Pu31Rh20 Structure : A31B20_tI204_140_b2gh3m_ac2fh3l

Picture of Structure; Click for Big Picture
Prototype : Pu31Rh20
AFLOW prototype label : A31B20_tI204_140_b2gh3m_ac2fh3l
Strukturbericht designation : None
Pearson symbol : tI204
Space group number : 140
Space group symbol : $I4/mcm$
AFLOW prototype command : aflow --proto=A31B20_tI204_140_b2gh3m_ac2fh3l
--params=
$a$,$c/a$,$z_{4}$,$z_{5}$,$z_{6}$,$z_{7}$,$x_{8}$,$x_{9}$,$x_{10}$,$z_{10}$,$x_{11}$,$z_{11}$,$x_{12}$,$z_{12}$,$x_{13}$,$y_{13}$,$z_{13}$,$x_{14}$,$y_{14}$,$z_{14}$,$x_{15}$,$y_{15}$,$z_{15}$


Other compounds with this structure

  • Pu31Pt20 and Ca31Sn20

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

References

  • D. T. Cromer and A. C. Larson, The Crystal Structure of Pu31Pt20 and Pu31Rh20, Acta Crystallogr. Sect. B Struct. Sci. 33, 2620–2627 (1977), doi:10.1107/S0567740877009030.

Geometry files


Prototype Generator

aflow --proto=A31B20_tI204_140_b2gh3m_ac2fh3l --params=

Species:

Running:

Output: