Information of spin space group $I{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}\text{a}{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}\text{-}\text{3}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{d}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$ ( nSSG:220.230.1.1 )

General Positions

The continuously infinite group ^∞1 is omitted.

Coordinates	Seitz symbol
a, b, c | x, y, z	{ 1 ‖ 1 | 0 }
a, -b, -c+1/2 | x, y, z	{ 1 ‖ 2100 | 0 0 1/2 }
-a+1/2, b, -c | x, y, z	{ 1 ‖ 2010 | 1/2 0 0 }
-a, -b+1/2, c | x, y, z	{ 1 ‖ 2001 | 0 1/2 0 }
c, a, b | x, y, z	{ 1 ‖ 3+111 | 0 }
b, c, a | x, y, z	{ 1 ‖ 3-111 | 0 }
-b+1/2, c, -a | x, y, z	{ 1 ‖ 3-1-1-1 | 1/2 0 0 }
-c, -a+1/2, b | x, y, z	{ 1 ‖ 3+1-1-1 | 0 1/2 0 }
-b, -c+1/2, a | x, y, z	{ 1 ‖ 3--11-1 | 0 1/2 0 }
c, -a, -b+1/2 | x, y, z	{ 1 ‖ 3+-11-1 | 0 0 1/2 }
b, -c, -a+1/2 | x, y, z	{ 1 ‖ 3--1-11 | 0 0 1/2 }
-c+1/2, a, -b | x, y, z	{ 1 ‖ 3+-1-11 | 1/2 0 0 }
-a+1/4, c+1/4, -b+3/4 | x, y, z	{ 1 ‖ -4+100 | 1/4 1/4 3/4 }
-a+3/4, -c+1/4, b+1/4 | x, y, z	{ 1 ‖ -4-100 | 3/4 1/4 1/4 }
-c+3/4, -b+1/4, a+1/4 | x, y, z	{ 1 ‖ -4+010 | 3/4 1/4 1/4 }
c+1/4, -b+3/4, -a+1/4 | x, y, z	{ 1 ‖ -4-010 | 1/4 3/4 1/4 }
b+1/4, -a+3/4, -c+1/4 | x, y, z	{ 1 ‖ -4+001 | 1/4 3/4 1/4 }
-b+1/4, a+1/4, -c+3/4 | x, y, z	{ 1 ‖ -4-001 | 1/4 1/4 3/4 }
-b+3/4, -a+1/4, c+1/4 | x, y, z	{ 1 ‖ m110 | 3/4 1/4 1/4 }
b+1/4, a+1/4, c+1/4 | x, y, z	{ 1 ‖ m1-10 | 1/4 1/4 1/4 }
a+1/4, -c+3/4, -b+1/4 | x, y, z	{ 1 ‖ m011 | 1/4 3/4 1/4 }
a+1/4, c+1/4, b+1/4 | x, y, z	{ 1 ‖ m01-1 | 1/4 1/4 1/4 }
-c+1/4, b+1/4, -a+3/4 | x, y, z	{ 1 ‖ m101 | 1/4 1/4 3/4 }
c+1/4, b+1/4, a+1/4 | x, y, z	{ 1 ‖ m-101 | 1/4 1/4 1/4 }
a+1/4, -c+1/4, b+3/4 | -x, -y, -z	{ -1 ‖ 4+100 | 1/4 1/4 3/4 }
a+3/4, c+1/4, -b+1/4 | -x, -y, -z	{ -1 ‖ 4-100 | 3/4 1/4 1/4 }
c+3/4, b+1/4, -a+1/4 | -x, -y, -z	{ -1 ‖ 4+010 | 3/4 1/4 1/4 }
-c+1/4, b+3/4, a+1/4 | -x, -y, -z	{ -1 ‖ 4-010 | 1/4 3/4 1/4 }
-b+1/4, a+3/4, c+1/4 | -x, -y, -z	{ -1 ‖ 4+001 | 1/4 3/4 1/4 }
b+1/4, -a+1/4, c+3/4 | -x, -y, -z	{ -1 ‖ 4-001 | 1/4 1/4 3/4 }
b+3/4, a+1/4, -c+1/4 | -x, -y, -z	{ -1 ‖ 2110 | 3/4 1/4 1/4 }
-b+1/4, -a+1/4, -c+1/4 | -x, -y, -z	{ -1 ‖ 21-10 | 1/4 1/4 1/4 }
-a+1/4, c+3/4, b+1/4 | -x, -y, -z	{ -1 ‖ 2011 | 1/4 3/4 1/4 }
-a+1/4, -c+1/4, -b+1/4 | -x, -y, -z	{ -1 ‖ 201-1 | 1/4 1/4 1/4 }
c+1/4, -b+1/4, a+3/4 | -x, -y, -z	{ -1 ‖ 2101 | 1/4 1/4 3/4 }
-c+1/4, -b+1/4, -a+1/4 | -x, -y, -z	{ -1 ‖ 2-101 | 1/4 1/4 1/4 }
-a, -b, -c | -x, -y, -z	{ -1 ‖ -1 | 0 }
-a, b, c+1/2 | -x, -y, -z	{ -1 ‖ m100 | 0 0 1/2 }
a+1/2, -b, c | -x, -y, -z	{ -1 ‖ m010 | 1/2 0 0 }
a, b+1/2, -c | -x, -y, -z	{ -1 ‖ m001 | 0 1/2 0 }
-c, -a, -b | -x, -y, -z	{ -1 ‖ -3+111 | 0 }
-b, -c, -a | -x, -y, -z	{ -1 ‖ -3-111 | 0 }
b+1/2, -c, a | -x, -y, -z	{ -1 ‖ -3-1-1-1 | 1/2 0 0 }
c, a+1/2, -b | -x, -y, -z	{ -1 ‖ -3+1-1-1 | 0 1/2 0 }
b, c+1/2, -a | -x, -y, -z	{ -1 ‖ -3--11-1 | 0 1/2 0 }
-c, a, b+1/2 | -x, -y, -z	{ -1 ‖ -3+-11-1 | 0 0 1/2 }
-b, c, a+1/2 | -x, -y, -z	{ -1 ‖ -3--1-11 | 0 0 1/2 }
c+1/2, -a, b | -x, -y, -z	{ -1 ‖ -3+-1-11 | 1/2 0 0 }
a+1/2, b+1/2, c+1/2 | x, y, z	{ 1 ‖ 1 | 1/2 1/2 1/2 }
a+1/2, -b+1/2, -c | x, y, z	{ 1 ‖ 2100 | 1/2 1/2 0 }
-a, b+1/2, -c+1/2 | x, y, z	{ 1 ‖ 2010 | 0 1/2 1/2 }
-a+1/2, -b, c+1/2 | x, y, z	{ 1 ‖ 2001 | 1/2 0 1/2 }
c+1/2, a+1/2, b+1/2 | x, y, z	{ 1 ‖ 3+111 | 1/2 1/2 1/2 }
b+1/2, c+1/2, a+1/2 | x, y, z	{ 1 ‖ 3-111 | 1/2 1/2 1/2 }
-b, c+1/2, -a+1/2 | x, y, z	{ 1 ‖ 3-1-1-1 | 0 1/2 1/2 }
-c+1/2, -a, b+1/2 | x, y, z	{ 1 ‖ 3+1-1-1 | 1/2 0 1/2 }
-b+1/2, -c, a+1/2 | x, y, z	{ 1 ‖ 3--11-1 | 1/2 0 1/2 }
c+1/2, -a+1/2, -b | x, y, z	{ 1 ‖ 3+-11-1 | 1/2 1/2 0 }
b+1/2, -c+1/2, -a | x, y, z	{ 1 ‖ 3--1-11 | 1/2 1/2 0 }
-c, a+1/2, -b+1/2 | x, y, z	{ 1 ‖ 3+-1-11 | 0 1/2 1/2 }
-a+3/4, c+3/4, -b+1/4 | x, y, z	{ 1 ‖ -4+100 | 3/4 3/4 1/4 }
