Nb$_{7}$Rh$_{6}$B$_{8}$ Structure: A8B7C6_hP126_176_2h3i_acd6h

Basis vectors

		Lattice coordinates		Cartesian coordinates	Wyckoff position	Atom type
$B_{1}$	=	$\frac{1}{4} a_{3}$	=	$\frac{1}{4} c \hat{z}$	(2a)	Nb I
$B_{2}$	=	$\frac{3}{4} a_{3}$	=	$\frac{3}{4} c \hat{z}$	(2a)	Nb I
$B_{3}$	=	$\frac{1}{3} a_{1} + \frac{2}{3} a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a \hat{x} + \frac{3}{6} a \hat{y} + \frac{1}{4} c \hat{z}$	(2c)	Nb II
$B_{4}$	=	$\frac{2}{3} a_{1} + \frac{1}{3} a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a \hat{x} - \frac{3}{6} a \hat{y} + \frac{3}{4} c \hat{z}$	(2c)	Nb II
$B_{5}$	=	$\frac{2}{3} a_{1} + \frac{1}{3} a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a \hat{x} - \frac{3}{6} a \hat{y} + \frac{1}{4} c \hat{z}$	(2d)	Nb III
$B_{6}$	=	$\frac{1}{3} a_{1} + \frac{2}{3} a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a \hat{x} + \frac{3}{6} a \hat{y} + \frac{3}{4} c \hat{z}$	(2d)	Nb III
$B_{7}$	=	$x_{4} a_{1} + y_{4} a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a (x_{4} + y_{4}) \hat{x} - \frac{3}{2} a (x_{4} - y_{4}) \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	B I
$B_{8}$	=	$- y_{4} a_{1} + (x_{4} - y_{4}) a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a (x_{4} - 2 y_{4}) \hat{x} + \frac{3}{2} a x_{4} \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	B I
$B_{9}$	=	$- (x_{4} - y_{4}) a_{1} - x_{4} a_{2} + \frac{1}{4} a_{3}$	=	$- \frac{1}{2} a (2 x_{4} - y_{4}) \hat{x} - \frac{3}{2} a y_{4} \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	B I
$B_{10}$	=	$- x_{4} a_{1} - y_{4} a_{2} + \frac{3}{4} a_{3}$	=	$- \frac{1}{2} a (x_{4} + y_{4}) \hat{x} + \frac{3}{2} a (x_{4} - y_{4}) \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	B I
$B_{11}$	=	$y_{4} a_{1} - (x_{4} - y_{4}) a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a (- x_{4} + 2 y_{4}) \hat{x} - \frac{3}{2} a x_{4} \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	B I
$B_{12}$	=	$(x_{4} - y_{4}) a_{1} + x_{4} a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a (2 x_{4} - y_{4}) \hat{x} + \frac{3}{2} a y_{4} \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	B I
$B_{13}$	=	$x_{5} a_{1} + y_{5} a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a (x_{5} + y_{5}) \hat{x} - \frac{3}{2} a (x_{5} - y_{5}) \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	B II
$B_{14}$	=	$- y_{5} a_{1} + (x_{5} - y_{5}) a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a (x_{5} - 2 y_{5}) \hat{x} + \frac{3}{2} a x_{5} \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	B II
$B_{15}$	=	$- (x_{5} - y_{5}) a_{1} - x_{5} a_{2} + \frac{1}{4} a_{3}$	=	$- \frac{1}{2} a (2 x_{5} - y_{5}) \hat{x} - \frac{3}{2} a y_{5} \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	B II
$B_{16}$	=	$- x_{5} a_{1} - y_{5} a_{2} + \frac{3}{4} a_{3}$	=	$- \frac{1}{2} a (x_{5} + y_{5}) \hat{x} + \frac{3}{2} a (x_{5} - y_{5}) \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	B II
$B_{17}$	=	$y_{5} a_{1} - (x_{5} - y_{5}) a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a (- x_{5} + 2 y_{5}) \hat{x} - \frac{3}{2} a x_{5} \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	B II
$B_{18}$	=	$(x_{5} - y_{5}) a_{1} + x_{5} a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a (2 x_{5} - y_{5}) \hat{x} + \frac{3}{2} a y_{5} \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	B II
$B_{19}$	=	$x_{6} a_{1} + y_{6} a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a (x_{6} + y_{6}) \hat{x} - \frac{3}{2} a (x_{6} - y_{6}) \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb IV
$B_{20}$	=	$- y_{6} a_{1} + (x_{6} - y_{6}) a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a (x_{6} - 2 y_{6}) \hat{x} + \frac{3}{2} a x_{6} \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb IV
$B_{21}$	=	$- (x_{6} - y_{6}) a_{1} - x_{6} a_{2} + \frac{1}{4} a_{3}$	=	$- \frac{1}{2} a (2 x_{6} - y_{6}) \hat{x} - \frac{3}{2} a y_{6} \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb IV
$B_{22}$	=	$- x_{6} a_{1} - y_{6} a_{2} + \frac{3}{4} a_{3}$	=	$- \frac{1}{2} a (x_{6} + y_{6}) \hat{x} + \frac{3}{2} a (x_{6} - y_{6}) \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb IV
$B_{23}$	=	$y_{6} a_{1} - (x_{6} - y_{6}) a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a (- x_{6} + 2 y_{6}) \hat{x} - \frac{3}{2} a x_{6} \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb IV
$B_{24}$	=	$(x_{6} - y_{6}) a_{1} + x_{6} a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a (2 x_{6} - y_{6}) \hat{x} + \frac{3}{2} a y_{6} \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb IV
$B_{25}$	=	$x_{7} a_{1} + y_{7} a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a (x_{7} + y_{7}) \hat{x} - \frac{3}{2} a (x_{7} - y_{7}) \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb V
$B_{26}$	=	$- y_{7} a_{1} + (x_{7} - y_{7}) a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a (x_{7} - 2 y_{7}) \hat{x} + \frac{3}{2} a x_{7} \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb V
$B_{27}$	=	$- (x_{7} - y_{7}) a_{1} - x_{7} a_{2} + \frac{1}{4} a_{3}$	=	$- \frac{1}{2} a (2 x_{7} - y_{7}) \hat{x} - \frac{3}{2} a y_{7} \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb V
$B_{28}$	=	$- x_{7} a_{1} - y_{7} a_{2} + \frac{3}{4} a_{3}$	=	$- \frac{1}{2} a (x_{7} + y_{7}) \hat{x} + \frac{3}{2} a (x_{7} - y_{7}) \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb V
$B_{29}$	=	$y_{7} a_{1} - (x_{7} - y_{7}) a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a (- x_{7} + 2 y_{7}) \hat{x} - \frac{3}{2} a x_{7} \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb V
$B_{30}$	=	$(x_{7} - y_{7}) a_{1} + x_{7} a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a (2 x_{7} - y_{7}) \hat{x} + \frac{3}{2} a y_{7} \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb V
$B_{31}$	=	$x_{8} a_{1} + y_{8} a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a (x_{8} + y_{8}) \hat{x} - \frac{3}{2} a (x_{8} - y_{8}) \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb VI
$B_{32}$	=	$- y_{8} a_{1} + (x_{8} - y_{8}) a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a (x_{8} - 2 y_{8}) \hat{x} + \frac{3}{2} a x_{8} \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb VI
$B_{33}$	=	$- (x_{8} - y_{8}) a_{1} - x_{8} a_{2} + \frac{1}{4} a_{3}$	=	$- \frac{1}{2} a (2 x_{8} - y_{8}) \hat{x} - \frac{3}{2} a y_{8} \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb VI
$B_{34}$	=	$- x_{8} a_{1} - y_{8} a_{2} + \frac{3}{4} a_{3}$	=	$- \frac{1}{2} a (x_{8} + y_{8}) \hat{x} + \frac{3}{2} a (x_{8} - y_{8}) \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb VI
$B_{35}$	=	$y_{8} a_{1} - (x_{8} - y_{8}) a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a (- x_{8} + 2 y_{8}) \hat{x} - \frac{3}{2} a x_{8} \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb VI
$B_{36}$	=	$(x_{8} - y_{8}) a_{1} + x_{8} a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a (2 x_{8} - y_{8}) \hat{x} + \frac{3}{2} a y_{8} \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb VI
$B_{37}$	=	$x_{9} a_{1} + y_{9} a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a (x_{9} + y_{9}) \hat{x} - \frac{3}{2} a (x_{9} - y_{9}) \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb VII
$B_{38}$	=	$- y_{9} a_{1} + (x_{9} - y_{9}) a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a (x_{9} - 2 y_{9}) \hat{x} + \frac{3}{2} a x_{9} \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb VII
$B_{39}$	=	$- (x_{9} - y_{9}) a_{1} - x_{9} a_{2} + \frac{1}{4} a_{3}$	=	$- \frac{1}{2} a (2 x_{9} - y_{9}) \hat{x} - \frac{3}{2} a y_{9} \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb VII
$B_{40}$	=	$- x_{9} a_{1} - y_{9} a_{2} + \frac{3}{4} a_{3}$	=	$- \frac{1}{2} a (x_{9} + y_{9}) \hat{x} + \frac{3}{2} a (x_{9} - y_{9}) \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb VII
$B_{41}$	=	$y_{9} a_{1} - (x_{9} - y_{9}) a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a (- x_{9} + 2 y_{9}) \hat{x} - \frac{3}{2} a x_{9} \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb VII
$B_{42}$	=	$(x_{9} - y_{9}) a_{1} + x_{9} a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a (2 x_{9} - y_{9}) \hat{x} + \frac{3}{2} a y_{9} \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb VII
$B_{43}$	=	$x_{10} a_{1} + y_{10} a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a (x_{10} + y_{10}) \hat{x} - \frac{3}{2} a (x_{10} - y_{10}) \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb VIII
$B_{44}$	=	$- y_{10} a_{1} + (x_{10} - y_{10}) a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a (x_{10} - 2 y_{10}) \hat{x} + \frac{3}{2} a x_{10} \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb VIII
$B_{45}$	=	$- (x_{10} - y_{10}) a_{1} - x_{10} a_{2} + \frac{1}{4} a_{3}$	=	$- \frac{1}{2} a (2 x_{10} - y_{10}) \hat{x} - \frac{3}{2} a y_{10} \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb VIII
$B_{46}$	=	$- x_{10} a_{1} - y_{10} a_{2} + \frac{3}{4} a_{3}$	=	$- \frac{1}{2} a (x_{10} + y_{10}) \hat{x} + \frac{3}{2} a (x_{10} - y_{10}) \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb VIII
$B_{47}$	=	$y_{10} a_{1} - (x_{10} - y_{10}) a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a (- x_{10} + 2 y_{10}) \hat{x} - \frac{3}{2} a x_{10} \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb VIII
$B_{48}$	=	$(x_{10} - y_{10}) a_{1} + x_{10} a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a (2 x_{10} - y_{10}) \hat{x} + \frac{3}{2} a y_{10} \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb VIII
$B_{49}$	=	$x_{11} a_{1} + y_{11} a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a (x_{11} + y_{11}) \hat{x} - \frac{3}{2} a (x_{11} - y_{11}) \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb IX
$B_{50}$	=	$- y_{11} a_{1} + (x_{11} - y_{11}) a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a (x_{11} - 2 y_{11}) \hat{x} + \frac{3}{2} a x_{11} \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb IX
$B_{51}$	=	$- (x_{11} - y_{11}) a_{1} - x_{11} a_{2} + \frac{1}{4} a_{3}$	=	$- \frac{1}{2} a (2 x_{11} - y_{11}) \hat{x} - \frac{3}{2} a y_{11} \hat{y} + \frac{1}{4} c \hat{z}$	(6h)	Nb IX
$B_{52}$	=	$- x_{11} a_{1} - y_{11} a_{2} + \frac{3}{4} a_{3}$	=	$- \frac{1}{2} a (x_{11} + y_{11}) \hat{x} + \frac{3}{2} a (x_{11} - y_{11}) \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb IX
$B_{53}$	=	$y_{11} a_{1} - (x_{11} - y_{11}) a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a (- x_{11} + 2 y_{11}) \hat{x} - \frac{3}{2} a x_{11} \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb IX
$B_{54}$	=	$(x_{11} - y_{11}) a_{1} + x_{11} a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a (2 x_{11} - y_{11}) \hat{x} + \frac{3}{2} a y_{11} \hat{y} + \frac{3}{4} c \hat{z}$	(6h)	Nb IX
$B_{55}$	=	$x_{12} a_{1} + y_{12} a_{2} + z_{12} a_{3}$	=	$\frac{1}{2} a (x_{12} + y_{12}) \hat{x} - \frac{3}{2} a (x_{12} - y_{12}) \hat{y} + c z_{12} \hat{z}$	(12i)	B III
$B_{56}$	=	$- y_{12} a_{1} + (x_{12} - y_{12}) a_{2} + z_{12} a_{3}$	=	$\frac{1}{2} a (x_{12} - 2 y_{12}) \hat{x} + \frac{3}{2} a x_{12} \hat{y} + c z_{12} \hat{z}$	(12i)	B III
$B_{57}$	=	$- (x_{12} - y_{12}) a_{1} - x_{12} a_{2} + z_{12} a_{3}$	=	$- \frac{1}{2} a (2 x_{12} - y_{12}) \hat{x} - \frac{3}{2} a y_{12} \hat{y} + c z_{12} \hat{z}$	(12i)	B III
$B_{58}$	=	$- x_{12} a_{1} - y_{12} a_{2} + (z_{12} + \frac{1}{2}) a_{3}$	=	$- \frac{1}{2} a (x_{12} + y_{12}) \hat{x} + \frac{3}{2} a (x_{12} - y_{12}) \hat{y} + c (z_{12} + \frac{1}{2}) \hat{z}$	(12i)	B III
$B_{59}$	=	$y_{12} a_{1} - (x_{12} - y_{12}) a_{2} + (z_{12} + \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (- x_{12} + 2 y_{12}) \hat{x} - \frac{3}{2} a x_{12} \hat{y} + c (z_{12} + \frac{1}{2}) \hat{z}$	(12i)	B III
$B_{60}$	=	$(x_{12} - y_{12}) a_{1} + x_{12} a_{2} + (z_{12} + \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (2 x_{12} - y_{12}) \hat{x} + \frac{3}{2} a y_{12} \hat{y} + c (z_{12} + \frac{1}{2}) \hat{z}$	(12i)	B III
$B_{61}$	=	$- x_{12} a_{1} - y_{12} a_{2} - z_{12} a_{3}$	=	$- \frac{1}{2} a (x_{12} + y_{12}) \hat{x} + \frac{3}{2} a (x_{12} - y_{12}) \hat{y} - c z_{12} \hat{z}$	(12i)	B III
$B_{62}$	=	$y_{12} a_{1} - (x_{12} - y_{12}) a_{2} - z_{12} a_{3}$	=	$\frac{1}{2} a (- x_{12} + 2 y_{12}) \hat{x} - \frac{3}{2} a x_{12} \hat{y} - c z_{12} \hat{z}$	(12i)	B III
$B_{63}$	=	$(x_{12} - y_{12}) a_{1} + x_{12} a_{2} - z_{12} a_{3}$	=	$\frac{1}{2} a (2 x_{12} - y_{12}) \hat{x} + \frac{3}{2} a y_{12} \hat{y} - c z_{12} \hat{z}$	(12i)	B III
$B_{64}$	=	$x_{12} a_{1} + y_{12} a_{2} - (z_{12} - \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (x_{12} + y_{12}) \hat{x} - \frac{3}{2} a (x_{12} - y_{12}) \hat{y} - c (z_{12} - \frac{1}{2}) \hat{z}$	(12i)	B III
$B_{65}$	=	$- y_{12} a_{1} + (x_{12} - y_{12}) a_{2} - (z_{12} - \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (x_{12} - 2 y_{12}) \hat{x} + \frac{3}{2} a x_{12} \hat{y} - c (z_{12} - \frac{1}{2}) \hat{z}$	(12i)	B III
$B_{66}$	=	$- (x_{12} - y_{12}) a_{1} - x_{12} a_{2} - (z_{12} - \frac{1}{2}) a_{3}$	=	$- \frac{1}{2} a (2 x_{12} - y_{12}) \hat{x} - \frac{3}{2} a y_{12} \hat{y} - c (z_{12} - \frac{1}{2}) \hat{z}$	(12i)	B III
$B_{67}$	=	$x_{13} a_{1} + y_{13} a_{2} + z_{13} a_{3}$	=	$\frac{1}{2} a (x_{13} + y_{13}) \hat{x} - \frac{3}{2} a (x_{13} - y_{13}) \hat{y} + c z_{13} \hat{z}$	(12i)	B IV
$B_{68}$	=	$- y_{13} a_{1} + (x_{13} - y_{13}) a_{2} + z_{13} a_{3}$	=	$\frac{1}{2} a (x_{13} - 2 y_{13}) \hat{x} + \frac{3}{2} a x_{13} \hat{y} + c z_{13} \hat{z}$	(12i)	B IV
$B_{69}$	=	$- (x_{13} - y_{13}) a_{1} - x_{13} a_{2} + z_{13} a_{3}$	=	$- \frac{1}{2} a (2 x_{13} - y_{13}) \hat{x} - \frac{3}{2} a y_{13} \hat{y} + c z_{13} \hat{z}$	(12i)	B IV
$B_{70}$	=	$- x_{13} a_{1} - y_{13} a_{2} + (z_{13} + \frac{1}{2}) a_{3}$	=	$- \frac{1}{2} a (x_{13} + y_{13}) \hat{x} + \frac{3}{2} a (x_{13} - y_{13}) \hat{y} + c (z_{13} + \frac{1}{2}) \hat{z}$	(12i)	B IV
$B_{71}$	=	$y_{13} a_{1} - (x_{13} - y_{13}) a_{2} + (z_{13} + \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (- x_{13} + 2 y_{13}) \hat{x} - \frac{3}{2} a x_{13} \hat{y} + c (z_{13} + \frac{1}{2}) \hat{z}$	(12i)	B IV
$B_{72}$	=	$(x_{13} - y_{13}) a_{1} + x_{13} a_{2} + (z_{13} + \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (2 x_{13} - y_{13}) \hat{x} + \frac{3}{2} a y_{13} \hat{y} + c (z_{13} + \frac{1}{2}) \hat{z}$	(12i)	B IV
$B_{73}$	=	$- x_{13} a_{1} - y_{13} a_{2} - z_{13} a_{3}$	=	$- \frac{1}{2} a (x_{13} + y_{13}) \hat{x} + \frac{3}{2} a (x_{13} - y_{13}) \hat{y} - c z_{13} \hat{z}$	(12i)	B IV
$B_{74}$	=	$y_{13} a_{1} - (x_{13} - y_{13}) a_{2} - z_{13} a_{3}$	=	$\frac{1}{2} a (- x_{13} + 2 y_{13}) \hat{x} - \frac{3}{2} a x_{13} \hat{y} - c z_{13} \hat{z}$	(12i)	B IV
$B_{75}$	=	$(x_{13} - y_{13}) a_{1} + x_{13} a_{2} - z_{13} a_{3}$	=	$\frac{1}{2} a (2 x_{13} - y_{13}) \hat{x} + \frac{3}{2} a y_{13} \hat{y} - c z_{13} \hat{z}$	(12i)	B IV
$B_{76}$	=	$x_{13} a_{1} + y_{13} a_{2} - (z_{13} - \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (x_{13} + y_{13}) \hat{x} - \frac{3}{2} a (x_{13} - y_{13}) \hat{y} - c (z_{13} - \frac{1}{2}) \hat{z}$	(12i)	B IV
$B_{77}$	=	$- y_{13} a_{1} + (x_{13} - y_{13}) a_{2} - (z_{13} - \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (x_{13} - 2 y_{13}) \hat{x} + \frac{3}{2} a x_{13} \hat{y} - c (z_{13} - \frac{1}{2}) \hat{z}$	(12i)	B IV
$B_{78}$	=	$- (x_{13} - y_{13}) a_{1} - x_{13} a_{2} - (z_{13} - \frac{1}{2}) a_{3}$	=	$- \frac{1}{2} a (2 x_{13} - y_{13}) \hat{x} - \frac{3}{2} a y_{13} \hat{y} - c (z_{13} - \frac{1}{2}) \hat{z}$	(12i)	B IV
$B_{79}$	=	$x_{14} a_{1} + y_{14} a_{2} + z_{14} a_{3}$	=	$\frac{1}{2} a (x_{14} + y_{14}) \hat{x} - \frac{3}{2} a (x_{14} - y_{14}) \hat{y} + c z_{14} \hat{z}$	(12i)	B V
$B_{80}$	=	$- y_{14} a_{1} + (x_{14} - y_{14}) a_{2} + z_{14} a_{3}$	=	$\frac{1}{2} a (x_{14} - 2 y_{14}) \hat{x} + \frac{3}{2} a x_{14} \hat{y} + c z_{14} \hat{z}$	(12i)	B V
$B_{81}$	=	$- (x_{14} - y_{14}) a_{1} - x_{14} a_{2} + z_{14} a_{3}$	=	$- \frac{1}{2} a (2 x_{14} - y_{14}) \hat{x} - \frac{3}{2} a y_{14} \hat{y} + c z_{14} \hat{z}$	(12i)	B V
$B_{82}$	=	$- x_{14} a_{1} - y_{14} a_{2} + (z_{14} + \frac{1}{2}) a_{3}$	=	$- \frac{1}{2} a (x_{14} + y_{14}) \hat{x} + \frac{3}{2} a (x_{14} - y_{14}) \hat{y} + c (z_{14} + \frac{1}{2}) \hat{z}$	(12i)	B V
$B_{83}$	=	$y_{14} a_{1} - (x_{14} - y_{14}) a_{2} + (z_{14} + \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (- x_{14} + 2 y_{14}) \hat{x} - \frac{3}{2} a x_{14} \hat{y} + c (z_{14} + \frac{1}{2}) \hat{z}$	(12i)	B V
$B_{84}$	=	$(x_{14} - y_{14}) a_{1} + x_{14} a_{2} + (z_{14} + \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (2 x_{14} - y_{14}) \hat{x} + \frac{3}{2} a y_{14} \hat{y} + c (z_{14} + \frac{1}{2}) \hat{z}$	(12i)	B V
$B_{85}$	=	$- x_{14} a_{1} - y_{14} a_{2} - z_{14} a_{3}$	=	$- \frac{1}{2} a (x_{14} + y_{14}) \hat{x} + \frac{3}{2} a (x_{14} - y_{14}) \hat{y} - c z_{14} \hat{z}$	(12i)	B V
$B_{86}$	=	$y_{14} a_{1} - (x_{14} - y_{14}) a_{2} - z_{14} a_{3}$	=	$\frac{1}{2} a (- x_{14} + 2 y_{14}) \hat{x} - \frac{3}{2} a x_{14} \hat{y} - c z_{14} \hat{z}$	(12i)	B V
$B_{87}$	=	$(x_{14} - y_{14}) a_{1} + x_{14} a_{2} - z_{14} a_{3}$	=	$\frac{1}{2} a (2 x_{14} - y_{14}) \hat{x} + \frac{3}{2} a y_{14} \hat{y} - c z_{14} \hat{z}$	(12i)	B V
$B_{88}$	=	$x_{14} a_{1} + y_{14} a_{2} - (z_{14} - \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (x_{14} + y_{14}) \hat{x} - \frac{3}{2} a (x_{14} - y_{14}) \hat{y} - c (z_{14} - \frac{1}{2}) \hat{z}$	(12i)	B V
$B_{89}$	=	$- y_{14} a_{1} + (x_{14} - y_{14}) a_{2} - (z_{14} - \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (x_{14} - 2 y_{14}) \hat{x} + \frac{3}{2} a x_{14} \hat{y} - c (z_{14} - \frac{1}{2}) \hat{z}$	(12i)	B V
$B_{90}$	=	$- (x_{14} - y_{14}) a_{1} - x_{14} a_{2} - (z_{14} - \frac{1}{2}) a_{3}$	=	$- \frac{1}{2} a (2 x_{14} - y_{14}) \hat{x} - \frac{3}{2} a y_{14} \hat{y} - c (z_{14} - \frac{1}{2}) \hat{z}$	(12i)	B V
$B_{91}$	=	$x_{15} a_{1} + y_{15} a_{2} + z_{15} a_{3}$	=	$\frac{1}{2} a (x_{15} + y_{15}) \hat{x} - \frac{3}{2} a (x_{15} - y_{15}) \hat{y} + c z_{15} \hat{z}$	(12i)	Rh I
$B_{92}$	=	$- y_{15} a_{1} + (x_{15} - y_{15}) a_{2} + z_{15} a_{3}$	=	$\frac{1}{2} a (x_{15} - 2 y_{15}) \hat{x} + \frac{3}{2} a x_{15} \hat{y} + c z_{15} \hat{z}$	(12i)	Rh I
$B_{93}$	=	$- (x_{15} - y_{15}) a_{1} - x_{15} a_{2} + z_{15} a_{3}$	=	$- \frac{1}{2} a (2 x_{15} - y_{15}) \hat{x} - \frac{3}{2} a y_{15} \hat{y} + c z_{15} \hat{z}$	(12i)	Rh I
$B_{94}$	=	$- x_{15} a_{1} - y_{15} a_{2} + (z_{15} + \frac{1}{2}) a_{3}$	=	$- \frac{1}{2} a (x_{15} + y_{15}) \hat{x} + \frac{3}{2} a (x_{15} - y_{15}) \hat{y} + c (z_{15} + \frac{1}{2}) \hat{z}$	(12i)	Rh I
$B_{95}$	=	$y_{15} a_{1} - (x_{15} - y_{15}) a_{2} + (z_{15} + \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (- x_{15} + 2 y_{15}) \hat{x} - \frac{3}{2} a x_{15} \hat{y} + c (z_{15} + \frac{1}{2}) \hat{z}$	(12i)	Rh I
$B_{96}$	=	$(x_{15} - y_{15}) a_{1} + x_{15} a_{2} + (z_{15} + \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (2 x_{15} - y_{15}) \hat{x} + \frac{3}{2} a y_{15} \hat{y} + c (z_{15} + \frac{1}{2}) \hat{z}$	(12i)	Rh I
$B_{97}$	=	$- x_{15} a_{1} - y_{15} a_{2} - z_{15} a_{3}$	=	$- \frac{1}{2} a (x_{15} + y_{15}) \hat{x} + \frac{3}{2} a (x_{15} - y_{15}) \hat{y} - c z_{15} \hat{z}$	(12i)	Rh I
$B_{98}$	=	$y_{15} a_{1} - (x_{15} - y_{15}) a_{2} - z_{15} a_{3}$	=	$\frac{1}{2} a (- x_{15} + 2 y_{15}) \hat{x} - \frac{3}{2} a x_{15} \hat{y} - c z_{15} \hat{z}$	(12i)	Rh I
$B_{99}$	=	$(x_{15} - y_{15}) a_{1} + x_{15} a_{2} - z_{15} a_{3}$	=	$\frac{1}{2} a (2 x_{15} - y_{15}) \hat{x} + \frac{3}{2} a y_{15} \hat{y} - c z_{15} \hat{z}$	(12i)	Rh I
$B_{100}$	=	$x_{15} a_{1} + y_{15} a_{2} - (z_{15} - \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (x_{15} + y_{15}) \hat{x} - \frac{3}{2} a (x_{15} - y_{15}) \hat{y} - c (z_{15} - \frac{1}{2}) \hat{z}$	(12i)	Rh I
$B_{101}$	=	$- y_{15} a_{1} + (x_{15} - y_{15}) a_{2} - (z_{15} - \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (x_{15} - 2 y_{15}) \hat{x} + \frac{3}{2} a x_{15} \hat{y} - c (z_{15} - \frac{1}{2}) \hat{z}$	(12i)	Rh I
$B_{102}$	=	$- (x_{15} - y_{15}) a_{1} - x_{15} a_{2} - (z_{15} - \frac{1}{2}) a_{3}$	=	$- \frac{1}{2} a (2 x_{15} - y_{15}) \hat{x} - \frac{3}{2} a y_{15} \hat{y} - c (z_{15} - \frac{1}{2}) \hat{z}$	(12i)	Rh I
$B_{103}$	=	$x_{16} a_{1} + y_{16} a_{2} + z_{16} a_{3}$	=	$\frac{1}{2} a (x_{16} + y_{16}) \hat{x} - \frac{3}{2} a (x_{16} - y_{16}) \hat{y} + c z_{16} \hat{z}$	(12i)	Rh II
$B_{104}$	=	$- y_{16} a_{1} + (x_{16} - y_{16}) a_{2} + z_{16} a_{3}$	=	$\frac{1}{2} a (x_{16} - 2 y_{16}) \hat{x} + \frac{3}{2} a x_{16} \hat{y} + c z_{16} \hat{z}$	(12i)	Rh II
$B_{105}$	=	$- (x_{16} - y_{16}) a_{1} - x_{16} a_{2} + z_{16} a_{3}$	=	$- \frac{1}{2} a (2 x_{16} - y_{16}) \hat{x} - \frac{3}{2} a y_{16} \hat{y} + c z_{16} \hat{z}$	(12i)	Rh II
$B_{106}$	=	$- x_{16} a_{1} - y_{16} a_{2} + (z_{16} + \frac{1}{2}) a_{3}$	=	$- \frac{1}{2} a (x_{16} + y_{16}) \hat{x} + \frac{3}{2} a (x_{16} - y_{16}) \hat{y} + c (z_{16} + \frac{1}{2}) \hat{z}$	(12i)	Rh II
$B_{107}$	=	$y_{16} a_{1} - (x_{16} - y_{16}) a_{2} + (z_{16} + \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (- x_{16} + 2 y_{16}) \hat{x} - \frac{3}{2} a x_{16} \hat{y} + c (z_{16} + \frac{1}{2}) \hat{z}$	(12i)	Rh II
$B_{108}$	=	$(x_{16} - y_{16}) a_{1} + x_{16} a_{2} + (z_{16} + \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (2 x_{16} - y_{16}) \hat{x} + \frac{3}{2} a y_{16} \hat{y} + c (z_{16} + \frac{1}{2}) \hat{z}$	(12i)	Rh II
$B_{109}$	=	$- x_{16} a_{1} - y_{16} a_{2} - z_{16} a_{3}$	=	$- \frac{1}{2} a (x_{16} + y_{16}) \hat{x} + \frac{3}{2} a (x_{16} - y_{16}) \hat{y} - c z_{16} \hat{z}$	(12i)	Rh II
$B_{110}$	=	$y_{16} a_{1} - (x_{16} - y_{16}) a_{2} - z_{16} a_{3}$	=	$\frac{1}{2} a (- x_{16} + 2 y_{16}) \hat{x} - \frac{3}{2} a x_{16} \hat{y} - c z_{16} \hat{z}$	(12i)	Rh II
$B_{111}$	=	$(x_{16} - y_{16}) a_{1} + x_{16} a_{2} - z_{16} a_{3}$	=	$\frac{1}{2} a (2 x_{16} - y_{16}) \hat{x} + \frac{3}{2} a y_{16} \hat{y} - c z_{16} \hat{z}$	(12i)	Rh II
$B_{112}$	=	$x_{16} a_{1} + y_{16} a_{2} - (z_{16} - \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (x_{16} + y_{16}) \hat{x} - \frac{3}{2} a (x_{16} - y_{16}) \hat{y} - c (z_{16} - \frac{1}{2}) \hat{z}$	(12i)	Rh II
$B_{113}$	=	$- y_{16} a_{1} + (x_{16} - y_{16}) a_{2} - (z_{16} - \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (x_{16} - 2 y_{16}) \hat{x} + \frac{3}{2} a x_{16} \hat{y} - c (z_{16} - \frac{1}{2}) \hat{z}$	(12i)	Rh II
$B_{114}$	=	$- (x_{16} - y_{16}) a_{1} - x_{16} a_{2} - (z_{16} - \frac{1}{2}) a_{3}$	=	$- \frac{1}{2} a (2 x_{16} - y_{16}) \hat{x} - \frac{3}{2} a y_{16} \hat{y} - c (z_{16} - \frac{1}{2}) \hat{z}$	(12i)	Rh II
$B_{115}$	=	$x_{17} a_{1} + y_{17} a_{2} + z_{17} a_{3}$	=	$\frac{1}{2} a (x_{17} + y_{17}) \hat{x} - \frac{3}{2} a (x_{17} - y_{17}) \hat{y} + c z_{17} \hat{z}$	(12i)	Rh III
$B_{116}$	=	$- y_{17} a_{1} + (x_{17} - y_{17}) a_{2} + z_{17} a_{3}$	=	$\frac{1}{2} a (x_{17} - 2 y_{17}) \hat{x} + \frac{3}{2} a x_{17} \hat{y} + c z_{17} \hat{z}$	(12i)	Rh III
$B_{117}$	=	$- (x_{17} - y_{17}) a_{1} - x_{17} a_{2} + z_{17} a_{3}$	=	$- \frac{1}{2} a (2 x_{17} - y_{17}) \hat{x} - \frac{3}{2} a y_{17} \hat{y} + c z_{17} \hat{z}$	(12i)	Rh III
$B_{118}$	=	$- x_{17} a_{1} - y_{17} a_{2} + (z_{17} + \frac{1}{2}) a_{3}$	=	$- \frac{1}{2} a (x_{17} + y_{17}) \hat{x} + \frac{3}{2} a (x_{17} - y_{17}) \hat{y} + c (z_{17} + \frac{1}{2}) \hat{z}$	(12i)	Rh III
$B_{119}$	=	$y_{17} a_{1} - (x_{17} - y_{17}) a_{2} + (z_{17} + \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (- x_{17} + 2 y_{17}) \hat{x} - \frac{3}{2} a x_{17} \hat{y} + c (z_{17} + \frac{1}{2}) \hat{z}$	(12i)	Rh III
$B_{120}$	=	$(x_{17} - y_{17}) a_{1} + x_{17} a_{2} + (z_{17} + \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (2 x_{17} - y_{17}) \hat{x} + \frac{3}{2} a y_{17} \hat{y} + c (z_{17} + \frac{1}{2}) \hat{z}$	(12i)	Rh III
$B_{121}$	=	$- x_{17} a_{1} - y_{17} a_{2} - z_{17} a_{3}$	=	$- \frac{1}{2} a (x_{17} + y_{17}) \hat{x} + \frac{3}{2} a (x_{17} - y_{17}) \hat{y} - c z_{17} \hat{z}$	(12i)	Rh III
$B_{122}$	=	$y_{17} a_{1} - (x_{17} - y_{17}) a_{2} - z_{17} a_{3}$	=	$\frac{1}{2} a (- x_{17} + 2 y_{17}) \hat{x} - \frac{3}{2} a x_{17} \hat{y} - c z_{17} \hat{z}$	(12i)	Rh III
$B_{123}$	=	$(x_{17} - y_{17}) a_{1} + x_{17} a_{2} - z_{17} a_{3}$	=	$\frac{1}{2} a (2 x_{17} - y_{17}) \hat{x} + \frac{3}{2} a y_{17} \hat{y} - c z_{17} \hat{z}$	(12i)	Rh III
$B_{124}$	=	$x_{17} a_{1} + y_{17} a_{2} - (z_{17} - \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (x_{17} + y_{17}) \hat{x} - \frac{3}{2} a (x_{17} - y_{17}) \hat{y} - c (z_{17} - \frac{1}{2}) \hat{z}$	(12i)	Rh III
$B_{125}$	=	$- y_{17} a_{1} + (x_{17} - y_{17}) a_{2} - (z_{17} - \frac{1}{2}) a_{3}$	=	$\frac{1}{2} a (x_{17} - 2 y_{17}) \hat{x} + \frac{3}{2} a x_{17} \hat{y} - c (z_{17} - \frac{1}{2}) \hat{z}$	(12i)	Rh III
$B_{126}$	=	$- (x_{17} - y_{17}) a_{1} - x_{17} a_{2} - (z_{17} - \frac{1}{2}) a_{3}$	=	$- \frac{1}{2} a (2 x_{17} - y_{17}) \hat{x} - \frac{3}{2} a y_{17} \hat{y} - c (z_{17} - \frac{1}{2}) \hat{z}$	(12i)	Rh III

Prototype	B $_{8}$ Nb $_{7}$ Rh $_{6}$
AFLOW prototype label	A8B7C6_hP126_176_2h3i_acd6h_3i-001
ICSD	263043
Pearson symbol	hP126
Space group number	176
Space group symbol	$P 6_{3} / m$
AFLOW prototype command	aflow --proto=A8B7C6_hP126_176_2h3i_acd6h_3i-001 --params= $a, c / a, x_{4}, y_{4}, x_{5}, y_{5}, x_{6}, y_{6}, x_{7}, y_{7}, x_{8}, y_{8}, x_{9}, y_{9}, x_{10}, y_{10}, x_{11}, y_{11}, x_{12}, y_{12}, z_{12}, x_{13}, y_{13}, z_{13}, x_{14}, y_{14}, z_{14}, x_{15}, y_{15}, z_{15}, x_{16}, y_{16}, z_{16}, x_{17}, y_{17}, z_{17}$

Encyclopedia of Crystallographic Prototypes

Nb $_{7}$ Rh $_{6}$ B $_{8}$ Structure: A8B7C6_hP126_176_2h3i_acd6h_3i-001

Hexagonal primitive vectors

References

Running:

Output:

Encyclopedia of Crystallographic Prototypes

Nb7​Rh6​B8​ Structure: A8B7C6_hP126_176_2h3i_acd6h_3i-001

Hexagonal primitive vectors

References

Running:

Output:

Nb $_{7}$ Rh $_{6}$ B $_{8}$ Structure: A8B7C6_hP126_176_2h3i_acd6h_3i-001