Ce$_{6}$Cd$_{37}$ Structure: A41B6_cP188_201_b2efg5h_h-001
| Prototype | Cd$_{37}$Ce$_{6}$ |
| AFLOW prototype label | A41B6_cP188_201_b2efg5h_h-001 |
| ICSD | 54599 |
| Pearson symbol | cP188 |
| Space group number | 201 |
| Space group symbol | $Pn\overline{3}$ |
| AFLOW prototype command |
aflow --proto=A41B6_cP188_201_b2efg5h_h-001
--params=$a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}$ |
- The compound now known as Ce$_{6}$Cd$_{37}$ was originally thought to have the YCd$_{6}$ structure, but (Armbrüster, 2000) found that it actually has the structure shown here.
- All of the sites are fully occupied except the one labeled Cd-X, where 2/3 of the sites are vacant, giving the correct stoichiometry. We use the data taken at 298K.
- (Armbrüster, 2000) give the structure of Ce$_{6}$Cd$_{37}$ in setting 1 of space group $Pn\overline{3}$ #201. We used FINDSYM to change this to the standard setting 2.
- (Armbrüster, 2000) also present a slightly different version of the YCd$_{6}$ structure than that presented in the prototype paper, (Larson, 1972).
- We used FINDSYM to transform this to the standard second setting, which places a cerium atom and the inversion site at the origin.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4b) | Cd I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (4b) | Cd I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (4b) | Cd I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (4b) | Cd I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8e) | Cd II |
| $\mathbf{B_{6}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8e) | Cd II |
| $\mathbf{B_{7}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | Cd II |
| $\mathbf{B_{8}}$ | = | $x_{2} \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | Cd II |
| $\mathbf{B_{9}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8e) | Cd II |
| $\mathbf{B_{10}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8e) | Cd II |
| $\mathbf{B_{11}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | Cd II |
| $\mathbf{B_{12}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | Cd II |
| $\mathbf{B_{13}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (8e) | Cd III |
| $\mathbf{B_{14}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (8e) | Cd III |
| $\mathbf{B_{15}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | Cd III |
| $\mathbf{B_{16}}$ | = | $x_{3} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | Cd III |
| $\mathbf{B_{17}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (8e) | Cd III |
| $\mathbf{B_{18}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (8e) | Cd III |
| $\mathbf{B_{19}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | Cd III |
| $\mathbf{B_{20}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | Cd III |
| $\mathbf{B_{21}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12f) | Cd IV |
| $\mathbf{B_{22}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12f) | Cd IV |
| $\mathbf{B_{23}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12f) | Cd IV |
| $\mathbf{B_{24}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12f) | Cd IV |
| $\mathbf{B_{25}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (12f) | Cd IV |
| $\mathbf{B_{26}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12f) | Cd IV |
| $\mathbf{B_{27}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (12f) | Cd IV |
| $\mathbf{B_{28}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (12f) | Cd IV |
| $\mathbf{B_{29}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (12f) | Cd IV |
| $\mathbf{B_{30}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (12f) | Cd IV |
| $\mathbf{B_{31}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (12f) | Cd IV |
| $\mathbf{B_{32}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12f) | Cd IV |
| $\mathbf{B_{33}}$ | = | $x_{5} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12g) | Cd V |
| $\mathbf{B_{34}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12g) | Cd V |
| $\mathbf{B_{35}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (12g) | Cd V |
| $\mathbf{B_{36}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (12g) | Cd V |
| $\mathbf{B_{37}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (12g) | Cd V |
| $\mathbf{B_{38}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12g) | Cd V |
| $\mathbf{B_{39}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (12g) | Cd V |
| $\mathbf{B_{40}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (12g) | Cd V |
| $\mathbf{B_{41}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12g) | Cd V |
| $\mathbf{B_{42}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12g) | Cd V |
| $\mathbf{B_{43}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (12g) | Cd V |
| $\mathbf{B_{44}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12g) | Cd V |
| $\mathbf{B_{45}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{46}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{47}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{48}}$ | = | $x_{6} \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{49}}$ | = | $z_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{50}}$ | = | $z_{6} \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{51}}$ | = | $- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{52}}$ | = | $- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{53}}$ | = | $y_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{54}}$ | = | $- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{55}}$ | = | $y_{6} \, \mathbf{a}_{1}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{56}}$ | = | $- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{57}}$ | = | $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{58}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{59}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{60}}$ | = | $- x_{6} \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{61}}$ | = | $- z_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{62}}$ | = | $- z_{6} \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{63}}$ | = | $\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{64}}$ | = | $\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{65}}$ | = | $- y_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{66}}$ | = | $\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{67}}$ | = | $- y_{6} \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{68}}$ | = | $\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (24h) | Cd VI |
| $\mathbf{B_{69}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{70}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{71}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{72}}$ | = | $x_{7} \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{73}}$ | = | $z_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+a y_{7} \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{74}}$ | = | $z_{7} \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{75}}$ | = | $- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ | = | $- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{7} \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{76}}$ | = | $- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{77}}$ | = | $y_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{78}}$ | = | $- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{79}}$ | = | $y_{7} \, \mathbf{a}_{1}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{80}}$ | = | $- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{81}}$ | = | $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{82}}$ | = | $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{83}}$ | = | $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{84}}$ | = | $- x_{7} \, \mathbf{a}_{1}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{85}}$ | = | $- z_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- y_{7} \, \mathbf{a}_{3}$ | = | $- a z_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- a y_{7} \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{86}}$ | = | $- z_{7} \, \mathbf{a}_{1}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{7} \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{87}}$ | = | $\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{7} \, \mathbf{a}_{3}$ | = | $a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{7} \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{88}}$ | = | $\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{89}}$ | = | $- y_{7} \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{90}}$ | = | $\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{91}}$ | = | $- y_{7} \, \mathbf{a}_{1}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{92}}$ | = | $\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (24h) | Cd VII |
| $\mathbf{B_{93}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{94}}$ | = | $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{95}}$ | = | $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{96}}$ | = | $x_{8} \, \mathbf{a}_{1}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{97}}$ | = | $z_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+y_{8} \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a y_{8} \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{98}}$ | = | $z_{8} \, \mathbf{a}_{1}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{99}}$ | = | $- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{8} \, \mathbf{a}_{3}$ | = | $- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{8} \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{100}}$ | = | $- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{101}}$ | = | $y_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{102}}$ | = | $- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{103}}$ | = | $y_{8} \, \mathbf{a}_{1}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{104}}$ | = | $- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{105}}$ | = | $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{106}}$ | = | $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{107}}$ | = | $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{108}}$ | = | $- x_{8} \, \mathbf{a}_{1}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{109}}$ | = | $- z_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- y_{8} \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a y_{8} \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{110}}$ | = | $- z_{8} \, \mathbf{a}_{1}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{111}}$ | = | $\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{8} \, \mathbf{a}_{3}$ | = | $a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{8} \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{112}}$ | = | $\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{113}}$ | = | $- y_{8} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{114}}$ | = | $\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{115}}$ | = | $- y_{8} \, \mathbf{a}_{1}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}+a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{116}}$ | = | $\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ | = | $a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (24h) | Cd VIII |
| $\mathbf{B_{117}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+a z_{9} \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{118}}$ | = | $- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{9} \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{119}}$ | = | $- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{120}}$ | = | $x_{9} \, \mathbf{a}_{1}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{121}}$ | = | $z_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+y_{9} \, \mathbf{a}_{3}$ | = | $a z_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+a y_{9} \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{122}}$ | = | $z_{9} \, \mathbf{a}_{1}- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{9} \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{123}}$ | = | $- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{9} \, \mathbf{a}_{3}$ | = | $- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{9} \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{124}}$ | = | $- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{125}}$ | = | $y_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}+a z_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{126}}$ | = | $- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{9} \,\mathbf{\hat{y}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{127}}$ | = | $y_{9} \, \mathbf{a}_{1}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{128}}$ | = | $- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{129}}$ | = | $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}- a z_{9} \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{130}}$ | = | $\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{9} \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{131}}$ | = | $\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}+a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{132}}$ | = | $- x_{9} \, \mathbf{a}_{1}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{133}}$ | = | $- z_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- y_{9} \, \mathbf{a}_{3}$ | = | $- a z_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- a y_{9} \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{134}}$ | = | $- z_{9} \, \mathbf{a}_{1}+\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{9} \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{135}}$ | = | $\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{9} \, \mathbf{a}_{3}$ | = | $a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{9} \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{136}}$ | = | $\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{137}}$ | = | $- y_{9} \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}- x_{9} \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}- a z_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{138}}$ | = | $\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}+\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{9} \,\mathbf{\hat{y}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{139}}$ | = | $- y_{9} \, \mathbf{a}_{1}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}+a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{140}}$ | = | $\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{9} \, \mathbf{a}_{3}$ | = | $a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (24h) | Cd IX |
| $\mathbf{B_{141}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+a z_{10} \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{142}}$ | = | $- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{10} \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{143}}$ | = | $- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}- a \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{144}}$ | = | $x_{10} \, \mathbf{a}_{1}- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{145}}$ | = | $z_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+y_{10} \, \mathbf{a}_{3}$ | = | $a z_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+a y_{10} \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{146}}$ | = | $z_{10} \, \mathbf{a}_{1}- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{10} \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{147}}$ | = | $- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{10} \, \mathbf{a}_{3}$ | = | $- a \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{10} \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{148}}$ | = | $- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{149}}$ | = | $y_{10} \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ | = | $a y_{10} \,\mathbf{\hat{x}}+a z_{10} \,\mathbf{\hat{y}}+a x_{10} \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{150}}$ | = | $- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{10} \,\mathbf{\hat{y}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{151}}$ | = | $y_{10} \, \mathbf{a}_{1}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{10} \,\mathbf{\hat{x}}- a \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{152}}$ | = | $- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ | = | $- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{10} \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{153}}$ | = | $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}- a z_{10} \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{154}}$ | = | $\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{10} \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{155}}$ | = | $\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}+a \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{156}}$ | = | $- x_{10} \, \mathbf{a}_{1}+\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{157}}$ | = | $- z_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- y_{10} \, \mathbf{a}_{3}$ | = | $- a z_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}- a y_{10} \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{158}}$ | = | $- z_{10} \, \mathbf{a}_{1}+\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{10} \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{159}}$ | = | $\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{10} \, \mathbf{a}_{3}$ | = | $a \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{10} \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{160}}$ | = | $\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}+a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{161}}$ | = | $- y_{10} \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{2}- x_{10} \, \mathbf{a}_{3}$ | = | $- a y_{10} \,\mathbf{\hat{x}}- a z_{10} \,\mathbf{\hat{y}}- a x_{10} \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{162}}$ | = | $\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{2}+\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{10} \,\mathbf{\hat{y}}+a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{163}}$ | = | $- y_{10} \, \mathbf{a}_{1}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{10} \,\mathbf{\hat{x}}+a \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{164}}$ | = | $\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{10} \, \mathbf{a}_{3}$ | = | $a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{10} \,\mathbf{\hat{z}}$ | (24h) | Cd X |
| $\mathbf{B_{165}}$ | = | $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+a z_{11} \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{166}}$ | = | $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{11} \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{167}}$ | = | $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}- a \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{168}}$ | = | $x_{11} \, \mathbf{a}_{1}- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{169}}$ | = | $z_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+y_{11} \, \mathbf{a}_{3}$ | = | $a z_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+a y_{11} \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{170}}$ | = | $z_{11} \, \mathbf{a}_{1}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{11} \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{171}}$ | = | $- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{11} \, \mathbf{a}_{3}$ | = | $- a \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{11} \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{172}}$ | = | $- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{173}}$ | = | $y_{11} \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}+a z_{11} \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{174}}$ | = | $- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{11} \,\mathbf{\hat{y}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{175}}$ | = | $y_{11} \, \mathbf{a}_{1}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}- a \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{176}}$ | = | $- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ | = | $- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{177}}$ | = | $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}- a z_{11} \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{178}}$ | = | $\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{11} \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{179}}$ | = | $\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}+a \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{180}}$ | = | $- x_{11} \, \mathbf{a}_{1}+\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{181}}$ | = | $- z_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- y_{11} \, \mathbf{a}_{3}$ | = | $- a z_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- a y_{11} \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{182}}$ | = | $- z_{11} \, \mathbf{a}_{1}+\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{11} \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{183}}$ | = | $\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{11} \, \mathbf{a}_{3}$ | = | $a \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{11} \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{184}}$ | = | $\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}+a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{185}}$ | = | $- y_{11} \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{2}- x_{11} \, \mathbf{a}_{3}$ | = | $- a y_{11} \,\mathbf{\hat{x}}- a z_{11} \,\mathbf{\hat{y}}- a x_{11} \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{186}}$ | = | $\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{2}+\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{11} \,\mathbf{\hat{y}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{187}}$ | = | $- y_{11} \, \mathbf{a}_{1}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{11} \,\mathbf{\hat{x}}+a \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24h) | Ce I |
| $\mathbf{B_{188}}$ | = | $\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{11} \, \mathbf{a}_{3}$ | = | $a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{11} \,\mathbf{\hat{z}}$ | (24h) | Ce I |
References
- M. Armbrüster and S. Lidin, Reassessing the compound CeCd$_{6}$: the structure of Ce$_{6}$Cd$_{37}$, J. Alloys Compd. 307, 141–148 (2000), doi:10.1016/S0925-8388(00)00881-1.
- A. C. Larson and D. T. Cromer, The Crystal Structure of YCd$_{6}$, Acta Crystallogr. Sect. B 27, 1875–1879 (1971), doi:10.1107/S0567740871005028.
Found in
- B. Skoƚyszewska-Kühberger, T. L. Reichmann, M. C. J. Marker, H. S. Effenberger, and H. Ipser, Re-investigation of the Cd-Ce Phase Diagram and Structural Characterization of the High-Temperature Phase Cd$_{17+2x}$Ce$_{2-x}$ ($x \sim 0.02$), J. Phase Equil. Diff. 37, 186–199 (2016), doi:10.1007/s11669-015-0441-z.
Prototype Generator
aflow --proto=A41B6_cP188_201_b2efg5h_h --params=$a,x_{2},x_{3},x_{4},x_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11}$