AFLOW Prototype: A5B40CD12_cP116_224_cd_e3k_a_k
Prototype | : | (H2.6O)5O40PW12 |
AFLOW prototype label | : | A5B40CD12_cP116_224_cd_e3k_a_k |
Strukturbericht designation | : | $H4_{16}$ |
Pearson symbol | : | cP116 |
Space group number | : | 224 |
Space group symbol | : | $Pn\bar{3}m$ |
AFLOW prototype command | : | aflow --proto=A5B40CD12_cP116_224_cd_e3k_a_k --params=$a$,$x_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$,$x_{7}$,$z_{7}$,$x_{8}$,$z_{8}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{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}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(2a\right) & \text{P} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(2a\right) & \text{P} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(4c\right) & \text{H$_{2}$O I} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{z}} & \left(4c\right) & \text{H$_{2}$O I} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{y}} & \left(4c\right) & \text{H$_{2}$O I} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{2}a \, \mathbf{\hat{x}} & \left(4c\right) & \text{H$_{2}$O I} \\ \mathbf{B}_{7} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(6d\right) & \text{H$_{2}$O II} \\ \mathbf{B}_{8} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(6d\right) & \text{H$_{2}$O II} \\ \mathbf{B}_{9} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(6d\right) & \text{H$_{2}$O II} \\ \mathbf{B}_{10} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(6d\right) & \text{H$_{2}$O II} \\ \mathbf{B}_{11} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(6d\right) & \text{H$_{2}$O II} \\ \mathbf{B}_{12} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(6d\right) & \text{H$_{2}$O II} \\ \mathbf{B}_{13} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(8e\right) & \text{O I} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(8e\right) & \text{O I} \\ \mathbf{B}_{15} & = & \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(8e\right) & \text{O I} \\ \mathbf{B}_{16} & = & x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(8e\right) & \text{O I} \\ \mathbf{B}_{17} & = & \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(8e\right) & \text{O I} \\ \mathbf{B}_{18} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(8e\right) & \text{O I} \\ \mathbf{B}_{19} & = & \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(8e\right) & \text{O I} \\ \mathbf{B}_{20} & = & -x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(8e\right) & \text{O I} \\ \mathbf{B}_{21} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + z_{5}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{y}} + z_{5}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{23} & = & \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{5}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{24} & = & x_{5} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{5}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{25} & = & z_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & z_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{26} & = & z_{5} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{3} & = & z_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{27} & = & \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{28} & = & \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{5}\right)a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{29} & = & x_{5} \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + z_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{30} & = & \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{x}} + z_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{31} & = & x_{5} \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{32} & = & \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{5}\right)a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{33} & = & \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{y}}-z_{5}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{34} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-z_{5}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{35} & = & \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{36} & = & -x_{5} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{37} & = & \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{5}\right)a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{38} & = & -x_{5} \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{39} & = & -x_{5} \, \mathbf{a}_{1}-z_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-z_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{40} & = & \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{1}-z_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}}-z_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{41} & = & \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{42} & = & \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{5}\right)a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{43} & = & -z_{5} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{3} & = & -z_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{44} & = & -z_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -z_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O II} \\ \mathbf{B}_{45} & = & x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{46} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{47} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{48} & = & x_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{49} & = & z_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{50} & = & z_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{51} & = & \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{52} & = & \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{53} & = & x_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{54} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{55} & = & x_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{56} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{57} & = & \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{58} & = & -x_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{59} & = & \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{60} & = & -x_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{61} & = & \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{62} & = & -x_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{63} & = & -x_{6} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{64} & = & \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{65} & = & \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{66} & = & \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{67} & = & -z_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{68} & = & -z_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O III} \\ \mathbf{B}_{69} & = & x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}} + z_{7}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{70} & = & \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{y}} + z_{7}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{71} & = & \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{7}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{72} & = & x_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{7}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{73} & = & z_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & z_{7}a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{74} & = & z_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{3} & = & z_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{75} & = & \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{76} & = & \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{7}\right)a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{77} & = & x_{7} \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + z_{7}a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{78} & = & \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{x}} + z_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{79} & = & x_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{80} & = & \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{7}\right)a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{81} & = & \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{y}}-z_{7}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{82} & = & -x_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}}-z_{7}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{83} & = & \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{7}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{84} & = & -x_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{7}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{85} & = & \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{7}\right)a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{86} & = & -x_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{87} & = & -x_{7} \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-z_{7}a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{88} & = & \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{x}}-z_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{89} & = & \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{90} & = & \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{7}\right)a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{91} & = & -z_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{3} & = & -z_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{92} & = & -z_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & -z_{7}a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{O IV} \\ \mathbf{B}_{93} & = & x_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + z_{8}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{94} & = & \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{y}} + z_{8}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{95} & = & \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{8}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{96} & = & x_{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{8}\right) \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{8}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{97} & = & z_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & z_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{98} & = & z_{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{3} & = & z_{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{99} & = & \left(\frac{1}{2} - z_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{100} & = & \left(\frac{1}{2} - z_{8}\right) \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{8}\right)a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{101} & = & x_{8} \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + z_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{102} & = & \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{x}} + z_{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{103} & = & x_{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{104} & = & \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{8}\right) \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{8}\right)a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{105} & = & \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{y}}-z_{8}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{106} & = & -x_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}}-z_{8}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{107} & = & \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{8}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{108} & = & -x_{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{8}\right) \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{8}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{109} & = & \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{8}\right) \, \mathbf{a}_{2}-x_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{8}\right)a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{110} & = & -x_{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{111} & = & -x_{8} \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{2}-x_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-z_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{112} & = & \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{x}}-z_{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{113} & = & \left(\frac{1}{2} +z_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{2}-x_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{114} & = & \left(\frac{1}{2} +z_{8}\right) \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{8}\right)a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{115} & = & -z_{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{3} & = & -z_{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \mathbf{B}_{116} & = & -z_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2}-x_{8} \, \mathbf{a}_{3} & = & -z_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(24k\right) & \text{W} \\ \end{array} \]