CuCrCl5[NH3]6 Structure: A5BCD6_cF416_228_eg_c_b_h

Picture of Structure; Click for Big Picture
Prototype : CuCrCl5[NH3]6
AFLOW prototype label : A5BCD6_cF416_228_eg_c_b_h
Strukturbericht designation : None
Pearson symbol : cF416
Space group number : 228
Space group symbol : $Fd\bar{3}c$
AFLOW prototype command : aflow --proto=A5BCD6_cF416_228_eg_c_b_h
--params=
$a$,$x_{3}$,$y_{4}$,$x_{5}$,$y_{5}$,$z_{5}$


  • The N atoms correspond to NH3 units centered on the ($192h$) Wyckoff positions.

Face-centered Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{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(32b\right) & \mbox{Cu} \\ \mathbf{B}_{2} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(32b\right) & \mbox{Cu} \\ \mathbf{B}_{3} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(32b\right) & \mbox{Cu} \\ \mathbf{B}_{4} & = & \frac{3}{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}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(32b\right) & \mbox{Cu} \\ \mathbf{B}_{5} & = & \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(32b\right) & \mbox{Cu} \\ \mathbf{B}_{6} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(32b\right) & \mbox{Cu} \\ \mathbf{B}_{7} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(32b\right) & \mbox{Cu} \\ \mathbf{B}_{8} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(32b\right) & \mbox{Cu} \\ \mathbf{B}_{9} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(32c\right) & \mbox{Cr} \\ \mathbf{B}_{10} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} & \left(32c\right) & \mbox{Cr} \\ \mathbf{B}_{11} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(32c\right) & \mbox{Cr} \\ \mathbf{B}_{12} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(32c\right) & \mbox{Cr} \\ \mathbf{B}_{13} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(32c\right) & \mbox{Cr} \\ \mathbf{B}_{14} & = & \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(32c\right) & \mbox{Cr} \\ \mathbf{B}_{15} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(32c\right) & \mbox{Cr} \\ \mathbf{B}_{16} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(32c\right) & \mbox{Cr} \\ \mathbf{B}_{17} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(64e\right) & \mbox{Cl I} \\ \mathbf{B}_{18} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 3x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{3}\right)a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(64e\right) & \mbox{Cl I} \\ \mathbf{B}_{19} & = & x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 3x_{3}\right) \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{3}\right)a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{3}\right)a \, \mathbf{\hat{z}} & \left(64e\right) & \mbox{Cl I} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} - 3x_{3}\right) \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{3}\right)a \, \mathbf{\hat{z}} & \left(64e\right) & \mbox{Cl I} \\ \mathbf{B}_{21} & = & \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{2} + 3x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - x_{3}\right)a \, \mathbf{\hat{z}} & \left(64e\right) & \mbox{Cl I} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - x_{3}\right)a \, \mathbf{\hat{z}} & \left(64e\right) & \mbox{Cl I} \\ \mathbf{B}_{23} & = & \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{1} + 3x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(64e\right) & \mbox{Cl I} \\ \mathbf{B}_{24} & = & 3x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(64e\right) & \mbox{Cl I} \\ \mathbf{B}_{25} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(64e\right) & \mbox{Cl I} \\ \mathbf{B}_{26} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +3x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(64e\right) & \mbox{Cl I} \\ \mathbf{B}_{27} & = & -x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} +3x_{3}\right) \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(64e\right) & \mbox{Cl I} \\ \mathbf{B}_{28} & = & \left(\frac{1}{2} +3x_{3}\right) \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(64e\right) & \mbox{Cl I} \\ \mathbf{B}_{29} & = & \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{2}-3x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(64e\right) & \mbox{Cl I} \\ \mathbf{B}_{30} & = & \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(64e\right) & \mbox{Cl I} \\ \mathbf{B}_{31} & = & \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{1}-3x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{3}\right)a \, \mathbf{\hat{z}} & \left(64e\right) & \mbox{Cl I} \\ \mathbf{B}_{32} & = & -3x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{3}\right)a \, \mathbf{\hat{z}} & \left(64e\right) & \mbox{Cl I} \\ \mathbf{B}_{33} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{1}{4} - 2y_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +2y_{4}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{34} & = & \left(\frac{1}{4} - 2y_{4}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - y_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{35} & = & \left(\frac{1}{4} +2y_{4}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{36} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{1}{4} +2y_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - 2y_{4}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - y_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{37} & = & \left(\frac{1}{4} +2y_{4}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{4} - 2y_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{4}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{38} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{1}{4} - 2y_{4}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{4}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - y_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{39} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{1}{4} +2y_{4}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{4}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{40} & = & \left(\frac{1}{4} - 2y_{4}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{4} +2y_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{4}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - y_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{41} & = & \left(\frac{1}{4} - 2y_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +2y_{4}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{42} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{4} - 2y_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{43} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{4} +2y_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{44} & = & \left(\frac{1}{4} +2y_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - 2y_{4}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{45} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{3}{4} +2y_{4}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - 2y_{4}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{46} & = & \left(\frac{3}{4} +2y_{4}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \left(\frac{3}{4} +y_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{47} & = & \left(\frac{3}{4} - 2y_{4}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{3}{4} - y_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{48} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{3}{4} - 2y_{4}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} +2y_{4}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \left(\frac{3}{4} +y_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{3}{4} - y_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{49} & = & \left(\frac{3}{4} - 2y_{4}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{3}{4} +2y_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{50} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{3}{4} +2y_{4}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +y_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{51} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{3}{4} - 2y_{4}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \left(\frac{3}{4} - y_{4}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{52} & = & \left(\frac{3}{4} +2y_{4}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{3}{4} - 2y_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{3}{4} - y_{4}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +y_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{53} & = & \left(\frac{3}{4} +2y_{4}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} - 2y_{4}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{54} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{3}{4} +2y_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{3}{4} +y_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{55} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{3}{4} - 2y_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{3}{4} - y_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{56} & = & \left(\frac{3}{4} - 2y_{4}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +2y_{4}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \left(\frac{3}{4} +y_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{3}{4} - y_{4}\right)a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Cl II} \\ \mathbf{B}_{57} & = & \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + y_{5}a \, \mathbf{\hat{y}} + z_{5}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{58} & = & \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{y}} + z_{5}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{59} & = & \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{x}} + y_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{60} & = & \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{61} & = & \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & z_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + y_{5}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{62} & = & \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & z_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{63} & = & \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{y}} + y_{5}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{64} & = & \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{65} & = & \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{x}} + z_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{66} & = & \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{x}} + z_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{67} & = & \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{68} & = & \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{69} & = & \left(\frac{1}{2} +x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{70} & = & \left(\frac{1}{2} - x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{5}\right)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(192h\right) & \mbox{N} \\ \mathbf{B}_{71} & = & \left(\frac{1}{2} - x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{72} & = & \left(x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{73} & = & \left(\frac{1}{2} - x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{74} & = & \left(x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{75} & = & \left(\frac{1}{2} +x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} + y_{5} - z_{5}\right) \, \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}} + \left(\frac{1}{2} - y_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{76} & = & \left(\frac{1}{2} - x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{77} & = & \left(\frac{1}{2} - x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - x_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{78} & = & \left(\frac{1}{2} +x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{79} & = & \left(x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - z_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{80} & = & \left(\frac{1}{2} - x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - z_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - x_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{81} & = & \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-y_{5}a \, \mathbf{\hat{y}}-z_{5}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{82} & = & \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{y}}-z_{5}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{83} & = & \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{x}}-y_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{84} & = & \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{85} & = & \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & -z_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-y_{5}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{86} & = & \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & -z_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{87} & = & \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{y}}-y_{5}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{88} & = & \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{89} & = & \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{x}}-z_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{90} & = & \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{x}}-z_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{91} & = & \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{92} & = & \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{93} & = & \left(\frac{1}{2} - x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{94} & = & \left(\frac{1}{2} +x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{5}\right)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(192h\right) & \mbox{N} \\ \mathbf{B}_{95} & = & \left(\frac{1}{2} +x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{96} & = & \left(-x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{97} & = & \left(\frac{1}{2} +x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{98} & = & \left(-x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{99} & = & \left(\frac{1}{2} - x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} - y_{5} + z_{5}\right) \, \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}} + \left(\frac{1}{2} +y_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{100} & = & \left(\frac{1}{2} +x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{101} & = & \left(\frac{1}{2} +x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{102} & = & \left(\frac{1}{2} - x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{103} & = & \left(-x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \mathbf{B}_{104} & = & \left(\frac{1}{2} +x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{N} \\ \end{array} \]

References

  • M. Mori, Y. Saito, and T. Watanabe, The Crystal Structure of [Cr(NH3)6] [CuCl5], Bull. Chem. Soc. Jpn. 34, 295–296 (1961), doi:10.1246/bcsj.34.295.

Found in

  • P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds, ASM International (2013).

Geometry files


Prototype Generator

aflow --proto=A5BCD6_cF416_228_eg_c_b_h --params=

Species:

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