-a+1/4, -c+3/4, b+3/4 | x, y, z	{ 1 ‖ -4-100 | 1/4 3/4 3/4 }
-c+1/4, -b+3/4, a+3/4 | x, y, z	{ 1 ‖ -4+010 | 1/4 3/4 3/4 }
c+3/4, -b+1/4, -a+3/4 | x, y, z	{ 1 ‖ -4-010 | 3/4 1/4 3/4 }
b+3/4, -a+1/4, -c+3/4 | x, y, z	{ 1 ‖ -4+001 | 3/4 1/4 3/4 }
-b+3/4, a+3/4, -c+1/4 | x, y, z	{ 1 ‖ -4-001 | 3/4 3/4 1/4 }
-b+1/4, -a+3/4, c+3/4 | x, y, z	{ 1 ‖ m110 | 1/4 3/4 3/4 }
b+3/4, a+3/4, c+3/4 | x, y, z	{ 1 ‖ m1-10 | 3/4 3/4 3/4 }
a+3/4, -c+1/4, -b+3/4 | x, y, z	{ 1 ‖ m011 | 3/4 1/4 3/4 }
a+3/4, c+3/4, b+3/4 | x, y, z	{ 1 ‖ m01-1 | 3/4 3/4 3/4 }
-c+3/4, b+3/4, -a+1/4 | x, y, z	{ 1 ‖ m101 | 3/4 3/4 1/4 }
c+3/4, b+3/4, a+3/4 | x, y, z	{ 1 ‖ m-101 | 3/4 3/4 3/4 }
a+3/4, -c+3/4, b+1/4 | -x, -y, -z	{ -1 ‖ 4+100 | 3/4 3/4 1/4 }
a+1/4, c+3/4, -b+3/4 | -x, -y, -z	{ -1 ‖ 4-100 | 1/4 3/4 3/4 }
c+1/4, b+3/4, -a+3/4 | -x, -y, -z	{ -1 ‖ 4+010 | 1/4 3/4 3/4 }
-c+3/4, b+1/4, a+3/4 | -x, -y, -z	{ -1 ‖ 4-010 | 3/4 1/4 3/4 }
-b+3/4, a+1/4, c+3/4 | -x, -y, -z	{ -1 ‖ 4+001 | 3/4 1/4 3/4 }
b+3/4, -a+3/4, c+1/4 | -x, -y, -z	{ -1 ‖ 4-001 | 3/4 3/4 1/4 }
b+1/4, a+3/4, -c+3/4 | -x, -y, -z	{ -1 ‖ 2110 | 1/4 3/4 3/4 }
-b+3/4, -a+3/4, -c+3/4 | -x, -y, -z	{ -1 ‖ 21-10 | 3/4 3/4 3/4 }
-a+3/4, c+1/4, b+3/4 | -x, -y, -z	{ -1 ‖ 2011 | 3/4 1/4 3/4 }
-a+3/4, -c+3/4, -b+3/4 | -x, -y, -z	{ -1 ‖ 201-1 | 3/4 3/4 3/4 }
c+3/4, -b+3/4, a+1/4 | -x, -y, -z	{ -1 ‖ 2101 | 3/4 3/4 1/4 }
-c+3/4, -b+3/4, -a+3/4 | -x, -y, -z	{ -1 ‖ 2-101 | 3/4 3/4 3/4 }
-a+1/2, -b+1/2, -c+1/2 | -x, -y, -z	{ -1 ‖ -1 | 1/2 1/2 1/2 }
-a+1/2, b+1/2, c | -x, -y, -z	{ -1 ‖ m100 | 1/2 1/2 0 }
a, -b+1/2, c+1/2 | -x, -y, -z	{ -1 ‖ m010 | 0 1/2 1/2 }
a+1/2, b, -c+1/2 | -x, -y, -z	{ -1 ‖ m001 | 1/2 0 1/2 }
-c+1/2, -a+1/2, -b+1/2 | -x, -y, -z	{ -1 ‖ -3+111 | 1/2 1/2 1/2 }
-b+1/2, -c+1/2, -a+1/2 | -x, -y, -z	{ -1 ‖ -3-111 | 1/2 1/2 1/2 }
b, -c+1/2, a+1/2 | -x, -y, -z	{ -1 ‖ -3-1-1-1 | 0 1/2 1/2 }
c+1/2, a, -b+1/2 | -x, -y, -z	{ -1 ‖ -3+1-1-1 | 1/2 0 1/2 }
