La$_{3}$Rh$_{4}$Sn$_{13}$ Structure: A3B4C13_cI320_214_gh_abgh_e4i-001
| Prototype | La$_{3}$Rh$_{4}$Sn$_{13}$ |
| AFLOW prototype label | A3B4C13_cI320_214_gh_abgh_e4i-001 |
| ICSD | 54367 |
| Pearson symbol | cI320 |
| Space group number | 214 |
| Space group symbol | $I4_132$ |
| AFLOW prototype command |
aflow --proto=A3B4C13_cI320_214_gh_abgh_e4i-001
--params=$a, \allowbreak x_{3}, \allowbreak y_{4}, \allowbreak y_{5}, \allowbreak y_{6}, \allowbreak y_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}$ |
Other compounds with this structure
Ca$_{3}$Rh$_{4}$Sn$_{13}$, Ce$_{3}$Rh$_{4}$Sn$_{13}$, Gd$_{3}$Rh$_{4}$Sn$_{13}$, Nd$_{3}$Rh$_{4}$Sn$_{13}$, Pr$_{3}$Rh$_{4}$Sn$_{13}$, Sm$_{3}$Rh$_{4}$Sn$_{13}$, Tb$_{3}$Rh$_{4}$Sn$_{13}$, Th$_{3}$Rh$_{4}$Sn$_{13}$, Yb$_{3}$Rh$_{4}$Sn$_{13}$
- (Bordet, 1991) refers to this as the
phase I'
structure of materials with the formula M$_{3}$Rh$_{4}$Sn$_{13}$, with thephase I
structure represented by the centrosymmetric Yb$_{3}$Rh$_{4}$Sn$_{13}$ phase. - (Villars, 2016) calls this the high-temperature phase of La$_{3}$Rh$_{4}$Sn$_{13}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (8a) | Rh I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (8a) | Rh I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}- \frac{1}{8}a \,\mathbf{\hat{z}}$ | (8a) | Rh I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}- \frac{1}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (8a) | Rh I |
| $\mathbf{B_{5}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (8b) | Rh II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}- \frac{1}{8}a \,\mathbf{\hat{z}}$ | (8b) | Rh II |
| $\mathbf{B_{7}}$ | = | $\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}- \frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (8b) | Rh II |
| $\mathbf{B_{8}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $- \frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (8b) | Rh II |
| $\mathbf{B_{9}}$ | = | $2 x_{3} \, \mathbf{a}_{1}+2 x_{3} \, \mathbf{a}_{2}+2 x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{11}}$ | = | $- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{12}}$ | = | $- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{13}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+2 x_{3} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{14}}$ | = | $- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{15}}$ | = | $2 x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{16}}$ | = | $2 x_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{17}}$ | = | $\left(2 y_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{3}{8}\right) \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24g) | La I |
| $\mathbf{B_{18}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24g) | La I |
| $\mathbf{B_{19}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(y_{4} + \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24g) | La I |
| $\mathbf{B_{20}}$ | = | $- \left(2 y_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{3}{8}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24g) | La I |
| $\mathbf{B_{21}}$ | = | $\left(y_{4} + \frac{1}{8}\right) \, \mathbf{a}_{1}+\left(2 y_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(y_{4} + \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (24g) | La I |
| $\mathbf{B_{22}}$ | = | $- \left(y_{4} - \frac{3}{8}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{8}a \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24g) | La I |
| $\mathbf{B_{23}}$ | = | $\left(y_{4} + \frac{3}{8}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{8}a \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24g) | La I |
| $\mathbf{B_{24}}$ | = | $- \left(y_{4} - \frac{1}{8}\right) \, \mathbf{a}_{1}- \left(2 y_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (24g) | La I |
| $\mathbf{B_{25}}$ | = | $\left(y_{4} + \frac{3}{8}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(2 y_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (24g) | La I |
| $\mathbf{B_{26}}$ | = | $\left(y_{4} + \frac{1}{8}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{3}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}a \,\mathbf{\hat{z}}$ | (24g) | La I |
| $\mathbf{B_{27}}$ | = | $- \left(y_{4} - \frac{1}{8}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{3}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}a \,\mathbf{\hat{z}}$ | (24g) | La I |
| $\mathbf{B_{28}}$ | = | $- \left(y_{4} - \frac{3}{8}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(2 y_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (24g) | La I |
| $\mathbf{B_{29}}$ | = | $\left(2 y_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{5} + \frac{3}{8}\right) \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24g) | Rh III |
| $\mathbf{B_{30}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(y_{5} - \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24g) | Rh III |
| $\mathbf{B_{31}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(y_{5} + \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24g) | Rh III |
| $\mathbf{B_{32}}$ | = | $- \left(2 y_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(y_{5} - \frac{3}{8}\right) \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24g) | Rh III |
| $\mathbf{B_{33}}$ | = | $\left(y_{5} + \frac{1}{8}\right) \, \mathbf{a}_{1}+\left(2 y_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(y_{5} + \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (24g) | Rh III |
| $\mathbf{B_{34}}$ | = | $- \left(y_{5} - \frac{3}{8}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{8}a \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24g) | Rh III |
