + z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl II |
$\mathbf{B_{14}}$ | = | $- z_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{6} - z_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{6} - y_{6} - z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl II |
$\mathbf{B_{15}}$ | = | $- y_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} + y_{6} - 2 z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl II |
$\mathbf{B_{16}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{7} - 2 y_{7} + z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6f) | Cu II |
$\mathbf{B_{17}}$ | = | $z_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{7} - z_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{7} - y_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6f) | Cu II |
$\mathbf{B_{18}}$ | = | $y_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{7} + y_{7} - 2 z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6f) | Cu II |
$\mathbf{B_{19}}$ | = | $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{7} - 2 y_{7} + z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6f) | Cu II |
$\mathbf{B_{20}}$ | = | $- z_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- y_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{7} - z_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{7} - y_{7} - z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6f) | Cu II |
$\mathbf{B_{21}}$ | = | $- y_{7} \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{7} + y_{7} - 2 z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6f) | Cu II |
$\mathbf{B_{22}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{8} - 2 y_{8} + z_{8}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6f) | H I |
$\mathbf{B_{23}}$ | = | $z_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+y_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{8} - z_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{8} - y_{8} - z_{8}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6f) | H I |
$\mathbf{B_{24}}$ | = | $y_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{8} + y_{8} - 2 z_{8}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6f) | H I |
$\mathbf{B_{25}}$ | = | $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{8} - 2 y_{8} + z_{8}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6f) | H I |
$\mathbf{B_{26}}$ | = | $- z_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- y_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{8} - z_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{8} - y_{8} - z_{8}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6f) | H I |
$\mathbf{B_{27}}$ | = | $- y_{8} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{8} + y_{8} - 2 z_{8}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6f) | H I |
$\mathbf{B_{28}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{9} - 2 y_{9} + z_{9}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{9} + y_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6f) | H II |
$\mathbf{B_{29}}$ | = | $z_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+y_{9} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{9} - z_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{9} - y_{9} - z_{9}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{9} + y_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6f) | H II |
$\mathbf{B_{30}}$ | = | $y_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{9} - y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{9} + y_{9} - 2 z_{9}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{9} + y_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6f) | H II |
$\mathbf{B_{31}}$ | = | $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{9} - 2 y_{9} + z_{9}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{9} + y_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6f) | H II |
$\mathbf{B_{32}}$ | = | $- z_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- y_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{9} - z_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{9} - y_{9} - z_{9}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{9} + y_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6f) | H II |
$\mathbf{B_{33}}$ | = | $- y_{9} \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}- x_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} - y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{9} + y_{9} - 2 z_{9}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{9} + y_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6f) | H II |
$\mathbf{B_{34}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} - z_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{10} - 2 y_{10} + z_{10}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{10} + y_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ | (6f) | H III |
$\mathbf{B_{35}}$ | = | $z_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+y_{10} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{10} - z_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{10} - y_{10} - z_{10}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{10} + y_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ | (6f) | H III |
$\mathbf{B_{36}}$ | = | $y_{10} \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{10} - y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{10} + y_{10} - 2 z_{10}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{10} + y_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ | (6f) | H III |
$\mathbf{B_{37}}$ | = | $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{10} - z_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{10} - 2 y_{10} + z_{10}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{10} + y_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ | (6f) | H III |
$\mathbf{B_{38}}$ | = | $- z_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- y_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{10} - z_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{10} - y_{10} - z_{10}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{10} + y_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ | (6f) | H III |
$\mathbf{B_{39}}$ | = | $- y_{10} \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{2}- x_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} - y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{10} + y_{10} - 2 z_{10}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{10} + y_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ | (6f) | H III |
$\mathbf{B_{40}}$ | = | $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{11} - z_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{11} - 2 y_{11} + z_{11}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{11} + y_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ | (6f) | H IV |
$\mathbf{B_{41}}$ | = | $z_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+y_{11} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{11} - z_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{11} - y_{11} - z_{11}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{11} + y_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ | (6f) | H IV |
$\mathbf{B_{42}}$ | = | $y_{11} \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{11} - y_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{11} + y_{11} - 2 z_{11}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{11} + y_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ | (6f) | H IV |
$\mathbf{B_{43}}$ | = | $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{11} - z_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{11} - 2 y_{11} + z_{11}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{11} + y_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ | (6f) | H IV |
$\mathbf{B_{44}}$ | = | $- z_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- y_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{11} - z_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{11} - y_{11} - z_{11}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{11} + y_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ | (6f) | H IV |
$\mathbf{B_{45}}$ | = | $- y_{11} \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{2}- x_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{11} - y_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{11} + y_{11} - 2 z_{11}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{11} + y_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ | (6f) | H IV |
$\mathbf{B_{46}}$ | = | $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} - z_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{12} - 2 y_{12} + z_{12}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (6f) | O II |
$\mathbf{B_{47}}$ | = | $z_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+y_{12} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{12} - z_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{12} - y_{12} - z_{12}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (6f) | O II |
$\mathbf{B_{48}}$ | = | $y_{12} \, \mathbf{a}_{1}+z_{12} \, \mathbf{a}_{2}+x_{12} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{12} + y_{12} - 2 z_{12}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (6f) | O II |
$\mathbf{B_{49}}$ | = | $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{12} - z_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{12} - 2 y_{12} + z_{12}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (6f) | O II |
$\mathbf{B_{50}}$ | = | $- z_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}- y_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{12} - z_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{12} - y_{12} - z_{12}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (6f) | O II |
$\mathbf{B_{51}}$ | = | $- y_{12} \, \mathbf{a}_{1}- z_{12} \, \mathbf{a}_{2}- x_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{12} + y_{12} - 2 z_{12}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (6f) | O II |
$\mathbf{B_{52}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} - z_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{13} - 2 y_{13} + z_{13}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (6f) | O III |
$\mathbf{B_{53}}$ | = | $z_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+y_{13} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{13} - z_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{13} - y_{13} - z_{13}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (6f) | O III |
$\mathbf{B_{54}}$ | = | $y_{13} \, \mathbf{a}_{1}+z_{13} \, \mathbf{a}_{2}+x_{13} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{13} + y_{13} - 2 z_{13}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (6f) | O III |
$\mathbf{B_{55}}$ | = | $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{13} - z_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{13} - 2 y_{13} + z_{13}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (6f) | O III |
$\mathbf{B_{56}}$ | = | $- z_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}- y_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{13} - z_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{13} - y_{13} - z_{13}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (6f) | O III |
$\mathbf{B_{57}}$ | = | $- y_{13} \, \mathbf{a}_{1}- z_{13} \, \mathbf{a}_{2}- x_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{13} + y_{13} - 2 z_{13}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (6f) | O III |
$\mathbf{B_{58}}$ | = | $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{14} - z_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{14} - 2 y_{14} + z_{14}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (6f) | O IV |
$\mathbf{B_{59}}$ | = | $z_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+y_{14} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{14} - z_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{14} - y_{14} - z_{14}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (6f) | O IV |
$\mathbf{B_{60}}$ | = | $y_{14} \, \mathbf{a}_{1}+z_{14} \, \mathbf{a}_{2}+x_{14} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{14} - y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{14} + y_{14} - 2 z_{14}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (6f) | O IV |
$\mathbf{B_{61}}$ | = | $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{14} - z_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{14} - 2 y_{14} + z_{14}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (6f) | O IV |
$\mathbf{B_{62}}$ | = | $- z_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}- y_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{14} - z_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{14} - y_{14} - z_{14}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (6f) | O IV |
$\mathbf{B_{63}}$ | = | $- y_{14} \, \mathbf{a}_{1}- z_{14} \, \mathbf{a}_{2}- x_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{14} - y_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{14} + y_{14} - 2 z_{14}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (6f) | O IV |