Retgersite (α-NiSO$_{4}\cdot$6H$_{2}$O, $H4_{5}$) Structure: A12BC10D_tP96_92_6b_a_5b_a-001
| Prototype | H$_{12}$NiO$_{10}$S |
| AFLOW prototype label | A12BC10D_tP96_92_6b_a_5b_a-001 |
| Strukturbericht designation | $H4_{5}$ |
| Mineral name | retgersite |
| ICSD | 62051 |
| Pearson symbol | tP96 |
| Space group number | 92 |
| Space group symbol | $P4_12_12$ |
| AFLOW prototype command |
aflow --proto=A12BC10D_tP96_92_6b_a_5b_a-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}$ |
- This structure is nearly identical to the one presented in (Hermann, 1937) as $H4_{5}$, but now includes the positions of the hydrogen atoms.
- This compound can also be found in the enantiomorphic space group $P4_{3}2_{1}2$ #98.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}$ | (4a) | Ni I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4a) | Ni I |
| $\mathbf{B_{3}}$ | = | $- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | Ni I |
| $\mathbf{B_{4}}$ | = | $\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4a) | Ni I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}$ | (4a) | S I |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4a) | S I |
| $\mathbf{B_{7}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | S I |
| $\mathbf{B_{8}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4a) | S I |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8b) | H I |
| $\mathbf{B_{10}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | H I |
| $\mathbf{B_{11}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H I |
| $\mathbf{B_{12}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H I |
| $\mathbf{B_{13}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H I |
| $\mathbf{B_{14}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H I |
| $\mathbf{B_{15}}$ | = | $y_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (8b) | H I |
| $\mathbf{B_{16}}$ | = | $- y_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | H I |
| $\mathbf{B_{17}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8b) | H II |
| $\mathbf{B_{18}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | H II |
| $\mathbf{B_{19}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H II |
| $\mathbf{B_{20}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H II |
| $\mathbf{B_{21}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H II |
| $\mathbf{B_{22}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H II |
| $\mathbf{B_{23}}$ | = | $y_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (8b) | H II |
| $\mathbf{B_{24}}$ | = | $- y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | H II |
| $\mathbf{B_{25}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8b) | H III |
| $\mathbf{B_{26}}$ | = | $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | H III |
| $\mathbf{B_{27}}$ | = | $- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H III |
| $\mathbf{B_{28}}$ | = | $\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H III |
| $\mathbf{B_{29}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H III |
| $\mathbf{B_{30}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{5} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H III |
| $\mathbf{B_{31}}$ | = | $y_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (8b) | H III |
| $\mathbf{B_{32}}$ | = | $- y_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | H III |
| $\mathbf{B_{33}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8b) | H IV |
| $\mathbf{B_{34}}$ | = | $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | H IV |
| $\mathbf{B_{35}}$ | = | $- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H IV |
| $\mathbf{B_{36}}$ | = | $\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H IV |
| $\mathbf{B_{37}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H IV |
| $\mathbf{B_{38}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H IV |
| $\mathbf{B_{39}}$ | = | $y_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (8b) | H IV |
| $\mathbf{B_{40}}$ | = | $- y_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | H IV |
| $\mathbf{B_{41}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8b) | H V |
| $\mathbf{B_{42}}$ | = | $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | H V |
| $\mathbf{B_{43}}$ | = | $- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H V |
| $\mathbf{B_{44}}$ | = | $\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H V |
| $\mathbf{B_{45}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H V |
| $\mathbf{B_{46}}$ | = | $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H V |
| $\mathbf{B_{47}}$ | = | $y_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8b) | H V |
| $\mathbf{B_{48}}$ | = | $- y_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | H V |
| $\mathbf{B_{49}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8b) | H VI |
| $\mathbf{B_{50}}$ | = | $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | H VI |
| $\mathbf{B_{51}}$ | = | $- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H VI |
| $\mathbf{B_{52}}$ | = | $\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H VI |
| $\mathbf{B_{53}}$ | = | $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H VI |
| $\mathbf{B_{54}}$ | = | $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | H VI |
| $\mathbf{B_{55}}$ | = | $y_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8b) | H VI |
| $\mathbf{B_{56}}$ | = | $- y_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | H VI |
| $\mathbf{B_{57}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{58}}$ | = | $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{59}}$ | = | $- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{60}}$ | = | $\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{61}}$ | = | $- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{62}}$ | = | $\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{9} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{63}}$ | = | $y_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{64}}$ | = | $- y_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{65}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8b) | O II |
| $\mathbf{B_{66}}$ | = | $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | O II |
| $\mathbf{B_{67}}$ | = | $- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O II |
| $\mathbf{B_{68}}$ | = | $\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{10} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O II |
| $\mathbf{B_{69}}$ | = | $- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O II |
| $\mathbf{B_{70}}$ | = | $\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{10} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O II |
| $\mathbf{B_{71}}$ | = | $y_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $a y_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (8b) | O II |
| $\mathbf{B_{72}}$ | = | $- y_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | O II |
| $\mathbf{B_{73}}$ | = | $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (8b) | O III |
| $\mathbf{B_{74}}$ | = | $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | O III |
| $\mathbf{B_{75}}$ | = | $- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O III |
| $\mathbf{B_{76}}$ | = | $\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{11} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O III |
| $\mathbf{B_{77}}$ | = | $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O III |
| $\mathbf{B_{78}}$ | = | $\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{11} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O III |
| $\mathbf{B_{79}}$ | = | $y_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (8b) | O III |
| $\mathbf{B_{80}}$ | = | $- y_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | O III |
| $\mathbf{B_{81}}$ | = | $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+a y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (8b) | O IV |
| $\mathbf{B_{82}}$ | = | $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}- a y_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | O IV |
| $\mathbf{B_{83}}$ | = | $- \left(y_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O IV |
| $\mathbf{B_{84}}$ | = | $\left(y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{12} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O IV |
| $\mathbf{B_{85}}$ | = | $- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{12} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O IV |
| $\mathbf{B_{86}}$ | = | $\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{12} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O IV |
| $\mathbf{B_{87}}$ | = | $y_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $a y_{12} \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (8b) | O IV |
| $\mathbf{B_{88}}$ | = | $- y_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{12} \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | O IV |
| $\mathbf{B_{89}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (8b) | O V |
| $\mathbf{B_{90}}$ | = | $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | O V |
| $\mathbf{B_{91}}$ | = | $- \left(y_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O V |
| $\mathbf{B_{92}}$ | = | $\left(y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{13} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O V |
| $\mathbf{B_{93}}$ | = | $- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O V |
| $\mathbf{B_{94}}$ | = | $\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{13} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O V |
| $\mathbf{B_{95}}$ | = | $y_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $a y_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (8b) | O V |
| $\mathbf{B_{96}}$ | = | $- y_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | O V |
References
- K. Stadnicka, A. M. Glazer, and M. Koralewski, Structure, absolute configuration and optical activity of α-nickel sulfate hexahydrate, Acta Crystallogr. Sect. B 43, 319–325 (1987), doi:10.1107/S0108768187097787.
- C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928-1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
Found in
- J. W. Anthony, R. A. Bideaux, K. W. Bladh, and M. C. Nichols, eds., Handbook of Mineralogy (Mineralogical Society of America, 2004), chap. Retgersite, NiSO$_4$$\cdot$6H$_2$O.
Prototype Generator
aflow --proto=A12BC10D_tP96_92_6b_a_5b_a --params=$a,c/a,x_{1},x_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13}$