Retgersite ($\alpha$–NiSO4·6H2O, $H4_{5}$) Structure : A12BC10D_tP96_92_6b_a_5b_a

Picture of Structure; Click for Big Picture
Prototype : H12NiO10S
AFLOW prototype label : A12BC10D_tP96_92_6b_a_5b_a
Strukturbericht designation : $H4_{5}$
Pearson symbol : tP96
Space group number : 92
Space group symbol : $P4_{1}2_{1}2$
AFLOW prototype command : aflow --proto=A12BC10D_tP96_92_6b_a_5b_a
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$,$x_{9}$,$y_{9}$,$z_{9}$,$x_{10}$,$y_{10}$,$z_{10}$,$x_{11}$,$y_{11}$,$z_{11}$,$x_{12}$,$y_{12}$,$z_{12}$,$x_{13}$,$y_{13}$,$z_{13}$


  • This structure is nearly identical to the one presented in (Hermann, 1937) as $H4_{5}$, but now includes the positions of the hydrogen atoms.
  • This compound can also be found in the enantiomorphic space group $P4_32_12$ #98.

Simple Tetragonal primitive vectors:

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

Basis vectors:

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

References

  • K. Stadnicka, A. M. Glazer, and M. Koralewski, Structure, absolute configuration and optical activity of $\alpha$–nickel sulfate hexahydrate, Acta Crystallogr. Sect. B Struct. Sci. 43, 319–325 (1987), doi:10.1107/S0108768187097787.
  • C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928–1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).

Found in

  • J. W. Anthony, R. A. Bideaux, K. W. Bladh, and M. C. Nichols, eds., Handbook of Mineralogy (Mineralogical Society of America, 2004), chap. Retgersite, NiSO4·6H2O.

Geometry files


Prototype Generator

aflow --proto=A12BC10D_tP96_92_6b_a_5b_a --params=

Species:

Running:

Output: