Be[BH4]2 Structure: A2BC8_tI176_110_2b_b_8b

Picture of Structure; Click for Big Picture
Prototype : Be[BH4]2
AFLOW prototype label : A2BC8_tI176_110_2b_b_8b
Strukturbericht designation : None
Pearson symbol : tI176
Space group number : 110
Space group symbol : $I4_{1}cd$
AFLOW prototype command : aflow --proto=A2BC8_tI176_110_2b_b_8b
--params=
$a$,$c/a$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$ 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}$


Body-centered Tetragonal primitive vectors:

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

Basis vectors:

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

References

  • D. S. Marynick and W. N. Lipscomb, Crystal structure of beryllium borohydride, Inorg. Chem. 11, 820–823 (1972), doi:10.1021/ic50110a033.

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=A2BC8_tI176_110_2b_b_8b --params=

Species:

Running:

Output: