H$_{3}$PW$_{12}$O$_{40}\cdot$29H$_{2}$O ($H4_{21}$) Structure: A29B40CD12_cF656_227_ae2fg_e3g_b_g-001
| Prototype | H$_{3}$(H$_{2}$O)$_{29}$O$_{40}$PW$_{12}$ |
| AFLOW prototype label | A29B40CD12_cF656_227_ae2fg_e3g_b_g-001 |
| Strukturbericht designation | $H4_{21}$ |
| Mineral name | 29-phosphotungstic acid (PWA-29) |
| ICSD | 36274 |
| Pearson symbol | cF656 |
| Space group number | 227 |
| Space group symbol | $Fd\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A29B40CD12_cF656_227_ae2fg_e3g_b_g-001
--params=$a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak x_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak z_{11}$ |
Other compounds with this structure
H$_{3}$PMo$_{12}$O$_{40}\cdot$30H$_{2}$O
- This compound is often colloquially called
PWA-29.
On heating some water molecules will disassociate, leaving H$_{3}$PW$_{12}$O$_{40}$ · 6H$_{2}$O, H$_{3}$PW$_{12}$O$_{40}$ · 5H$_{2}$O ($H4_{16}$), or H$_{3}$PW$_{12}$O$_{40}$ · 3H$_{2}$O. - The three hydrogen atoms not formally associated with the water molecules are not located. Presumably they join with some water molecules to form form H$_{3}$O$^+$ ions.
- Even the exact number and position of the water molecules is uncertain. (Clark, 1976), studying the related compound H$_{3}$PMo$_{12}$O$_{40}$ · 30H$_{2}$O, states that the composition is approximately 30H$_{2}$O and that
only six of the water molecules occupy ordered sites.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (8a) | H I |
| $\mathbf{B_{2}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+\frac{7}{8}a \,\mathbf{\hat{y}}+\frac{7}{8}a \,\mathbf{\hat{z}}$ | (8a) | H I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (8b) | P I |
| $\mathbf{B_{4}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (8b) | P I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (32e) | H II |
| $\mathbf{B_{6}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- \left(3 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (32e) | H II |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}- \left(3 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | H II |
| $\mathbf{B_{8}}$ | = | $- \left(3 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | H II |
| $\mathbf{B_{9}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(3 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (32e) | H II |
| $\mathbf{B_{10}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (32e) | H II |
| $\mathbf{B_{11}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(3 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | H II |
| $\mathbf{B_{12}}$ | = | $\left(3 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | H II |
| $\mathbf{B_{13}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{14}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- \left(3 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{15}}$ | = | $x_{4} \, \mathbf{a}_{1}- \left(3 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{16}}$ | = | $- \left(3 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{17}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(3 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{18}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{19}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\left(3 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{20}}$ | = | $\left(3 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{21}}$ | = | $- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | H III |
| $\mathbf{B_{22}}$ | = | $x_{5} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | H III |
| $\mathbf{B_{23}}$ | = | $x_{5} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | H III |
| $\mathbf{B_{24}}$ | = | $- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | H III |
| $\mathbf{B_{25}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (48f) | H III |
| $\mathbf{B_{26}}$ | = | $- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | H III |
| $\mathbf{B_{27}}$ | = | $\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | H III |
| $\mathbf{B_{28}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | H III |
| $\mathbf{B_{29}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | H III |
| $\mathbf{B_{30}}$ | = | $\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | H III |
| $\mathbf{B_{31}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (48f) | H III |
| $\mathbf{B_{32}}$ | = | $\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | H III |
| $\mathbf{B_{33}}$ | = | $- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | H IV |
| $\mathbf{B_{34}}$ | = | $x_{6} \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | H IV |
| $\mathbf{B_{35}}$ | = | $x_{6} \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | H IV |
| $\mathbf{B_{36}}$ | = | $- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | H IV |
| $\mathbf{B_{37}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (48f) | H IV |
| $\mathbf{B_{38}}$ | = | $- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | H IV |
| $\mathbf{B_{39}}$ | = | $\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | H IV |
| $\mathbf{B_{40}}$ | = | $- x_{6} \, \mathbf{a}_{1}+\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | H IV |
| $\mathbf{B_{41}}$ | = | $- x_{6} \, \mathbf{a}_{1}+\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | H IV |
| $\mathbf{B_{42}}$ | = | $\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | H IV |
| $\mathbf{B_{43}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (48f) | H IV |
| $\mathbf{B_{44}}$ | = | $\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | H IV |
| $\mathbf{B_{45}}$ | = | $z_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+\left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{46}}$ | = | $z_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}- \left(2 x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{47}}$ | = | $\left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(2 x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{48}}$ | = | $- \left(2 x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{49}}$ | = | $\left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{50}}$ | = | $- \left(2 x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{51}}$ | = | $z_{7} \, \mathbf{a}_{1}+\left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(2 x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{52}}$ | = | $z_{7} \, \mathbf{a}_{1}- \left(2 x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{53}}$ | = | $z_{7} \, \mathbf{a}_{1}+\left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{54}}$ | = | $z_{7} \, \mathbf{a}_{1}- \left(2 x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{55}}$ | = | $- \left(2 x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+\left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{56}}$ | = | $\left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}- \left(2 x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{57}}$ | = | $- z_{7} \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}+\left(2 x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{58}}$ | = | $- z_{7} \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- \left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{59}}$ | = | $- \left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(2 x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{60}}$ | = | $\left(2 x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{61}}$ | = | $- \left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}+\left(2 x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{62}}$ | = | $\left(2 x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- \left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{63}}$ | = | $- z_{7} \, \mathbf{a}_{1}- \left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{64}}$ | = | $- z_{7} \, \mathbf{a}_{1}+\left(2 x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{65}}$ | = | $- z_{7} \, \mathbf{a}_{1}- \left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{2}+\left(2 x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{66}}$ | = | $- z_{7} \, \mathbf{a}_{1}+\left(2 x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{67}}$ | = | $\left(2 x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- a z_{7} \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{68}}$ | = | $- \left(2 x_{7} - z_{7}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- a z_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (96g) | H V |
| $\mathbf{B_{69}}$ | = | $z_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{70}}$ | = | $z_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}- \left(2 x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{71}}$ | = | $\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(2 x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{72}}$ | = | $- \left(2 x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{73}}$ | = | $\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{74}}$ | = | $- \left(2 x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{75}}$ | = | $z_{8} \, \mathbf{a}_{1}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(2 x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{76}}$ | = | $z_{8} \, \mathbf{a}_{1}- \left(2 x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{77}}$ | = | $z_{8} \, \mathbf{a}_{1}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{78}}$ | = | $z_{8} \, \mathbf{a}_{1}- \left(2 x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{79}}$ | = | $- \left(2 x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{80}}$ | = | $\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}- \left(2 x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{81}}$ | = | $- z_{8} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}+\left(2 x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{82}}$ | = | $- z_{8} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}- \left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{83}}$ | = | $- \left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{1}+\left(2 x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+a \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{84}}$ | = | $\left(2 x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{85}}$ | = | $- \left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}+\left(2 x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{86}}$ | = | $\left(2 x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}- \left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{87}}$ | = | $- z_{8} \, \mathbf{a}_{1}- \left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{88}}$ | = | $- z_{8} \, \mathbf{a}_{1}+\left(2 x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}+a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{89}}$ | = | $- z_{8} \, \mathbf{a}_{1}- \left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{2}+\left(2 x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{90}}$ | = | $- z_{8} \, \mathbf{a}_{1}+\left(2 x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{91}}$ | = | $\left(2 x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{92}}$ | = | $- \left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{93}}$ | = | $z_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+a z_{9} \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{94}}$ | = | $z_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}- \left(2 x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a z_{9} \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{95}}$ | = | $\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{1}- \left(2 x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- a \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{96}}$ | = | $- \left(2 x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{97}}$ | = | $\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a z_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{98}}$ | = | $- \left(2 x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a z_{9} \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{99}}$ | = | $z_{9} \, \mathbf{a}_{1}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{2}- \left(2 x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{100}}$ | = | $z_{9} \, \mathbf{a}_{1}- \left(2 x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{101}}$ | = | $z_{9} \, \mathbf{a}_{1}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a z_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{102}}$ | = | $z_{9} \, \mathbf{a}_{1}- \left(2 x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a z_{9} \,\mathbf{\hat{y}}- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{103}}$ | = | $- \left(2 x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- a \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{104}}$ | = | $\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}- \left(2 x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{105}}$ | = | $- z_{9} \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}+\left(2 x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a z_{9} \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{106}}$ | = | $- z_{9} \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}- \left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- a z_{9} \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{107}}$ | = | $- \left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{1}+\left(2 x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+a \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{108}}$ | = | $\left(2 x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{109}}$ | = | $- \left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}+\left(2 x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{110}}$ | = | $\left(2 x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}- \left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+a \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{111}}$ | = | $- z_{9} \, \mathbf{a}_{1}- \left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a z_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{112}}$ | = | $- z_{9} \, \mathbf{a}_{1}+\left(2 x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a z_{9} \,\mathbf{\hat{y}}+a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{113}}$ | = | $- z_{9} \, \mathbf{a}_{1}- \left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{2}+\left(2 x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{114}}$ | = | $- z_{9} \, \mathbf{a}_{1}+\left(2 x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{115}}$ | = | $\left(2 x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- a z_{9} \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{116}}$ | = | $- \left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- a z_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (96g) | O III |
| $\mathbf{B_{117}}$ | = | $z_{10} \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}+\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+a z_{10} \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{118}}$ | = | $z_{10} \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}- \left(2 x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a z_{10} \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{119}}$ | = | $\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{1}- \left(2 x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}- a \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{120}}$ | = | $- \left(2 x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{121}}$ | = | $\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a z_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+a x_{10} \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{122}}$ | = | $- \left(2 x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a z_{10} \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{123}}$ | = | $z_{10} \, \mathbf{a}_{1}+\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{2}- \left(2 x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{10} \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{124}}$ | = | $z_{10} \, \mathbf{a}_{1}- \left(2 x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{125}}$ | = | $z_{10} \, \mathbf{a}_{1}+\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a z_{10} \,\mathbf{\hat{y}}+a x_{10} \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{126}}$ | = | $z_{10} \, \mathbf{a}_{1}- \left(2 x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a z_{10} \,\mathbf{\hat{y}}- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{127}}$ | = | $- \left(2 x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}+\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- a \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{128}}$ | = | $\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}- \left(2 x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{10} \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{129}}$ | = | $- z_{10} \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{2}+\left(2 x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a z_{10} \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{130}}$ | = | $- z_{10} \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{2}- \left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}- a z_{10} \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{131}}$ | = | $- \left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{1}+\left(2 x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}+a \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{132}}$ | = | $\left(2 x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{133}}$ | = | $- \left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{2}+\left(2 x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{10} \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{134}}$ | = | $\left(2 x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{2}- \left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+a \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{135}}$ | = | $- z_{10} \, \mathbf{a}_{1}- \left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a z_{10} \,\mathbf{\hat{y}}- a x_{10} \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{136}}$ | = | $- z_{10} \, \mathbf{a}_{1}+\left(2 x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a z_{10} \,\mathbf{\hat{y}}+a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{137}}$ | = | $- z_{10} \, \mathbf{a}_{1}- \left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{2}+\left(2 x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{10} \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{138}}$ | = | $- z_{10} \, \mathbf{a}_{1}+\left(2 x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}+a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{139}}$ | = | $\left(2 x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- a z_{10} \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{140}}$ | = | $- \left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- a z_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}- a x_{10} \,\mathbf{\hat{z}}$ | (96g) | O IV |
| $\mathbf{B_{141}}$ | = | $z_{11} \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}+\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+a z_{11} \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{142}}$ | = | $z_{11} \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}- \left(2 x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a z_{11} \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{143}}$ | = | $\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{1}- \left(2 x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}- a \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{144}}$ | = | $- \left(2 x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{145}}$ | = | $\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a z_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{146}}$ | = | $- \left(2 x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a z_{11} \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{147}}$ | = | $z_{11} \, \mathbf{a}_{1}+\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{2}- \left(2 x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{148}}$ | = | $z_{11} \, \mathbf{a}_{1}- \left(2 x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{149}}$ | = | $z_{11} \, \mathbf{a}_{1}+\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a z_{11} \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{150}}$ | = | $z_{11} \, \mathbf{a}_{1}- \left(2 x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a z_{11} \,\mathbf{\hat{y}}- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{151}}$ | = | $- \left(2 x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}+\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- a \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{152}}$ | = | $\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}- \left(2 x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{153}}$ | = | $- z_{11} \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{2}+\left(2 x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a z_{11} \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{154}}$ | = | $- z_{11} \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{2}- \left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- a z_{11} \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{155}}$ | = | $- \left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{1}+\left(2 x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}+a \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{156}}$ | = | $\left(2 x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{157}}$ | = | $- \left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{2}+\left(2 x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{11} \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{158}}$ | = | $\left(2 x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{2}- \left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+a \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{159}}$ | = | $- z_{11} \, \mathbf{a}_{1}- \left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a z_{11} \,\mathbf{\hat{y}}- a x_{11} \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{160}}$ | = | $- z_{11} \, \mathbf{a}_{1}+\left(2 x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a z_{11} \,\mathbf{\hat{y}}+a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{161}}$ | = | $- z_{11} \, \mathbf{a}_{1}- \left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{2}+\left(2 x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{11} \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{162}}$ | = | $- z_{11} \, \mathbf{a}_{1}+\left(2 x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}+a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{163}}$ | = | $\left(2 x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- a z_{11} \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | W I |
| $\mathbf{B_{164}}$ | = | $- \left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- a z_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- a x_{11} \,\mathbf{\hat{z}}$ | (96g) | W I |
References
- A. J. Bradley and J. W. Illinworth, The Crystal Structure of H$_{3}$PW$_{12}$O$_{40}$$\cdot$29H$_{2}$O, Proc. Roy. Soc. London A 157, 113–131 (1936), doi:10.1098/rspa.1936.0183.
- C. J. Clark and D. Hall, Dodecamolybdophosphoric acid {\em circa} 30-hydrate, Acta Crystallogr. Sect. B 32, 1545–1547 (1976), doi:10.1107/S0567740876005748.
Found in
- C. Gottfried, ed., Strukturbericht Band IV 1936 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1938).
Prototype Generator
aflow --proto=A29B40CD12_cF656_227_ae2fg_e3g_b_g --params=$a,x_{3},x_{4},x_{5},x_{6},x_{7},z_{7},x_{8},z_{8},x_{9},z_{9},x_{10},z_{10},x_{11},z_{11}$