Mg(BrO$_{3}$)$_{2}$ $\cdot$ 6H$_{2}$O ($J1_{10}$) Structure: A2B12CD12_cP108_205_c_2d_a_2d-001
| Prototype | Br$_{2}$H$_{12}$MgO$_{12}$ |
| AFLOW prototype label | A2B12CD12_cP108_205_c_2d_a_2d-001 |
| Strukturbericht designation | $J1_{10}$ |
| ICSD | 404779 |
| CCDC | 1725136 |
| Pearson symbol | cP108 |
| Space group number | 205 |
| Space group symbol | $Pa\overline{3}$ |
| AFLOW prototype command |
aflow --proto=A2B12CD12_cP108_205_c_2d_a_2d-001
--params=$a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}$ |
Other compounds with this structure
Br$_{2}$(H$_{2}$O)$_{6}$O$_{6}$Co, Br$_{2}$(H$_{2}$O)$_{6}$O$_{6}$Cu, Br$_{2}$(H$_{2}$O)$_{6}$O$_{6}$Mg, Br$_{2}$(H$_{2}$O)$_{6}$O$_{6}$Ni, Cl$_{2}$(H$_{2}$O)$_{6}$O$_{6}$Ni
- This is the modern form of the Zn(BrO$_{3}$)$_{2}$ · 6H$_{2}$O ($J1_{10}$) structure, with the locations of the hydrogen atoms specified.
- The O I atoms form the water molecules along with the hydrogen atoms. (Peter, 1996) listed these oxygens after the ones we label O II.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Mg I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (4a) | Mg I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (4a) | Mg I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (4a) | Mg I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Br I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Br I |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Br I |
| $\mathbf{B_{8}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Br I |
| $\mathbf{B_{9}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Br I |
| $\mathbf{B_{10}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Br I |
| $\mathbf{B_{11}}$ | = | $x_{2} \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Br I |
| $\mathbf{B_{12}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Br I |
| $\mathbf{B_{13}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{14}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{15}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{16}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{17}}$ | = | $z_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{18}}$ | = | $\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{19}}$ | = | $- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{20}}$ | = | $- z_{3} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{21}}$ | = | $y_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{22}}$ | = | $- y_{3} \, \mathbf{a}_{1}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{23}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{24}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{25}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{26}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{27}}$ | = | $x_{3} \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{28}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{29}}$ | = | $- z_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{30}}$ | = | $- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{31}}$ | = | $\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{32}}$ | = | $z_{3} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{33}}$ | = | $- y_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{34}}$ | = | $y_{3} \, \mathbf{a}_{1}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{35}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{36}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H I |
| $\mathbf{B_{37}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{38}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{39}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{40}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{41}}$ | = | $z_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{42}}$ | = | $\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{43}}$ | = | $- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{44}}$ | = | $- z_{4} \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{45}}$ | = | $y_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{46}}$ | = | $- y_{4} \, \mathbf{a}_{1}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{47}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{48}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{49}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{50}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{51}}$ | = | $x_{4} \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{52}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{53}}$ | = | $- z_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{54}}$ | = | $- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{55}}$ | = | $\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{56}}$ | = | $z_{4} \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{57}}$ | = | $- y_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{58}}$ | = | $y_{4} \, \mathbf{a}_{1}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{59}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{60}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | H II |
| $\mathbf{B_{61}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{62}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{63}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{64}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{65}}$ | = | $z_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{66}}$ | = | $\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ | = | $a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{67}}$ | = | $- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{68}}$ | = | $- z_{5} \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{69}}$ | = | $y_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{70}}$ | = | $- y_{5} \, \mathbf{a}_{1}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{71}}$ | = | $\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{72}}$ | = | $- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{73}}$ | = | $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{74}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{75}}$ | = | $x_{5} \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{76}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{77}}$ | = | $- z_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{78}}$ | = | $- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ | = | $- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{79}}$ | = | $\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{80}}$ | = | $z_{5} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{81}}$ | = | $- y_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{82}}$ | = | $y_{5} \, \mathbf{a}_{1}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{83}}$ | = | $- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{84}}$ | = | $\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O I |
| $\mathbf{B_{85}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{86}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{87}}$ | = | $- x_{6} \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{88}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{89}}$ | = | $z_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{90}}$ | = | $\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{91}}$ | = | $- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{92}}$ | = | $- z_{6} \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{93}}$ | = | $y_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{94}}$ | = | $- y_{6} \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{95}}$ | = | $\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{96}}$ | = | $- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{97}}$ | = | $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{98}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{99}}$ | = | $x_{6} \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{100}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{101}}$ | = | $- z_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{102}}$ | = | $- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{103}}$ | = | $\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{104}}$ | = | $z_{6} \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{105}}$ | = | $- y_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{106}}$ | = | $y_{6} \, \mathbf{a}_{1}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{107}}$ | = | $- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (24d) | O II |
| $\mathbf{B_{108}}$ | = | $\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24d) | O II |
References
- S. Peter, E. Suchanek, D. E{ß}er, and H. D. Lutz, Die Zwillings-Kristallstruktur von Mg(BrO$_{3}$)$_{2}$$\cdot$6H$_{2}$O, Z. Naturforsch. B 51, 1072–1078 (1996), doi:10.1515/znb-1996-0804.
Found in
- Inorganic Crystal Structure Database. Entry 404779 [Br2(H2O)6O6Mg].
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A2B12CD12_cP108_205_c_2d_a_2d --params=$a,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}$