La43Ni17Mg5 Structure: A43B5C17_oC260_63_c8fg6h_cfg_ce3f2h

Picture of Structure; Click for Big Picture
Prototype : La43Ni17Mg5
AFLOW prototype label : A43B5C17_oC260_63_c8fg6h_cfg_ce3f2h
Strukturbericht designation : None
Pearson symbol : oC260
Space group number : 63
Space group symbol : $Cmcm$
AFLOW prototype command : aflow --proto=A43B5C17_oC260_63_c8fg6h_cfg_ce3f2h
--params=
$a$,$b/a$,$c/a$,$y_{1}$,$y_{2}$,$y_{3}$,$x_{4}$,$y_{5}$,$z_{5}$,$y_{6}$,$z_{6}$,$y_{7}$,$z_{7}$,$y_{8}$,$z_{8}$,$y_{9}$,$z_{9}$,$y_{10}$,$z_{10}$,$y_{11}$,$ z_{11}$,$y_{12}$,$z_{12}$,$y_{13}$,$z_{13}$,$y_{14}$,$z_{14}$,$y_{15}$,$z_{15}$,$y_{16}$,$z_{16}$,$x_{17}$,$y_{17}$,$x_{18}$,$y_{18}$,$x_{19}$,$y_{19}$,$z_{19}$,$x_{20}$,$y_{20}$,$ z_{20}$,$x_{21}$,$y_{21}$,$z_{21}$,$x_{22}$,$y_{22}$,$z_{22}$,$x_{23}$,$y_{23}$,$z_{23}$,$x_{24}$,$y_{24}$,$z_{24}$,$x_{25}$,$y_{25}$,$z_{25}$,$x_{26}$,$y_{26}$,$z_{26}$


Base-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & -y_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & y_{1}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{La I} \\ \mathbf{B}_{2} & = & y_{1} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -y_{1}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{La I} \\ \mathbf{B}_{3} & = & -y_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & y_{2}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mg I} \\ \mathbf{B}_{4} & = & y_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -y_{2}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mg I} \\ \mathbf{B}_{5} & = & -y_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & y_{3}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Ni I} \\ \mathbf{B}_{6} & = & y_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -y_{3}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Ni I} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} & = & x_{4}a \, \mathbf{\hat{x}} & \left(8e\right) & \mbox{Ni II} \\ \mathbf{B}_{8} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Ni II} \\ \mathbf{B}_{9} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} & = & -x_{4}a \, \mathbf{\hat{x}} & \left(8e\right) & \mbox{Ni II} \\ \mathbf{B}_{10} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Ni II} \\ \mathbf{B}_{11} & = & -y_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & y_{5}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La II} \\ \mathbf{B}_{12} & = & y_{5} \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{3} & = & -y_{5}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La II} \\ \mathbf{B}_{13} & = & -y_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{3} & = & y_{5}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{5}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La II} \\ \mathbf{B}_{14} & = & y_{5} \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & -y_{5}b \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La II} \\ \mathbf{B}_{15} & = & -y_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La III} \\ \mathbf{B}_{16} & = & y_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & -y_{6}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La III} \\ \mathbf{B}_{17} & = & -y_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{3} & = & y_{6}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{6}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La III} \\ \mathbf{B}_{18} & = & y_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -y_{6}b \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La III} \\ \mathbf{B}_{19} & = & -y_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La IV} \\ \mathbf{B}_{20} & = & y_{7} \, \mathbf{a}_{1}-y_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{3} & = & -y_{7}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{7}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La IV} \\ \mathbf{B}_{21} & = & -y_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{3} & = & y_{7}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{7}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La IV} \\ \mathbf{B}_{22} & = & y_{7} \, \mathbf{a}_{1}-y_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -y_{7}b \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La IV} \\ \mathbf{B}_{23} & = & -y_{8} \, \mathbf{a}_{1} + y_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La V} \\ \mathbf{B}_{24} & = & y_{8} \, \mathbf{a}_{1}-y_{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{8}\right) \, \mathbf{a}_{3} & = & -y_{8}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{8}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La V} \\ \mathbf{B}_{25} & = & -y_{8} \, \mathbf{a}_{1} + y_{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{8}\right) \, \mathbf{a}_{3} & = & y_{8}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{8}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La V} \\ \mathbf{B}_{26} & = & y_{8} \, \mathbf{a}_{1}-y_{8} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & -y_{8}b \, \mathbf{\hat{y}}-z_{8}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La V} \\ \mathbf{B}_{27} & = & -y_{9} \, \mathbf{a}_{1} + y_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La VI} \\ \mathbf{B}_{28} & = & y_{9} \, \mathbf{a}_{1}-y_{9} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{9}\right) \, \mathbf{a}_{3} & = & -y_{9}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{9}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La VI} \\ \mathbf{B}_{29} & = & -y_{9} \, \mathbf{a}_{1} + y_{9} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{9}\right) \, \mathbf{a}_{3} & = & y_{9}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{9}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La VI} \\ \mathbf{B}_{30} & = & y_{9} \, \mathbf{a}_{1}-y_{9} \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & -y_{9}b \, \mathbf{\hat{y}}-z_{9}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La VI} \\ \mathbf{B}_{31} & = & -y_{10} \, \mathbf{a}_{1} + y_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La VII} \\ \mathbf{B}_{32} & = & y_{10} \, \mathbf{a}_{1}-y_{10} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{10}\right) \, \mathbf{a}_{3} & = & -y_{10}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{10}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La VII} \\ \mathbf{B}_{33} & = & -y_{10} \, \mathbf{a}_{1} + y_{10} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{10}\right) \, \mathbf{a}_{3} & = & y_{10}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{10}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La VII} \\ \mathbf{B}_{34} & = & y_{10} \, \mathbf{a}_{1}-y_{10} \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & -y_{10}b \, \mathbf{\hat{y}}-z_{10}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La VII} \\ \mathbf{B}_{35} & = & -y_{11} \, \mathbf{a}_{1} + y_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & y_{11}b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La VIII} \\ \mathbf{B}_{36} & = & y_{11} \, \mathbf{a}_{1}-y_{11} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{11}\right) \, \mathbf{a}_{3} & = & -y_{11}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{11}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La VIII} \\ \mathbf{B}_{37} & = & -y_{11} \, \mathbf{a}_{1} + y_{11} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{11}\right) \, \mathbf{a}_{3} & = & y_{11}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{11}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La VIII} \\ \mathbf{B}_{38} & = & y_{11} \, \mathbf{a}_{1}-y_{11} \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & -y_{11}b \, \mathbf{\hat{y}}-z_{11}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La VIII} \\ \mathbf{B}_{39} & = & -y_{12} \, \mathbf{a}_{1} + y_{12} \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & y_{12}b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La IX} \\ \mathbf{B}_{40} & = & y_{12} \, \mathbf{a}_{1}-y_{12} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{12}\right) \, \mathbf{a}_{3} & = & -y_{12}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{12}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La IX} \\ \mathbf{B}_{41} & = & -y_{12} \, \mathbf{a}_{1} + y_{12} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{12}\right) \, \mathbf{a}_{3} & = & y_{12}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{12}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La IX} \\ \mathbf{B}_{42} & = & y_{12} \, \mathbf{a}_{1}-y_{12} \, \mathbf{a}_{2}-z_{12} \, \mathbf{a}_{3} & = & -y_{12}b \, \mathbf{\hat{y}}-z_{12}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{La IX} \\ \mathbf{B}_{43} & = & -y_{13} \, \mathbf{a}_{1} + y_{13} \, \mathbf{a}_{2} + z_{13} \, \mathbf{a}_{3} & = & y_{13}b \, \mathbf{\hat{y}} + z_{13}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Mg II} \\ \mathbf{B}_{44} & = & y_{13} \, \mathbf{a}_{1}-y_{13} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{13}\right) \, \mathbf{a}_{3} & = & -y_{13}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{13}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Mg II} \\ \mathbf{B}_{45} & = & -y_{13} \, \mathbf{a}_{1} + y_{13} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{13}\right) \, \mathbf{a}_{3} & = & y_{13}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{13}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Mg II} \\ \mathbf{B}_{46} & = & y_{13} \, \mathbf{a}_{1}-y_{13} \, \mathbf{a}_{2}-z_{13} \, \mathbf{a}_{3} & = & -y_{13}b \, \mathbf{\hat{y}}-z_{13}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Mg II} \\ \mathbf{B}_{47} & = & -y_{14} \, \mathbf{a}_{1} + y_{14} \, \mathbf{a}_{2} + z_{14} \, \mathbf{a}_{3} & = & y_{14}b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Ni III} \\ \mathbf{B}_{48} & = & y_{14} \, \mathbf{a}_{1}-y_{14} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{14}\right) \, \mathbf{a}_{3} & = & -y_{14}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{14}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Ni III} \\ \mathbf{B}_{49} & = & -y_{14} \, \mathbf{a}_{1} + y_{14} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{14}\right) \, \mathbf{a}_{3} & = & y_{14}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{14}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Ni III} \\ \mathbf{B}_{50} & = & y_{14} \, \mathbf{a}_{1}-y_{14} \, \mathbf{a}_{2}-z_{14} \, \mathbf{a}_{3} & = & -y_{14}b \, \mathbf{\hat{y}}-z_{14}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Ni III} \\ \mathbf{B}_{51} & = & -y_{15} \, \mathbf{a}_{1} + y_{15} \, \mathbf{a}_{2} + z_{15} \, \mathbf{a}_{3} & = & y_{15}b \, \mathbf{\hat{y}} + z_{15}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Ni IV} \\ \mathbf{B}_{52} & = & y_{15} \, \mathbf{a}_{1}-y_{15} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{15}\right) \, \mathbf{a}_{3} & = & -y_{15}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{15}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Ni IV} \\ \mathbf{B}_{53} & = & -y_{15} \, \mathbf{a}_{1} + y_{15} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{15}\right) \, \mathbf{a}_{3} & = & y_{15}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{15}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Ni IV} \\ \mathbf{B}_{54} & = & y_{15} \, \mathbf{a}_{1}-y_{15} \, \mathbf{a}_{2}-z_{15} \, \mathbf{a}_{3} & = & -y_{15}b \, \mathbf{\hat{y}}-z_{15}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Ni IV} \\ \mathbf{B}_{55} & = & -y_{16} \, \mathbf{a}_{1} + y_{16} \, \mathbf{a}_{2} + z_{16} \, \mathbf{a}_{3} & = & y_{16}b \, \mathbf{\hat{y}} + z_{16}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Ni V} \\ \mathbf{B}_{56} & = & y_{16} \, \mathbf{a}_{1}-y_{16} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{16}\right) \, \mathbf{a}_{3} & = & -y_{16}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{16}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Ni V} \\ \mathbf{B}_{57} & = & -y_{16} \, \mathbf{a}_{1} + y_{16} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{16}\right) \, \mathbf{a}_{3} & = & y_{16}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{16}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Ni V} \\ \mathbf{B}_{58} & = & y_{16} \, \mathbf{a}_{1}-y_{16} \, \mathbf{a}_{2}-z_{16} \, \mathbf{a}_{3} & = & -y_{16}b \, \mathbf{\hat{y}}-z_{16}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Ni V} \\ \mathbf{B}_{59} & = & \left(x_{17}-y_{17}\right) \, \mathbf{a}_{1} + \left(x_{17}+y_{17}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & x_{17}a \, \mathbf{\hat{x}} + y_{17}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{La X} \\ \mathbf{B}_{60} & = & \left(-x_{17}+y_{17}\right) \, \mathbf{a}_{1} + \left(-x_{17}-y_{17}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -x_{17}a \, \mathbf{\hat{x}}-y_{17}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{La X} \\ \mathbf{B}_{61} & = & \left(-x_{17}-y_{17}\right) \, \mathbf{a}_{1} + \left(-x_{17}+y_{17}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -x_{17}a \, \mathbf{\hat{x}} + y_{17}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{La X} \\ \mathbf{B}_{62} & = & \left(x_{17}+y_{17}\right) \, \mathbf{a}_{1} + \left(x_{17}-y_{17}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & x_{17}a \, \mathbf{\hat{x}}-y_{17}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{La X} \\ \mathbf{B}_{63} & = & \left(x_{18}-y_{18}\right) \, \mathbf{a}_{1} + \left(x_{18}+y_{18}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & x_{18}a \, \mathbf{\hat{x}} + y_{18}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Mg III} \\ \mathbf{B}_{64} & = & \left(-x_{18}+y_{18}\right) \, \mathbf{a}_{1} + \left(-x_{18}-y_{18}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -x_{18}a \, \mathbf{\hat{x}}-y_{18}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Mg III} \\ \mathbf{B}_{65} & = & \left(-x_{18}-y_{18}\right) \, \mathbf{a}_{1} + \left(-x_{18}+y_{18}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -x_{18}a \, \mathbf{\hat{x}} + y_{18}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Mg III} \\ \mathbf{B}_{66} & = & \left(x_{18}+y_{18}\right) \, \mathbf{a}_{1} + \left(x_{18}-y_{18}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & x_{18}a \, \mathbf{\hat{x}}-y_{18}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Mg III} \\ \mathbf{B}_{67} & = & \left(x_{19}-y_{19}\right) \, \mathbf{a}_{1} + \left(x_{19}+y_{19}\right) \, \mathbf{a}_{2} + z_{19} \, \mathbf{a}_{3} & = & x_{19}a \, \mathbf{\hat{x}} + y_{19}b \, \mathbf{\hat{y}} + z_{19}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XI} \\ \mathbf{B}_{68} & = & \left(-x_{19}+y_{19}\right) \, \mathbf{a}_{1} + \left(-x_{19}-y_{19}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{19}\right) \, \mathbf{a}_{3} & = & -x_{19}a \, \mathbf{\hat{x}}-y_{19}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{19}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XI} \\ \mathbf{B}_{69} & = & \left(-x_{19}-y_{19}\right) \, \mathbf{a}_{1} + \left(-x_{19}+y_{19}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{19}\right) \, \mathbf{a}_{3} & = & -x_{19}a \, \mathbf{\hat{x}} + y_{19}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{19}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XI} \\ \mathbf{B}_{70} & = & \left(x_{19}+y_{19}\right) \, \mathbf{a}_{1} + \left(x_{19}-y_{19}\right) \, \mathbf{a}_{2}-z_{19} \, \mathbf{a}_{3} & = & x_{19}a \, \mathbf{\hat{x}}-y_{19}b \, \mathbf{\hat{y}}-z_{19}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XI} \\ \mathbf{B}_{71} & = & \left(-x_{19}+y_{19}\right) \, \mathbf{a}_{1} + \left(-x_{19}-y_{19}\right) \, \mathbf{a}_{2}-z_{19} \, \mathbf{a}_{3} & = & -x_{19}a \, \mathbf{\hat{x}}-y_{19}b \, \mathbf{\hat{y}}-z_{19}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XI} \\ \mathbf{B}_{72} & = & \left(x_{19}-y_{19}\right) \, \mathbf{a}_{1} + \left(x_{19}+y_{19}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{19}\right) \, \mathbf{a}_{3} & = & x_{19}a \, \mathbf{\hat{x}} + y_{19}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{19}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XI} \\ \mathbf{B}_{73} & = & \left(x_{19}+y_{19}\right) \, \mathbf{a}_{1} + \left(x_{19}-y_{19}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{19}\right) \, \mathbf{a}_{3} & = & x_{19}a \, \mathbf{\hat{x}}-y_{19}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{19}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XI} \\ \mathbf{B}_{74} & = & \left(-x_{19}-y_{19}\right) \, \mathbf{a}_{1} + \left(-x_{19}+y_{19}\right) \, \mathbf{a}_{2} + z_{19} \, \mathbf{a}_{3} & = & -x_{19}a \, \mathbf{\hat{x}} + y_{19}b \, \mathbf{\hat{y}} + z_{19}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XI} \\ \mathbf{B}_{75} & = & \left(x_{20}-y_{20}\right) \, \mathbf{a}_{1} + \left(x_{20}+y_{20}\right) \, \mathbf{a}_{2} + z_{20} \, \mathbf{a}_{3} & = & x_{20}a \, \mathbf{\hat{x}} + y_{20}b \, \mathbf{\hat{y}} + z_{20}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XII} \\ \mathbf{B}_{76} & = & \left(-x_{20}+y_{20}\right) \, \mathbf{a}_{1} + \left(-x_{20}-y_{20}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{20}\right) \, \mathbf{a}_{3} & = & -x_{20}a \, \mathbf{\hat{x}}-y_{20}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{20}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XII} \\ \mathbf{B}_{77} & = & \left(-x_{20}-y_{20}\right) \, \mathbf{a}_{1} + \left(-x_{20}+y_{20}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{20}\right) \, \mathbf{a}_{3} & = & -x_{20}a \, \mathbf{\hat{x}} + y_{20}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{20}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XII} \\ \mathbf{B}_{78} & = & \left(x_{20}+y_{20}\right) \, \mathbf{a}_{1} + \left(x_{20}-y_{20}\right) \, \mathbf{a}_{2}-z_{20} \, \mathbf{a}_{3} & = & x_{20}a \, \mathbf{\hat{x}}-y_{20}b \, \mathbf{\hat{y}}-z_{20}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XII} \\ \mathbf{B}_{79} & = & \left(-x_{20}+y_{20}\right) \, \mathbf{a}_{1} + \left(-x_{20}-y_{20}\right) \, \mathbf{a}_{2}-z_{20} \, \mathbf{a}_{3} & = & -x_{20}a \, \mathbf{\hat{x}}-y_{20}b \, \mathbf{\hat{y}}-z_{20}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XII} \\ \mathbf{B}_{80} & = & \left(x_{20}-y_{20}\right) \, \mathbf{a}_{1} + \left(x_{20}+y_{20}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{20}\right) \, \mathbf{a}_{3} & = & x_{20}a \, \mathbf{\hat{x}} + y_{20}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{20}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XII} \\ \mathbf{B}_{81} & = & \left(x_{20}+y_{20}\right) \, \mathbf{a}_{1} + \left(x_{20}-y_{20}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{20}\right) \, \mathbf{a}_{3} & = & x_{20}a \, \mathbf{\hat{x}}-y_{20}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{20}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XII} \\ \mathbf{B}_{82} & = & \left(-x_{20}-y_{20}\right) \, \mathbf{a}_{1} + \left(-x_{20}+y_{20}\right) \, \mathbf{a}_{2} + z_{20} \, \mathbf{a}_{3} & = & -x_{20}a \, \mathbf{\hat{x}} + y_{20}b \, \mathbf{\hat{y}} + z_{20}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XII} \\ \mathbf{B}_{83} & = & \left(x_{21}-y_{21}\right) \, \mathbf{a}_{1} + \left(x_{21}+y_{21}\right) \, \mathbf{a}_{2} + z_{21} \, \mathbf{a}_{3} & = & x_{21}a \, \mathbf{\hat{x}} + y_{21}b \, \mathbf{\hat{y}} + z_{21}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XIII} \\ \mathbf{B}_{84} & = & \left(-x_{21}+y_{21}\right) \, \mathbf{a}_{1} + \left(-x_{21}-y_{21}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{21}\right) \, \mathbf{a}_{3} & = & -x_{21}a \, \mathbf{\hat{x}}-y_{21}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{21}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XIII} \\ \mathbf{B}_{85} & = & \left(-x_{21}-y_{21}\right) \, \mathbf{a}_{1} + \left(-x_{21}+y_{21}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{21}\right) \, \mathbf{a}_{3} & = & -x_{21}a \, \mathbf{\hat{x}} + y_{21}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{21}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XIII} \\ \mathbf{B}_{86} & = & \left(x_{21}+y_{21}\right) \, \mathbf{a}_{1} + \left(x_{21}-y_{21}\right) \, \mathbf{a}_{2}-z_{21} \, \mathbf{a}_{3} & = & x_{21}a \, \mathbf{\hat{x}}-y_{21}b \, \mathbf{\hat{y}}-z_{21}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XIII} \\ \mathbf{B}_{87} & = & \left(-x_{21}+y_{21}\right) \, \mathbf{a}_{1} + \left(-x_{21}-y_{21}\right) \, \mathbf{a}_{2}-z_{21} \, \mathbf{a}_{3} & = & -x_{21}a \, \mathbf{\hat{x}}-y_{21}b \, \mathbf{\hat{y}}-z_{21}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XIII} \\ \mathbf{B}_{88} & = & \left(x_{21}-y_{21}\right) \, \mathbf{a}_{1} + \left(x_{21}+y_{21}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{21}\right) \, \mathbf{a}_{3} & = & x_{21}a \, \mathbf{\hat{x}} + y_{21}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{21}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XIII} \\ \mathbf{B}_{89} & = & \left(x_{21}+y_{21}\right) \, \mathbf{a}_{1} + \left(x_{21}-y_{21}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{21}\right) \, \mathbf{a}_{3} & = & x_{21}a \, \mathbf{\hat{x}}-y_{21}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{21}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XIII} \\ \mathbf{B}_{90} & = & \left(-x_{21}-y_{21}\right) \, \mathbf{a}_{1} + \left(-x_{21}+y_{21}\right) \, \mathbf{a}_{2} + z_{21} \, \mathbf{a}_{3} & = & -x_{21}a \, \mathbf{\hat{x}} + y_{21}b \, \mathbf{\hat{y}} + z_{21}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XIII} \\ \mathbf{B}_{91} & = & \left(x_{22}-y_{22}\right) \, \mathbf{a}_{1} + \left(x_{22}+y_{22}\right) \, \mathbf{a}_{2} + z_{22} \, \mathbf{a}_{3} & = & x_{22}a \, \mathbf{\hat{x}} + y_{22}b \, \mathbf{\hat{y}} + z_{22}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XIV} \\ \mathbf{B}_{92} & = & \left(-x_{22}+y_{22}\right) \, \mathbf{a}_{1} + \left(-x_{22}-y_{22}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{22}\right) \, \mathbf{a}_{3} & = & -x_{22}a \, \mathbf{\hat{x}}-y_{22}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{22}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XIV} \\ \mathbf{B}_{93} & = & \left(-x_{22}-y_{22}\right) \, \mathbf{a}_{1} + \left(-x_{22}+y_{22}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{22}\right) \, \mathbf{a}_{3} & = & -x_{22}a \, \mathbf{\hat{x}} + y_{22}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{22}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XIV} \\ \mathbf{B}_{94} & = & \left(x_{22}+y_{22}\right) \, \mathbf{a}_{1} + \left(x_{22}-y_{22}\right) \, \mathbf{a}_{2}-z_{22} \, \mathbf{a}_{3} & = & x_{22}a \, \mathbf{\hat{x}}-y_{22}b \, \mathbf{\hat{y}}-z_{22}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XIV} \\ \mathbf{B}_{95} & = & \left(-x_{22}+y_{22}\right) \, \mathbf{a}_{1} + \left(-x_{22}-y_{22}\right) \, \mathbf{a}_{2}-z_{22} \, \mathbf{a}_{3} & = & -x_{22}a \, \mathbf{\hat{x}}-y_{22}b \, \mathbf{\hat{y}}-z_{22}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XIV} \\ \mathbf{B}_{96} & = & \left(x_{22}-y_{22}\right) \, \mathbf{a}_{1} + \left(x_{22}+y_{22}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{22}\right) \, \mathbf{a}_{3} & = & x_{22}a \, \mathbf{\hat{x}} + y_{22}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{22}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XIV} \\ \mathbf{B}_{97} & = & \left(x_{22}+y_{22}\right) \, \mathbf{a}_{1} + \left(x_{22}-y_{22}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{22}\right) \, \mathbf{a}_{3} & = & x_{22}a \, \mathbf{\hat{x}}-y_{22}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{22}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XIV} \\ \mathbf{B}_{98} & = & \left(-x_{22}-y_{22}\right) \, \mathbf{a}_{1} + \left(-x_{22}+y_{22}\right) \, \mathbf{a}_{2} + z_{22} \, \mathbf{a}_{3} & = & -x_{22}a \, \mathbf{\hat{x}} + y_{22}b \, \mathbf{\hat{y}} + z_{22}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XIV} \\ \mathbf{B}_{99} & = & \left(x_{23}-y_{23}\right) \, \mathbf{a}_{1} + \left(x_{23}+y_{23}\right) \, \mathbf{a}_{2} + z_{23} \, \mathbf{a}_{3} & = & x_{23}a \, \mathbf{\hat{x}} + y_{23}b \, \mathbf{\hat{y}} + z_{23}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XV} \\ \mathbf{B}_{100} & = & \left(-x_{23}+y_{23}\right) \, \mathbf{a}_{1} + \left(-x_{23}-y_{23}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{23}\right) \, \mathbf{a}_{3} & = & -x_{23}a \, \mathbf{\hat{x}}-y_{23}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{23}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XV} \\ \mathbf{B}_{101} & = & \left(-x_{23}-y_{23}\right) \, \mathbf{a}_{1} + \left(-x_{23}+y_{23}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{23}\right) \, \mathbf{a}_{3} & = & -x_{23}a \, \mathbf{\hat{x}} + y_{23}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{23}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XV} \\ \mathbf{B}_{102} & = & \left(x_{23}+y_{23}\right) \, \mathbf{a}_{1} + \left(x_{23}-y_{23}\right) \, \mathbf{a}_{2}-z_{23} \, \mathbf{a}_{3} & = & x_{23}a \, \mathbf{\hat{x}}-y_{23}b \, \mathbf{\hat{y}}-z_{23}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XV} \\ \mathbf{B}_{103} & = & \left(-x_{23}+y_{23}\right) \, \mathbf{a}_{1} + \left(-x_{23}-y_{23}\right) \, \mathbf{a}_{2}-z_{23} \, \mathbf{a}_{3} & = & -x_{23}a \, \mathbf{\hat{x}}-y_{23}b \, \mathbf{\hat{y}}-z_{23}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XV} \\ \mathbf{B}_{104} & = & \left(x_{23}-y_{23}\right) \, \mathbf{a}_{1} + \left(x_{23}+y_{23}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{23}\right) \, \mathbf{a}_{3} & = & x_{23}a \, \mathbf{\hat{x}} + y_{23}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{23}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XV} \\ \mathbf{B}_{105} & = & \left(x_{23}+y_{23}\right) \, \mathbf{a}_{1} + \left(x_{23}-y_{23}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{23}\right) \, \mathbf{a}_{3} & = & x_{23}a \, \mathbf{\hat{x}}-y_{23}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{23}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XV} \\ \mathbf{B}_{106} & = & \left(-x_{23}-y_{23}\right) \, \mathbf{a}_{1} + \left(-x_{23}+y_{23}\right) \, \mathbf{a}_{2} + z_{23} \, \mathbf{a}_{3} & = & -x_{23}a \, \mathbf{\hat{x}} + y_{23}b \, \mathbf{\hat{y}} + z_{23}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XV} \\ \mathbf{B}_{107} & = & \left(x_{24}-y_{24}\right) \, \mathbf{a}_{1} + \left(x_{24}+y_{24}\right) \, \mathbf{a}_{2} + z_{24} \, \mathbf{a}_{3} & = & x_{24}a \, \mathbf{\hat{x}} + y_{24}b \, \mathbf{\hat{y}} + z_{24}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XVI} \\ \mathbf{B}_{108} & = & \left(-x_{24}+y_{24}\right) \, \mathbf{a}_{1} + \left(-x_{24}-y_{24}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{24}\right) \, \mathbf{a}_{3} & = & -x_{24}a \, \mathbf{\hat{x}}-y_{24}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{24}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XVI} \\ \mathbf{B}_{109} & = & \left(-x_{24}-y_{24}\right) \, \mathbf{a}_{1} + \left(-x_{24}+y_{24}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{24}\right) \, \mathbf{a}_{3} & = & -x_{24}a \, \mathbf{\hat{x}} + y_{24}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{24}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XVI} \\ \mathbf{B}_{110} & = & \left(x_{24}+y_{24}\right) \, \mathbf{a}_{1} + \left(x_{24}-y_{24}\right) \, \mathbf{a}_{2}-z_{24} \, \mathbf{a}_{3} & = & x_{24}a \, \mathbf{\hat{x}}-y_{24}b \, \mathbf{\hat{y}}-z_{24}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XVI} \\ \mathbf{B}_{111} & = & \left(-x_{24}+y_{24}\right) \, \mathbf{a}_{1} + \left(-x_{24}-y_{24}\right) \, \mathbf{a}_{2}-z_{24} \, \mathbf{a}_{3} & = & -x_{24}a \, \mathbf{\hat{x}}-y_{24}b \, \mathbf{\hat{y}}-z_{24}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XVI} \\ \mathbf{B}_{112} & = & \left(x_{24}-y_{24}\right) \, \mathbf{a}_{1} + \left(x_{24}+y_{24}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{24}\right) \, \mathbf{a}_{3} & = & x_{24}a \, \mathbf{\hat{x}} + y_{24}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{24}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XVI} \\ \mathbf{B}_{113} & = & \left(x_{24}+y_{24}\right) \, \mathbf{a}_{1} + \left(x_{24}-y_{24}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{24}\right) \, \mathbf{a}_{3} & = & x_{24}a \, \mathbf{\hat{x}}-y_{24}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{24}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XVI} \\ \mathbf{B}_{114} & = & \left(-x_{24}-y_{24}\right) \, \mathbf{a}_{1} + \left(-x_{24}+y_{24}\right) \, \mathbf{a}_{2} + z_{24} \, \mathbf{a}_{3} & = & -x_{24}a \, \mathbf{\hat{x}} + y_{24}b \, \mathbf{\hat{y}} + z_{24}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{La XVI} \\ \mathbf{B}_{115} & = & \left(x_{25}-y_{25}\right) \, \mathbf{a}_{1} + \left(x_{25}+y_{25}\right) \, \mathbf{a}_{2} + z_{25} \, \mathbf{a}_{3} & = & x_{25}a \, \mathbf{\hat{x}} + y_{25}b \, \mathbf{\hat{y}} + z_{25}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{Ni VI} \\ \mathbf{B}_{116} & = & \left(-x_{25}+y_{25}\right) \, \mathbf{a}_{1} + \left(-x_{25}-y_{25}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{25}\right) \, \mathbf{a}_{3} & = & -x_{25}a \, \mathbf{\hat{x}}-y_{25}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{25}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{Ni VI} \\ \mathbf{B}_{117} & = & \left(-x_{25}-y_{25}\right) \, \mathbf{a}_{1} + \left(-x_{25}+y_{25}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{25}\right) \, \mathbf{a}_{3} & = & -x_{25}a \, \mathbf{\hat{x}} + y_{25}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{25}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{Ni VI} \\ \mathbf{B}_{118} & = & \left(x_{25}+y_{25}\right) \, \mathbf{a}_{1} + \left(x_{25}-y_{25}\right) \, \mathbf{a}_{2}-z_{25} \, \mathbf{a}_{3} & = & x_{25}a \, \mathbf{\hat{x}}-y_{25}b \, \mathbf{\hat{y}}-z_{25}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{Ni VI} \\ \mathbf{B}_{119} & = & \left(-x_{25}+y_{25}\right) \, \mathbf{a}_{1} + \left(-x_{25}-y_{25}\right) \, \mathbf{a}_{2}-z_{25} \, \mathbf{a}_{3} & = & -x_{25}a \, \mathbf{\hat{x}}-y_{25}b \, \mathbf{\hat{y}}-z_{25}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{Ni VI} \\ \mathbf{B}_{120} & = & \left(x_{25}-y_{25}\right) \, \mathbf{a}_{1} + \left(x_{25}+y_{25}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{25}\right) \, \mathbf{a}_{3} & = & x_{25}a \, \mathbf{\hat{x}} + y_{25}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{25}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{Ni VI} \\ \mathbf{B}_{121} & = & \left(x_{25}+y_{25}\right) \, \mathbf{a}_{1} + \left(x_{25}-y_{25}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{25}\right) \, \mathbf{a}_{3} & = & x_{25}a \, \mathbf{\hat{x}}-y_{25}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{25}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{Ni VI} \\ \mathbf{B}_{122} & = & \left(-x_{25}-y_{25}\right) \, \mathbf{a}_{1} + \left(-x_{25}+y_{25}\right) \, \mathbf{a}_{2} + z_{25} \, \mathbf{a}_{3} & = & -x_{25}a \, \mathbf{\hat{x}} + y_{25}b \, \mathbf{\hat{y}} + z_{25}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{Ni VI} \\ \mathbf{B}_{123} & = & \left(x_{26}-y_{26}\right) \, \mathbf{a}_{1} + \left(x_{26}+y_{26}\right) \, \mathbf{a}_{2} + z_{26} \, \mathbf{a}_{3} & = & x_{26}a \, \mathbf{\hat{x}} + y_{26}b \, \mathbf{\hat{y}} + z_{26}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{Ni VII} \\ \mathbf{B}_{124} & = & \left(-x_{26}+y_{26}\right) \, \mathbf{a}_{1} + \left(-x_{26}-y_{26}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{26}\right) \, \mathbf{a}_{3} & = & -x_{26}a \, \mathbf{\hat{x}}-y_{26}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{26}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{Ni VII} \\ \mathbf{B}_{125} & = & \left(-x_{26}-y_{26}\right) \, \mathbf{a}_{1} + \left(-x_{26}+y_{26}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{26}\right) \, \mathbf{a}_{3} & = & -x_{26}a \, \mathbf{\hat{x}} + y_{26}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{26}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{Ni VII} \\ \mathbf{B}_{126} & = & \left(x_{26}+y_{26}\right) \, \mathbf{a}_{1} + \left(x_{26}-y_{26}\right) \, \mathbf{a}_{2}-z_{26} \, \mathbf{a}_{3} & = & x_{26}a \, \mathbf{\hat{x}}-y_{26}b \, \mathbf{\hat{y}}-z_{26}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{Ni VII} \\ \mathbf{B}_{127} & = & \left(-x_{26}+y_{26}\right) \, \mathbf{a}_{1} + \left(-x_{26}-y_{26}\right) \, \mathbf{a}_{2}-z_{26} \, \mathbf{a}_{3} & = & -x_{26}a \, \mathbf{\hat{x}}-y_{26}b \, \mathbf{\hat{y}}-z_{26}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{Ni VII} \\ \mathbf{B}_{128} & = & \left(x_{26}-y_{26}\right) \, \mathbf{a}_{1} + \left(x_{26}+y_{26}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{26}\right) \, \mathbf{a}_{3} & = & x_{26}a \, \mathbf{\hat{x}} + y_{26}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{26}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{Ni VII} \\ \mathbf{B}_{129} & = & \left(x_{26}+y_{26}\right) \, \mathbf{a}_{1} + \left(x_{26}-y_{26}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{26}\right) \, \mathbf{a}_{3} & = & x_{26}a \, \mathbf{\hat{x}}-y_{26}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{26}\right)c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{Ni VII} \\ \mathbf{B}_{130} & = & \left(-x_{26}-y_{26}\right) \, \mathbf{a}_{1} + \left(-x_{26}+y_{26}\right) \, \mathbf{a}_{2} + z_{26} \, \mathbf{a}_{3} & = & -x_{26}a \, \mathbf{\hat{x}} + y_{26}b \, \mathbf{\hat{y}} + z_{26}c \, \mathbf{\hat{z}} & \left(16h\right) & \mbox{Ni VII} \\ \end{array} \]

References

  • P. Solokha, S. De Negri, V. Pavlyuk, and A. Saccone, Anti–Mackay Polyicosahedral Clusters in La–Ni–Mg Ternary Compounds: Synthesis and Crystal Structure of the La43Ni17Mg5 New Intermetallic Phase, Inorg. Chem. 48, 11586–11593 (2009), doi:10.1021/ic901422v.

Geometry files


Prototype Generator

aflow --proto=A43B5C17_oC260_63_c8fg6h_cfg_ce3f2h --params=

Species:

Running:

Output: