Pu$_{31}$Rh$_{20}$ Structure: A31B20_tI204_140_b2gh3m_ac2fh3l-001
| Prototype | Pu$_{31}$Rh$_{20}$ |
| AFLOW prototype label | A31B20_tI204_140_b2gh3m_ac2fh3l-001 |
| ICSD | 1111 |
| Pearson symbol | tI204 |
| Space group number | 140 |
| Space group symbol | $I4/mcm$ |
| AFLOW prototype command |
aflow --proto=A31B20_tI204_140_b2gh3m_ac2fh3l-001
--params=$a, \allowbreak c/a, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak x_{9}, \allowbreak x_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}$ |
Other compounds with this structure
Pu$_{31}$Pt$_{20}$, Ca$_{31}$Sn$_{20}$
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | Rh I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4a) | Rh I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4b) | Pu I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4b) | Pu I |
| $\mathbf{B_{5}}$ | = | $0$ | = | $0$ | (4c) | Rh II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4c) | Rh II |
| $\mathbf{B_{7}}$ | = | $z_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (8f) | Rh III |
| $\mathbf{B_{8}}$ | = | $- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}$ | = | $- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Rh III |
| $\mathbf{B_{9}}$ | = | $- z_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}$ | = | $- c z_{4} \,\mathbf{\hat{z}}$ | (8f) | Rh III |
| $\mathbf{B_{10}}$ | = | $\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}$ | = | $c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Rh III |
| $\mathbf{B_{11}}$ | = | $z_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}$ | = | $c z_{5} \,\mathbf{\hat{z}}$ | (8f) | Rh IV |
| $\mathbf{B_{12}}$ | = | $- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}$ | = | $- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Rh IV |
| $\mathbf{B_{13}}$ | = | $- z_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}$ | = | $- c z_{5} \,\mathbf{\hat{z}}$ | (8f) | Rh IV |
| $\mathbf{B_{14}}$ | = | $\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}$ | = | $c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Rh IV |
| $\mathbf{B_{15}}$ | = | $\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8g) | Pu II |
| $\mathbf{B_{16}}$ | = | $z_{6} \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{6} \,\mathbf{\hat{z}}$ | (8g) | Pu II |
| $\mathbf{B_{17}}$ | = | $- z_{6} \, \mathbf{a}_{1}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{6} \,\mathbf{\hat{z}}$ | (8g) | Pu II |
| $\mathbf{B_{18}}$ | = | $- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (8g) | Pu II |
| $\mathbf{B_{19}}$ | = | $\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8g) | Pu III |
| $\mathbf{B_{20}}$ | = | $z_{7} \, \mathbf{a}_{1}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{7} \,\mathbf{\hat{z}}$ | (8g) | Pu III |
| $\mathbf{B_{21}}$ | = | $- z_{7} \, \mathbf{a}_{1}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{7} \,\mathbf{\hat{z}}$ | (8g) | Pu III |
| $\mathbf{B_{22}}$ | = | $- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8g) | Pu III |
| $\mathbf{B_{23}}$ | = | $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+\left(2 x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (8h) | Pu IV |
| $\mathbf{B_{24}}$ | = | $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- \left(2 x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (8h) | Pu IV |
| $\mathbf{B_{25}}$ | = | $x_{8} \, \mathbf{a}_{1}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}$ | (8h) | Pu IV |
| $\mathbf{B_{26}}$ | = | $- x_{8} \, \mathbf{a}_{1}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}$ | (8h) | Pu IV |
| $\mathbf{B_{27}}$ | = | $\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+\left(2 x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (8h) | Rh V |
| $\mathbf{B_{28}}$ | = | $- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- \left(2 x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (8h) | Rh V |
| $\mathbf{B_{29}}$ | = | $x_{9} \, \mathbf{a}_{1}- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}$ | (8h) | Rh V |
| $\mathbf{B_{30}}$ | = | $- x_{9} \, \mathbf{a}_{1}+\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}$ | (8h) | Rh V |
| $\mathbf{B_{31}}$ | = | $\left(x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(2 x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16l) | Rh VI |
| $\mathbf{B_{32}}$ | = | $\left(- x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}- \left(2 x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16l) | Rh VI |
| $\mathbf{B_{33}}$ | = | $\left(x_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(- x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16l) | Rh VI |
| $\mathbf{B_{34}}$ | = | $- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16l) | Rh VI |
| $\mathbf{B_{35}}$ | = | $\left(x_{10} - z_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (16l) | Rh VI |
| $\mathbf{B_{36}}$ | = | $- \left(x_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (16l) | Rh VI |
| $\mathbf{B_{37}}$ | = | $\left(x_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}+\left(2 x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (16l) | Rh VI |
| $\mathbf{B_{38}}$ | = | $- \left(x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}- \left(2 x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (16l) | Rh VI |
| $\mathbf{B_{39}}$ | = | $\left(x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(2 x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16l) | Rh VII |
| $\mathbf{B_{40}}$ | = | $\left(- x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} - z_{11}\right) \, \mathbf{a}_{2}- \left(2 x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16l) | Rh VII |
| $\mathbf{B_{41}}$ | = | $\left(x_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(- x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16l) | Rh VII |
| $\mathbf{B_{42}}$ | = | $- \left(x_{11} - z_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16l) | Rh VII |
| $\mathbf{B_{43}}$ | = | $\left(x_{11} - z_{11}\right) \, \mathbf{a}_{1}- \left(x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16l) | Rh VII |
| $\mathbf{B_{44}}$ | = | $- \left(x_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} - z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16l) | Rh VII |
| $\mathbf{B_{45}}$ | = | $\left(x_{11} - z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} - z_{11}\right) \, \mathbf{a}_{2}+\left(2 x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16l) | Rh VII |
| $\mathbf{B_{46}}$ | = | $- \left(x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} + z_{11}\right) \, \mathbf{a}_{2}- \left(2 x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16l) | Rh VII |
| $\mathbf{B_{47}}$ | = | $\left(x_{12} + z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{12} + z_{12}\right) \, \mathbf{a}_{2}+\left(2 x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (16l) | Rh VIII |
| $\mathbf{B_{48}}$ | = | $\left(- x_{12} + z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{12} - z_{12}\right) \, \mathbf{a}_{2}- \left(2 x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (16l) | Rh VIII |
| $\mathbf{B_{49}}$ | = | $\left(x_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(- x_{12} + z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (16l) | Rh VIII |
| $\mathbf{B_{50}}$ | = | $- \left(x_{12} - z_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} + z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (16l) | Rh VIII |
| $\mathbf{B_{51}}$ | = | $\left(x_{12} - z_{12}\right) \, \mathbf{a}_{1}- \left(x_{12} + z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (16l) | Rh VIII |
| $\mathbf{B_{52}}$ | = | $- \left(x_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} - z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (16l) | Rh VIII |
| $\mathbf{B_{53}}$ | = | $\left(x_{12} - z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{12} - z_{12}\right) \, \mathbf{a}_{2}+\left(2 x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (16l) | Rh VIII |
| $\mathbf{B_{54}}$ | = | $- \left(x_{12} + z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{12} + z_{12}\right) \, \mathbf{a}_{2}- \left(2 x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (16l) | Rh VIII |
| $\mathbf{B_{55}}$ | = | $\left(y_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} + z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} + y_{13}\right) \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (32m) | Pu V |
| $\mathbf{B_{56}}$ | = | $- \left(y_{13} - z_{13}\right) \, \mathbf{a}_{1}- \left(x_{13} - z_{13}\right) \, \mathbf{a}_{2}- \left(x_{13} + y_{13}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (32m) | Pu V |
| $\mathbf{B_{57}}$ | = | $\left(x_{13} + z_{13}\right) \, \mathbf{a}_{1}- \left(y_{13} - z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} - y_{13}\right) \, \mathbf{a}_{3}$ | = | $- a y_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (32m) | Pu V |
| $\mathbf{B_{58}}$ | = | $- \left(x_{13} - z_{13}\right) \, \mathbf{a}_{1}+\left(y_{13} + z_{13}\right) \, \mathbf{a}_{2}- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{3}$ | = | $a y_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (32m) | Pu V |
| $\mathbf{B_{59}}$ | = | $\left(y_{13} - z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{13} + z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu V |
| $\mathbf{B_{60}}$ | = | $- \left(y_{13} + z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{13} - z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{13} - y_{13}\right) \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu V |
| $\mathbf{B_{61}}$ | = | $\left(x_{13} - z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{13} - z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{13} + y_{13}\right) \, \mathbf{a}_{3}$ | = | $a y_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu V |
| $\mathbf{B_{62}}$ | = | $- \left(x_{13} + z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{13} + z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{13} + y_{13}\right) \, \mathbf{a}_{3}$ | = | $- a y_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu V |
| $\mathbf{B_{63}}$ | = | $- \left(y_{13} + z_{13}\right) \, \mathbf{a}_{1}- \left(x_{13} + z_{13}\right) \, \mathbf{a}_{2}- \left(x_{13} + y_{13}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (32m) | Pu V |
| $\mathbf{B_{64}}$ | = | $\left(y_{13} - z_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} - z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} + y_{13}\right) \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (32m) | Pu V |
| $\mathbf{B_{65}}$ | = | $- \left(x_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(y_{13} - z_{13}\right) \, \mathbf{a}_{2}- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{3}$ | = | $a y_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (32m) | Pu V |
| $\mathbf{B_{66}}$ | = | $\left(x_{13} - z_{13}\right) \, \mathbf{a}_{1}- \left(y_{13} + z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} - y_{13}\right) \, \mathbf{a}_{3}$ | = | $- a y_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (32m) | Pu V |
| $\mathbf{B_{67}}$ | = | $\left(- y_{13} + z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{13} + z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{13} - y_{13}\right) \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu V |
| $\mathbf{B_{68}}$ | = | $\left(y_{13} + z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{13} + z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu V |
| $\mathbf{B_{69}}$ | = | $\left(- x_{13} + z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{13} + z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{13} + y_{13}\right) \, \mathbf{a}_{3}$ | = | $- a y_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu V |
| $\mathbf{B_{70}}$ | = | $\left(x_{13} + z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{13} + z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{13} + y_{13}\right) \, \mathbf{a}_{3}$ | = | $a y_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu V |
| $\mathbf{B_{71}}$ | = | $\left(y_{14} + z_{14}\right) \, \mathbf{a}_{1}+\left(x_{14} + z_{14}\right) \, \mathbf{a}_{2}+\left(x_{14} + y_{14}\right) \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (32m) | Pu VI |
| $\mathbf{B_{72}}$ | = | $- \left(y_{14} - z_{14}\right) \, \mathbf{a}_{1}- \left(x_{14} - z_{14}\right) \, \mathbf{a}_{2}- \left(x_{14} + y_{14}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}- a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (32m) | Pu VI |
| $\mathbf{B_{73}}$ | = | $\left(x_{14} + z_{14}\right) \, \mathbf{a}_{1}- \left(y_{14} - z_{14}\right) \, \mathbf{a}_{2}+\left(x_{14} - y_{14}\right) \, \mathbf{a}_{3}$ | = | $- a y_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (32m) | Pu VI |
| $\mathbf{B_{74}}$ | = | $- \left(x_{14} - z_{14}\right) \, \mathbf{a}_{1}+\left(y_{14} + z_{14}\right) \, \mathbf{a}_{2}- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{3}$ | = | $a y_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (32m) | Pu VI |
| $\mathbf{B_{75}}$ | = | $\left(y_{14} - z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{14} + z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}+a y_{14} \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu VI |
| $\mathbf{B_{76}}$ | = | $- \left(y_{14} + z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{14} - z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{14} - y_{14}\right) \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}- a y_{14} \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu VI |
| $\mathbf{B_{77}}$ | = | $\left(x_{14} - z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{14} - z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{14} + y_{14}\right) \, \mathbf{a}_{3}$ | = | $a y_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu VI |
| $\mathbf{B_{78}}$ | = | $- \left(x_{14} + z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{14} + z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{14} + y_{14}\right) \, \mathbf{a}_{3}$ | = | $- a y_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu VI |
| $\mathbf{B_{79}}$ | = | $- \left(y_{14} + z_{14}\right) \, \mathbf{a}_{1}- \left(x_{14} + z_{14}\right) \, \mathbf{a}_{2}- \left(x_{14} + y_{14}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}- a y_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (32m) | Pu VI |
| $\mathbf{B_{80}}$ | = | $\left(y_{14} - z_{14}\right) \, \mathbf{a}_{1}+\left(x_{14} - z_{14}\right) \, \mathbf{a}_{2}+\left(x_{14} + y_{14}\right) \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+a y_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (32m) | Pu VI |
| $\mathbf{B_{81}}$ | = | $- \left(x_{14} + z_{14}\right) \, \mathbf{a}_{1}+\left(y_{14} - z_{14}\right) \, \mathbf{a}_{2}- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{3}$ | = | $a y_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (32m) | Pu VI |
| $\mathbf{B_{82}}$ | = | $\left(x_{14} - z_{14}\right) \, \mathbf{a}_{1}- \left(y_{14} + z_{14}\right) \, \mathbf{a}_{2}+\left(x_{14} - y_{14}\right) \, \mathbf{a}_{3}$ | = | $- a y_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (32m) | Pu VI |
| $\mathbf{B_{83}}$ | = | $\left(- y_{14} + z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{14} + z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{14} - y_{14}\right) \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}- a y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu VI |
| $\mathbf{B_{84}}$ | = | $\left(y_{14} + z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{14} + z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}+a y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu VI |
| $\mathbf{B_{85}}$ | = | $\left(- x_{14} + z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{14} + z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{14} + y_{14}\right) \, \mathbf{a}_{3}$ | = | $- a y_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu VI |
| $\mathbf{B_{86}}$ | = | $\left(x_{14} + z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{14} + z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{14} + y_{14}\right) \, \mathbf{a}_{3}$ | = | $a y_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu VI |
| $\mathbf{B_{87}}$ | = | $\left(y_{15} + z_{15}\right) \, \mathbf{a}_{1}+\left(x_{15} + z_{15}\right) \, \mathbf{a}_{2}+\left(x_{15} + y_{15}\right) \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (32m) | Pu VII |
| $\mathbf{B_{88}}$ | = | $- \left(y_{15} - z_{15}\right) \, \mathbf{a}_{1}- \left(x_{15} - z_{15}\right) \, \mathbf{a}_{2}- \left(x_{15} + y_{15}\right) \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}- a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (32m) | Pu VII |
| $\mathbf{B_{89}}$ | = | $\left(x_{15} + z_{15}\right) \, \mathbf{a}_{1}- \left(y_{15} - z_{15}\right) \, \mathbf{a}_{2}+\left(x_{15} - y_{15}\right) \, \mathbf{a}_{3}$ | = | $- a y_{15} \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (32m) | Pu VII |
| $\mathbf{B_{90}}$ | = | $- \left(x_{15} - z_{15}\right) \, \mathbf{a}_{1}+\left(y_{15} + z_{15}\right) \, \mathbf{a}_{2}- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{3}$ | = | $a y_{15} \,\mathbf{\hat{x}}- a x_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (32m) | Pu VII |
| $\mathbf{B_{91}}$ | = | $\left(y_{15} - z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{15} + z_{15} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}+a y_{15} \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu VII |
| $\mathbf{B_{92}}$ | = | $- \left(y_{15} + z_{15} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{15} - z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{15} - y_{15}\right) \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}- a y_{15} \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu VII |
| $\mathbf{B_{93}}$ | = | $\left(x_{15} - z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{15} - z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{15} + y_{15}\right) \, \mathbf{a}_{3}$ | = | $a y_{15} \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu VII |
| $\mathbf{B_{94}}$ | = | $- \left(x_{15} + z_{15} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{15} + z_{15} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{15} + y_{15}\right) \, \mathbf{a}_{3}$ | = | $- a y_{15} \,\mathbf{\hat{x}}- a x_{15} \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu VII |
| $\mathbf{B_{95}}$ | = | $- \left(y_{15} + z_{15}\right) \, \mathbf{a}_{1}- \left(x_{15} + z_{15}\right) \, \mathbf{a}_{2}- \left(x_{15} + y_{15}\right) \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}- a y_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (32m) | Pu VII |
| $\mathbf{B_{96}}$ | = | $\left(y_{15} - z_{15}\right) \, \mathbf{a}_{1}+\left(x_{15} - z_{15}\right) \, \mathbf{a}_{2}+\left(x_{15} + y_{15}\right) \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+a y_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (32m) | Pu VII |
| $\mathbf{B_{97}}$ | = | $- \left(x_{15} + z_{15}\right) \, \mathbf{a}_{1}+\left(y_{15} - z_{15}\right) \, \mathbf{a}_{2}- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{3}$ | = | $a y_{15} \,\mathbf{\hat{x}}- a x_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (32m) | Pu VII |
| $\mathbf{B_{98}}$ | = | $\left(x_{15} - z_{15}\right) \, \mathbf{a}_{1}- \left(y_{15} + z_{15}\right) \, \mathbf{a}_{2}+\left(x_{15} - y_{15}\right) \, \mathbf{a}_{3}$ | = | $- a y_{15} \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (32m) | Pu VII |
| $\mathbf{B_{99}}$ | = | $\left(- y_{15} + z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{15} + z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{15} - y_{15}\right) \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}- a y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu VII |
| $\mathbf{B_{100}}$ | = | $\left(y_{15} + z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{15} + z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}+a y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu VII |
| $\mathbf{B_{101}}$ | = | $\left(- x_{15} + z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{15} + z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{15} + y_{15}\right) \, \mathbf{a}_{3}$ | = | $- a y_{15} \,\mathbf{\hat{x}}- a x_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu VII |
| $\mathbf{B_{102}}$ | = | $\left(x_{15} + z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{15} + z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{15} + y_{15}\right) \, \mathbf{a}_{3}$ | = | $a y_{15} \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | Pu VII |
References
- D. T. Cromer and A. C. Larson, The Crystal Structure of Pu$_{31}$Pt$_{20}$ and Pu$_{31}$Rh$_{20}$, Acta Crystallogr. Sect. B 33, 2620–2627 (1977), doi:10.1107/S0567740877009030.
Prototype Generator
aflow --proto=A31B20_tI204_140_b2gh3m_ac2fh3l --params=$a,c/a,z_{4},z_{5},z_{6},z_{7},x_{8},x_{9},x_{10},z_{10},x_{11},z_{11},x_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15}$