b+1/2, c, -a+1/2 | -x, -y, -z	{ -1 ‖ -3--11-1 | 1/2 0 1/2 }
-c+1/2, a+1/2, b | -x, -y, -z	{ -1 ‖ -3+-11-1 | 1/2 1/2 0 }
-b+1/2, c+1/2, a | -x, -y, -z	{ -1 ‖ -3--1-11 | 1/2 1/2 0 }
c, -a+1/2, b+1/2 | -x, -y, -z	{ -1 ‖ -3+-1-11 | 0 1/2 1/2 }
a, b, c | -x, y, z	{ m ‖ 1 | 0 }
a, -b, -c+1/2 | -x, y, z	{ m ‖ 2100 | 0 0 1/2 }
-a+1/2, b, -c | -x, y, z	{ m ‖ 2010 | 1/2 0 0 }
-a, -b+1/2, c | -x, y, z	{ m ‖ 2001 | 0 1/2 0 }
c, a, b | -x, y, z	{ m ‖ 3+111 | 0 }
b, c, a | -x, y, z	{ m ‖ 3-111 | 0 }
-b+1/2, c, -a | -x, y, z	{ m ‖ 3-1-1-1 | 1/2 0 0 }
-c, -a+1/2, b | -x, y, z	{ m ‖ 3+1-1-1 | 0 1/2 0 }
-b, -c+1/2, a | -x, y, z	{ m ‖ 3--11-1 | 0 1/2 0 }
c, -a, -b+1/2 | -x, y, z	{ m ‖ 3+-11-1 | 0 0 1/2 }
b, -c, -a+1/2 | -x, y, z	{ m ‖ 3--1-11 | 0 0 1/2 }
-c+1/2, a, -b | -x, y, z	{ m ‖ 3+-1-11 | 1/2 0 0 }
-a+1/4, c+1/4, -b+3/4 | -x, y, z	{ m ‖ -4+100 | 1/4 1/4 3/4 }
-a+3/4, -c+1/4, b+1/4 | -x, y, z	{ m ‖ -4-100 | 3/4 1/4 1/4 }
-c+3/4, -b+1/4, a+1/4 | -x, y, z	{ m ‖ -4+010 | 3/4 1/4 1/4 }
c+1/4, -b+3/4, -a+1/4 | -x, y, z	{ m ‖ -4-010 | 1/4 3/4 1/4 }
b+1/4, -a+3/4, -c+1/4 | -x, y, z	{ m ‖ -4+001 | 1/4 3/4 1/4 }
-b+1/4, a+1/4, -c+3/4 | -x, y, z	{ m ‖ -4-001 | 1/4 1/4 3/4 }
-b+3/4, -a+1/4, c+1/4 | -x, y, z	{ m ‖ m110 | 3/4 1/4 1/4 }
b+1/4, a+1/4, c+1/4 | -x, y, z	{ m ‖ m1-10 | 1/4 1/4 1/4 }
a+1/4, -c+3/4, -b+1/4 | -x, y, z	{ m ‖ m011 | 1/4 3/4 1/4 }
a+1/4, c+1/4, b+1/4 | -x, y, z	{ m ‖ m01-1 | 1/4 1/4 1/4 }
-c+1/4, b+1/4, -a+3/4 | -x, y, z	{ m ‖ m101 | 1/4 1/4 3/4 }
c+1/4, b+1/4, a+1/4 | -x, y, z	{ m ‖ m-101 | 1/4 1/4 1/4 }
a+1/4, -c+1/4, b+3/4 | x, -y, -z	{ 2 ‖ 4+100 | 1/4 1/4 3/4 }
a+3/4, c+1/4, -b+1/4 | x, -y, -z	{ 2 ‖ 4-100 | 3/4 1/4 1/4 }
c+3/4, b+1/4, -a+1/4 | x, -y, -z	{ 2 ‖ 4+010 | 3/4 1/4 1/4 }
-c+1/4, b+3/4, a+1/4 | x, -y, -z	{ 2 ‖ 4-010 | 1/4 3/4 1/4 }
-b+1/4, a+3/4, c+1/4 | x, -y, -z	{ 2 ‖ 4+001 | 1/4 3/4 1/4 }
b+1/4, -a+1/4, c+3/4 | x, -y, -z	{ 2 ‖ 4-001 | 1/4 1/4 3/4 }