| $\mathbf{B_{35}}$ | = | $\left(y_{5} + \frac{3}{8}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{8}a \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24g) | Rh III |
| $\mathbf{B_{36}}$ | = | $- \left(y_{5} - \frac{1}{8}\right) \, \mathbf{a}_{1}- \left(2 y_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(y_{5} - \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (24g) | Rh III |
| $\mathbf{B_{37}}$ | = | $\left(y_{5} + \frac{3}{8}\right) \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(2 y_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (24g) | Rh III |
| $\mathbf{B_{38}}$ | = | $\left(y_{5} + \frac{1}{8}\right) \, \mathbf{a}_{1}- \left(y_{5} - \frac{3}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}a \,\mathbf{\hat{z}}$ | (24g) | Rh III |
| $\mathbf{B_{39}}$ | = | $- \left(y_{5} - \frac{1}{8}\right) \, \mathbf{a}_{1}+\left(y_{5} + \frac{3}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}a \,\mathbf{\hat{z}}$ | (24g) | Rh III |
| $\mathbf{B_{40}}$ | = | $- \left(y_{5} - \frac{3}{8}\right) \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(2 y_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (24g) | Rh III |
| $\mathbf{B_{41}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(y_{6} - \frac{3}{8}\right) \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24h) | La II |
| $\mathbf{B_{42}}$ | = | $- \left(2 y_{6} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(y_{6} - \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24h) | La II |
| $\mathbf{B_{43}}$ | = | $\left(2 y_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(y_{6} + \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24h) | La II |
| $\mathbf{B_{44}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(y_{6} + \frac{3}{8}\right) \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24h) | La II |
| $\mathbf{B_{45}}$ | = | $\left(y_{6} + \frac{1}{8}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(y_{6} - \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (24h) | La II |
| $\mathbf{B_{46}}$ | = | $- \left(y_{6} - \frac{3}{8}\right) \, \mathbf{a}_{1}- \left(2 y_{6} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{8}a \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | La II |
| $\mathbf{B_{47}}$ | = | $\left(y_{6} + \frac{3}{8}\right) \, \mathbf{a}_{1}+\left(2 y_{6} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{8}a \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | La II |
| $\mathbf{B_{48}}$ | = | $- \left(y_{6} - \frac{1}{8}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\left(y_{6} + \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (24h) | La II |
| $\mathbf{B_{49}}$ | = | $- \left(y_{6} - \frac{3}{8}\right) \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (24h) | La II |
| $\mathbf{B_{50}}$ | = | $- \left(y_{6} - \frac{1}{8}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{3}{8}\right) \, \mathbf{a}_{2}- \left(2 y_{6} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}a \,\mathbf{\hat{z}}$ | (24h) | La II |
| $\mathbf{B_{51}}$ | = | $\left(y_{6} + \frac{1}{8}\right) \, \mathbf{a}_{1}+\left(y_{6} + \frac{3}{8}\right) \, \mathbf{a}_{2}+\left(2 y_{6} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}a \,\mathbf{\hat{z}}$ | (24h) | La II |
| $\mathbf{B_{52}}$ | = | $\left(y_{6} + \frac{3}{8}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (24h) | La II |
| $\mathbf{B_{53}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(y_{7} - \frac{3}{8}\right) \, \mathbf{a}_{2}+\left(y_{7} + \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24h) | Rh IV |
| $\mathbf{B_{54}}$ | = | $- \left(2 y_{7} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(y_{7} - \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24h) | Rh IV |
| $\mathbf{B_{55}}$ | = | $\left(2 y_{7} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{7} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(y_{7} + \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24h) | Rh IV |
| $\mathbf{B_{56}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(y_{7} + \frac{3}{8}\right) \, \mathbf{a}_{2}- \left(y_{7} - \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24h) | Rh IV |
| $\mathbf{B_{57}}$ | = | $\left(y_{7} + \frac{1}{8}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(y_{7} - \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a y_{7} \,\mathbf{\hat{z}}$ | (24h) | Rh IV |
| $\mathbf{B_{58}}$ | = | $- \left(y_{7} - \frac{3}{8}\right) \, \mathbf{a}_{1}- \left(2 y_{7} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(y_{7} - \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{8}a \,\mathbf{\hat{y}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Rh IV |
| $\mathbf{B_{59}}$ | = | $\left(y_{7} + \frac{3}{8}\right) \, \mathbf{a}_{1}+\left(2 y_{7} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(y_{7} + \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{8}a \,\mathbf{\hat{y}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Rh IV |
| $\mathbf{B_{60}}$ | = | $- \left(y_{7} - \frac{1}{8}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\left(y_{7} + \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}- a y_{7} \,\mathbf{\hat{z}}$ | (24h) | Rh IV |
| $\mathbf{B_{61}}$ | = | $- \left(y_{7} - \frac{3}{8}\right) \, \mathbf{a}_{1}+\left(y_{7} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (24h) | Rh IV |
| $\mathbf{B_{62}}$ | = | $- \left(y_{7} - \frac{1}{8}\right) \, \mathbf{a}_{1}- \left(y_{7} - \frac{3}{8}\right) \, \mathbf{a}_{2}- \left(2 y_{7} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}a \,\mathbf{\hat{z}}$ | (24h) | Rh IV |
| $\mathbf{B_{63}}$ | = | $\left(y_{7} + \frac{1}{8}\right) \, \mathbf{a}_{1}+\left(y_{7} + \frac{3}{8}\right) \, \mathbf{a}_{2}+\left(2 y_{7} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}a \,\mathbf{\hat{z}}$ | (24h) | Rh IV |
| $\mathbf{B_{64}}$ | = | $\left(y_{7} + \frac{3}{8}\right) \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (24h) | Rh IV |
| $\mathbf{B_{65}}$ | = | $\left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{66}}$ | = | $\left(- y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{67}}$ | = | $\left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{68}}$ | = | $- \left(y_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} - z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{69}}$ | = | $\left(x_{8} + y_{8}\right) \, \mathbf{a}_{1}+\left(y_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a y_{8} \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{70}}$ | = | $- \left(x_{8} + y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{71}}$ | = | $\left(- x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{8} \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{72}}$ | = | $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- \left(y_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} - z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a y_{8} \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{73}}$ | = | $\left(x_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{2}+\left(y_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{74}}$ | = | $- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} + y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{75}}$ | = | $- \left(x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{76}}$ | = | $\left(x_{8} - z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}- \left(y_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{77}}$ | = | $\left(x_{8} - z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{8} - z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{78}}$ | = | $- \left(x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{79}}$ | = | $- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{1}+\left(y_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(- x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{8} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{80}}$ | = | $\left(x_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(- y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{81}}$ | = | $\left(- y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{82}}$ | = | $\left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(- x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{83}}$ | = | $- \left(y_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{8} + y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{84}}$ | = | $\left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} - z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{85}}$ | = | $\left(- x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}+\left(y_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{8} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{86}}$ | = | $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(- y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{87}}$ | = | $\left(x_{8} + y_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} - z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{88}}$ | = | $- \left(x_{8} + y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn II |
| $\mathbf{B_{89}}$ | = | $\left(y_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+a z_{9} \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{90}}$ | = | $\left(- y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{9} - z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{9} \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{91}}$ | = | $\left(y_{9} - z_{9}\right) \, \mathbf{a}_{1}- \left(x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{9} + y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}- a z_{9} \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{92}}$ | = | $- \left(y_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{9} - z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{93}}$ | = | $\left(x_{9} + y_{9}\right) \, \mathbf{a}_{1}+\left(y_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $a z_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+a y_{9} \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{94}}$ | = | $- \left(x_{9} + y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $a z_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{95}}$ | = | $\left(- x_{9} + y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{9} - z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{9} \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{9} \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{96}}$ | = | $\left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}- \left(y_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{9} - z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- a y_{9} \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{97}}$ | = | $\left(x_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} + y_{9}\right) \, \mathbf{a}_{2}+\left(y_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}+a z_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{98}}$ | = | $- \left(x_{9} - z_{9}\right) \, \mathbf{a}_{1}- \left(x_{9} + y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{99}}$ | = | $- \left(x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{9} + y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}- a z_{9} \,\mathbf{\hat{y}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{100}}$ | = | $\left(x_{9} - z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}- \left(y_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{101}}$ | = | $\left(x_{9} - z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{9} - z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{102}}$ | = | $- \left(x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{103}}$ | = | $- \left(x_{9} - z_{9}\right) \, \mathbf{a}_{1}+\left(y_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(- x_{9} + y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{9} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{104}}$ | = | $\left(x_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(- y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{105}}$ | = | $\left(- y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{106}}$ | = | $\left(y_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(- x_{9} + y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{107}}$ | = | $- \left(y_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{9} + y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{108}}$ | = | $\left(y_{9} - z_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} + y_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} - z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{109}}$ | = | $\left(- x_{9} + y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{9} - z_{9}\right) \, \mathbf{a}_{2}+\left(y_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{9} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{110}}$ | = | $\left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(- y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{111}}$ | = | $\left(x_{9} + y_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} - z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{112}}$ | = | $- \left(x_{9} + y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn III |
| $\mathbf{B_{113}}$ | = | $\left(y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+a z_{10} \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{114}}$ | = | $\left(- y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{10} \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{115}}$ | = | $\left(y_{10} - z_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}- a z_{10} \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{116}}$ | = | $- \left(y_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}- a \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{117}}$ | = | $\left(x_{10} + y_{10}\right) \, \mathbf{a}_{1}+\left(y_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + z_{10}\right) \, \mathbf{a}_{3}$ | = | $a z_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+a y_{10} \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{118}}$ | = | $- \left(x_{10} + y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $a z_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{119}}$ | = | $\left(- x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{10} - z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{10} \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{10} \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{120}}$ | = | $\left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}- \left(y_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}- a y_{10} \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{121}}$ | = | $\left(x_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{2}+\left(y_{10} + z_{10}\right) \, \mathbf{a}_{3}$ | = | $a y_{10} \,\mathbf{\hat{x}}+a z_{10} \,\mathbf{\hat{y}}+a x_{10} \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{122}}$ | = | $- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} + y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{10} \,\mathbf{\hat{y}}- a x_{10} \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{123}}$ | = | $- \left(x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $a y_{10} \,\mathbf{\hat{x}}- a z_{10} \,\mathbf{\hat{y}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{124}}$ | = | $\left(x_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}- \left(y_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{10} \,\mathbf{\hat{x}}- a \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{10} \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{125}}$ | = | $\left(x_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{10} - z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{126}}$ | = | $- \left(x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{127}}$ | = | $- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{1}+\left(y_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(- x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{10} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{128}}$ | = | $\left(x_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(- y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{129}}$ | = | $\left(- y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + z_{10}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{130}}$ | = | $\left(y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(- x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{131}}$ | = | $- \left(y_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} + y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{132}}$ | = | $\left(y_{10} - z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{133}}$ | = | $\left(- x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}+\left(y_{10} + z_{10}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{10} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{134}}$ | = | $\left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(- y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{135}}$ | = | $\left(x_{10} + y_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{136}}$ | = | $- \left(x_{10} + y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn IV |
| $\mathbf{B_{137}}$ | = | $\left(y_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+a z_{11} \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{138}}$ | = | $\left(- y_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} - z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} + y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{11} \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{139}}$ | = | $\left(y_{11} - z_{11}\right) \, \mathbf{a}_{1}- \left(x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{11} + y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}- a z_{11} \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{140}}$ | = | $- \left(y_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} - z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}- a \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{141}}$ | = | $\left(x_{11} + y_{11}\right) \, \mathbf{a}_{1}+\left(y_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} + z_{11}\right) \, \mathbf{a}_{3}$ | = | $a z_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+a y_{11} \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{142}}$ | = | $- \left(x_{11} + y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{11} - z_{11}\right) \, \mathbf{a}_{3}$ | = | $a z_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{143}}$ | = | $\left(- x_{11} + y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{11} - z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{11} \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{11} \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{144}}$ | = | $\left(x_{11} - y_{11}\right) \, \mathbf{a}_{1}- \left(y_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{11} - z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}- a y_{11} \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{145}}$ | = | $\left(x_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} + y_{11}\right) \, \mathbf{a}_{2}+\left(y_{11} + z_{11}\right) \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}+a z_{11} \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{146}}$ | = | $- \left(x_{11} - z_{11}\right) \, \mathbf{a}_{1}- \left(x_{11} + y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{11} \,\mathbf{\hat{y}}- a x_{11} \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{147}}$ | = | $- \left(x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{11} + y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{11} - z_{11}\right) \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}- a z_{11} \,\mathbf{\hat{y}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{148}}$ | = | $\left(x_{11} - z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{2}- \left(y_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{11} \,\mathbf{\hat{x}}- a \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{149}}$ | = | $\left(x_{11} - z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{11} - z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{150}}$ | = | $- \left(x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{11} + y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{151}}$ | = | $- \left(x_{11} - z_{11}\right) \, \mathbf{a}_{1}+\left(y_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(- x_{11} + y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{11} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{152}}$ | = | $\left(x_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(- y_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{153}}$ | = | $\left(- y_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} + z_{11}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{154}}$ | = | $\left(y_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(- x_{11} + y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{11} - z_{11}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{155}}$ | = | $- \left(y_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} + y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{156}}$ | = | $\left(y_{11} - z_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} + y_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} - z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{157}}$ | = | $\left(- x_{11} + y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} - z_{11}\right) \, \mathbf{a}_{2}+\left(y_{11} + z_{11}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{11} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{158}}$ | = | $\left(x_{11} - y_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(- y_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{159}}$ | = | $\left(x_{11} + y_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} - z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{11} - z_{11}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn V |
| $\mathbf{B_{160}}$ | = | $- \left(x_{11} + y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48i) | Sn V |
References
- P. Bordet, D. E. Cox, G. P. Espinosa, J. L. Hodeau, and M. Marezio, Synchrotron X-ray powder diffraction study of the phase I' compound: SnLa$_{3}$Rh$_{4}$Sn$_{12}$, Solid State Commun. 78, 359–366 (1991), doi:10.1016/0038-1098(91)90684-N.
Found in
- P. Villars, La3Rh4Sn13 ht Crystal Structure (2016). PAULING FILE in: Inorganic Solid Phases, SpringerMaterials (online database), Springer, Heidelberg (ed.) SpringerMaterials.
Prototype Generator
aflow --proto=A3B4C13_cI320_214_gh_abgh_e4i --params=$a,x_{3},y_{4},y_{5},y_{6},y_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11}$