b+3/4, a+1/4, -c+1/4 | x, -y, -z	{ 2 ‖ 2110 | 3/4 1/4 1/4 }
-b+1/4, -a+1/4, -c+1/4 | x, -y, -z	{ 2 ‖ 21-10 | 1/4 1/4 1/4 }
-a+1/4, c+3/4, b+1/4 | x, -y, -z	{ 2 ‖ 2011 | 1/4 3/4 1/4 }
-a+1/4, -c+1/4, -b+1/4 | x, -y, -z	{ 2 ‖ 201-1 | 1/4 1/4 1/4 }
c+1/4, -b+1/4, a+3/4 | x, -y, -z	{ 2 ‖ 2101 | 1/4 1/4 3/4 }
-c+1/4, -b+1/4, -a+1/4 | x, -y, -z	{ 2 ‖ 2-101 | 1/4 1/4 1/4 }
-a, -b, -c | x, -y, -z	{ 2 ‖ -1 | 0 }
-a, b, c+1/2 | x, -y, -z	{ 2 ‖ m100 | 0 0 1/2 }
a+1/2, -b, c | x, -y, -z	{ 2 ‖ m010 | 1/2 0 0 }
a, b+1/2, -c | x, -y, -z	{ 2 ‖ m001 | 0 1/2 0 }
-c, -a, -b | x, -y, -z	{ 2 ‖ -3+111 | 0 }
-b, -c, -a | x, -y, -z	{ 2 ‖ -3-111 | 0 }
b+1/2, -c, a | x, -y, -z	{ 2 ‖ -3-1-1-1 | 1/2 0 0 }
c, a+1/2, -b | x, -y, -z	{ 2 ‖ -3+1-1-1 | 0 1/2 0 }
b, c+1/2, -a | x, -y, -z	{ 2 ‖ -3--11-1 | 0 1/2 0 }
-c, a, b+1/2 | x, -y, -z	{ 2 ‖ -3+-11-1 | 0 0 1/2 }
-b, c, a+1/2 | x, -y, -z	{ 2 ‖ -3--1-11 | 0 0 1/2 }
c+1/2, -a, b | x, -y, -z	{ 2 ‖ -3+-1-11 | 1/2 0 0 }
a+1/2, b+1/2, c+1/2 | -x, y, z	{ m ‖ 1 | 1/2 1/2 1/2 }
a+1/2, -b+1/2, -c | -x, y, z	{ m ‖ 2100 | 1/2 1/2 0 }
-a, b+1/2, -c+1/2 | -x, y, z	{ m ‖ 2010 | 0 1/2 1/2 }
-a+1/2, -b, c+1/2 | -x, y, z	{ m ‖ 2001 | 1/2 0 1/2 }
c+1/2, a+1/2, b+1/2 | -x, y, z	{ m ‖ 3+111 | 1/2 1/2 1/2 }
b+1/2, c+1/2, a+1/2 | -x, y, z	{ m ‖ 3-111 | 1/2 1/2 1/2 }
-b, c+1/2, -a+1/2 | -x, y, z	{ m ‖ 3-1-1-1 | 0 1/2 1/2 }
-c+1/2, -a, b+1/2 | -x, y, z	{ m ‖ 3+1-1-1 | 1/2 0 1/2 }
-b+1/2, -c, a+1/2 | -x, y, z	{ m ‖ 3--11-1 | 1/2 0 1/2 }
c+1/2, -a+1/2, -b | -x, y, z	{ m ‖ 3+-11-1 | 1/2 1/2 0 }
b+1/2, -c+1/2, -a | -x, y, z	{ m ‖ 3--1-11 | 1/2 1/2 0 }
-c, a+1/2, -b+1/2 | -x, y, z	{ m ‖ 3+-1-11 | 0 1/2 1/2 }
-a+3/4, c+3/4, -b+1/4 | -x, y, z	{ m ‖ -4+100 | 3/4 3/4 1/4 }
-a+1/4, -c+3/4, b+3/4 | -x, y, z	{ m ‖ -4-100 | 1/4 3/4 3/4 }
-c+1/4, -b+3/4, a+3/4 | -x, y, z	{ m ‖ -4+010 | 1/4 3/4 3/4 }
c+3/4, -b+1/4, -a+3/4 | -x, y, z	{ m ‖ -4-010 | 3/4 1/4 3/4 }
b+3/4, -a+1/4, -c+3/4 | -x, y, z	{ m ‖ -4+001 | 3/4 1/4 3/4 }
-b+3/4, a+3/4, -c+1/4 | -x, y, z	{ m ‖ -4-001 | 3/4 3/4 1/4 }
-b+1/4, -a+3/4, c+3/4 | -x, y, z	{ m ‖ m110 | 1/4 3/4 3/4 }
b+3/4, a+3/4, c+3/4 | -x, y, z	{ m ‖ m1-10 | 3/4 3/4 3/4 }
a+3/4, -c+1/4, -b+3/4 | -x, y, z	{ m ‖ m011 | 3/4 1/4 3/4 }
a+3/4, c+3/4, b+3/4 | -x, y, z	{ m ‖ m01-1 | 3/4 3/4 3/4 }
-c+3/4, b+3/4, -a+1/4 | -x, y, z	{ m ‖ m101 | 3/4 3/4 1/4 }
c+3/4, b+3/4, a+3/4 | -x, y, z	{ m ‖ m-101 | 3/4 3/4 3/4 }
a+3/4, -c+3/4, b+1/4 | x, -y, -z	{ 2 ‖ 4+100 | 3/4 3/4 1/4 }
a+1/4, c+3/4, -b+3/4 | x, -y, -z	{ 2 ‖ 4-100 | 1/4 3/4 3/4 }
c+1/4, b+3/4, -a+3/4 | x, -y, -z	{ 2 ‖ 4+010 | 1/4 3/4 3/4 }
-c+3/4, b+1/4, a+3/4 | x, -y, -z	{ 2 ‖ 4-010 | 3/4 1/4 3/4 }
-b+3/4, a+1/4, c+3/4 | x, -y, -z	{ 2 ‖ 4+001 | 3/4 1/4 3/4 }
b+3/4, -a+3/4, c+1/4 | x, -y, -z	{ 2 ‖ 4-001 | 3/4 3/4 1/4 }
b+1/4, a+3/4, -c+3/4 | x, -y, -z	{ 2 ‖ 2110 | 1/4 3/4 3/4 }
-b+3/4, -a+3/4, -c+3/4 | x, -y, -z	{ 2 ‖ 21-10 | 3/4 3/4 3/4 }
-a+3/4, c+1/4, b+3/4 | x, -y, -z	{ 2 ‖ 2011 | 3/4 1/4 3/4 }
-a+3/4, -c+3/4, -b+3/4 | x, -y, -z	{ 2 ‖ 201-1 | 3/4 3/4 3/4 }
c+3/4, -b+3/4, a+1/4 | x, -y, -z	{ 2 ‖ 2101 | 3/4 3/4 1/4 }
-c+3/4, -b+3/4, -a+3/4 | x, -y, -z	{ 2 ‖ 2-101 | 3/4 3/4 3/4 }
-a+1/2, -b+1/2, -c+1/2 | x, -y, -z	{ 2 ‖ -1 | 1/2 1/2 1/2 }
-a+1/2, b+1/2, c | x, -y, -z	{ 2 ‖ m100 | 1/2 1/2 0 }
a, -b+1/2, c+1/2 | x, -y, -z	{ 2 ‖ m010 | 0 1/2 1/2 }
a+1/2, b, -c+1/2 | x, -y, -z	{ 2 ‖ m001 | 1/2 0 1/2 }
-c+1/2, -a+1/2, -b+1/2 | x, -y, -z	{ 2 ‖ -3+111 | 1/2 1/2 1/2 }
-b+1/2, -c+1/2, -a+1/2 | x, -y, -z	{ 2 ‖ -3-111 | 1/2 1/2 1/2 }
b, -c+1/2, a+1/2 | x, -y, -z	{ 2 ‖ -3-1-1-1 | 0 1/2 1/2 }
c+1/2, a, -b+1/2 | x, -y, -z	{ 2 ‖ -3+1-1-1 | 1/2 0 1/2 }
b+1/2, c, -a+1/2 | x, -y, -z	{ 2 ‖ -3--11-1 | 1/2 0 1/2 }
-c+1/2, a+1/2, b | x, -y, -z	{ 2 ‖ -3+-11-1 | 1/2 1/2 0 }
-b+1/2, c+1/2, a | x, -y, -z	{ 2 ‖ -3--1-11 | 1/2 1/2 0 }
c, -a+1/2, b+1/2 | x, -y, -z	{ 2 ‖ -3+-1-11 | 0 1/2 1/2 }

Wyckoff Positions

WP	Site symmetry	Representative
16a	$.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{-3}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,0 | 0,0,0)
16b	$.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{3}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/8,1/8,1/8 | 0,0,0)
24c	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/8,0,1/4 | 0,0,0)
24d	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{-4}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(3/8,0,1/4 | 0,0,z)
32e	$.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{3}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,a,a | 0,0,z)
48f	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,0,1/4 | 0,0,z)
48g	$..{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/8,b,-b+1/4 | 0,0,0)
96h	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,b,c | 0,0,z)

Spin Brillouin Zone & k-little co-groups

Wavevector-k	Little co-group
Γ:(0,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{-3}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
H:(1,1,1)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{-3}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
P:(1/2,1/2,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{-3}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
N:(1/2,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
Δ:(0,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Λ:(u,u,u)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{-3}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
D:(1/2,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
G:(1+u,1-u,1)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Σ:(u,u,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
A:(u,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
C:(u,u,w)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
GP:(u,v,w)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{-1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$

Spin Brillouin Zone

Band Representations (Magnon)

12a

k-vector	A↑G(6)
Γ:(0,0,0)	${\Gamma }_1^S(1)\oplus {\Gamma }_3^S(2)\oplus {\Gamma }_5^S(3)$
H:(1,1,1)	$H_4^S{H}_5^S(6)$
P:(1/2,1/2,1/2)	$P_1^S(2)\oplus P_3^S(4)$
N:(1/2,1/2,0)	$3N_1^S(2)$
Δ:(0,v,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_2^S(1)\oplus {\Delta }_3^S{\Delta }_4^S(2)$
Λ:(u,u,u)	${\Lambda }_1^S(1)\oplus {\Lambda }_2^S(1)\oplus 2{\Lambda }_3^S(2)$
D:(1/2,1/2,w)	$3D_1^S(2)$
G:(1+u,1-u,1)	$3G_1^S{G}_2^S(2)$
Σ:(u,u,0)	$3{\Sigma }_1^S(1)\oplus 3{\Sigma }_2^S(1)$
A:(u,v,0)	$6A_1^S(1)$
C:(u,u,w)	$3C_1^S(1)\oplus 3C_2^S(1)$
GP:(u,v,w)	$6G{P}_1^S(1)$

12b

k-vector	A↑G(6)
Γ:(0,0,0)	${\Gamma }_1^S(1)\oplus {\Gamma }_3^S(2)\oplus {\Gamma }_5^S(3)$
H:(1,1,1)	$H_4^S{H}_5^S(6)$
P:(1/2,1/2,1/2)	$P_2^S(2)\oplus P_3^S(4)$
N:(1/2,1/2,0)	$3N_1^S(2)$
Δ:(0,v,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_2^S(1)\oplus {\Delta }_3^S{\Delta }_4^S(2)$
Λ:(u,u,u)	${\Lambda }_1^S(1)\oplus {\Lambda }_2^S(1)\oplus 2{\Lambda }_3^S(2)$
D:(1/2,1/2,w)	$3D_1^S(2)$
G:(1+u,1-u,1)	$3G_1^S{G}_2^S(2)$
Σ:(u,u,0)	$3{\Sigma }_1^S(1)\oplus 3{\Sigma }_2^S(1)$
A:(u,v,0)	$6A_1^S(1)$
C:(u,u,w)	$3C_1^S(1)\oplus 3C_2^S(1)$
GP:(u,v,w)	$6G{P}_1^S(1)$

16c

k-vector	A1↑G(8)
Γ:(0,0,0)	${\Gamma }_1^S(1)\oplus {\Gamma }_2^S(1)\oplus {\Gamma }_4^S(3)\oplus {\Gamma }_5^S(3)$
H:(1,1,1)	$H_1^S{H}_2^S(2)\oplus H_4^S{H}_5^S(6)$
P:(1/2,1/2,1/2)	$2P_3^S(4)$
N:(1/2,1/2,0)	$4N_1^S(2)$
Δ:(0,v,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_2^S(1)\oplus 2{\Delta }_3^S{\Delta }_4^S(2)$
Λ:(u,u,u)	$2{\Lambda }_1^S(1)\oplus 2{\Lambda }_2^S(1)\oplus 2{\Lambda }_3^S(2)$
D:(1/2,1/2,w)	$4D_1^S(2)$
G:(1+u,1-u,1)	$4G_1^S{G}_2^S(2)$
Σ:(u,u,0)	$4{\Sigma }_1^S(1)\oplus 4{\Sigma }_2^S(1)$
A:(u,v,0)	$8A_1^S(1)$
C:(u,u,w)	$4C_1^S(1)\oplus 4C_2^S(1)$
GP:(u,v,w)	$8G{P}_1^S(1)$

24d

k-vector	A↑G(12)
Γ:(0,0,0)	${\Gamma }_1^S(1)\oplus {\Gamma }_2^S(1)\oplus 2{\Gamma }_3^S(2)\oplus {\Gamma }_4^S(3)\oplus {\Gamma }_5^S(3)$
H:(1,1,1)	$2H_4^S{H}_5^S(6)$
P:(1/2,1/2,1/2)	$P_1^S(2)\oplus P_2^S(2)\oplus 2P_3^S(4)$
N:(1/2,1/2,0)	$6N_1^S(2)$
Δ:(0,v,0)	$4{\Delta }_1^S(1)\oplus 4{\Delta }_2^S(1)\oplus 2{\Delta }_3^S{\Delta }_4^S(2)$
Λ:(u,u,u)	$2{\Lambda }_1^S(1)\oplus 2{\Lambda }_2^S(1)\oplus 4{\Lambda }_3^S(2)$
D:(1/2,1/2,w)	$6D_1^S(2)$
G:(1+u,1-u,1)	$6G_1^S{G}_2^S(2)$
Σ:(u,u,0)	$6{\Sigma }_1^S(1)\oplus 6{\Sigma }_2^S(1)$
A:(u,v,0)	$12A_1^S(1)$
C:(u,u,w)	$6C_1^S(1)\oplus 6C_2^S(1)$
GP:(u,v,w)	$12G{P}_1^S(1)$

32e

k-vector	k-vector-G↑	A1↑G(16)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)\oplus {\Gamma }_2^S(2)\oplus {\Gamma }_4^S(6)\oplus {\Gamma }_5^S(6)$
H:(1,1,1)	H:(1,1,1)	$H_1^S{H}_2^S(4)\oplus H_4^S{H}_5^S(12)$
N:(1/2,1/2,0)	N:(1/2,1/2,0)	$4N_1^S(4)$
P:(1/2,1/2,1/2)	P:(1/2,1/2,1/2)	$2P_3^S(8)$
D:(1/2,1/2,w)	D:(1/2,1/2,w)	$4D_1^S(4)$
Δ:(0,v,0)	Δ:(0,v,0)	$2{\Delta }_1^S(2)\oplus 2{\Delta }_2^S(2)\oplus 2{\Delta }_3^S{\Delta }_4^S(4)$
G:(1+u,1-u,1)	G:(1+u,1-u,1)	$4G_1^S{G}_2^S(4)$
Λ:(u,u,u)	Λ:(u,u,u)	$2{\Lambda }_1^S(2)\oplus 2{\Lambda }_2^S(2)\oplus 2{\Lambda }_3^S(4)$
Σ:(u,u,0)	Σ:(u,u,0)	$4{\Sigma }_1^S(2)\oplus 4{\Sigma }_2^S(2)$
A:(u,v,0)	A:(u,v,0)	$8A_1^S(2)$
C:(u,u,w)	C:(u,u,w)	$4C_1^S(2)\oplus 4C_2^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$8G{P}_1^S(2)$

48e

k-vector	A↑G(24)
Γ:(0,0,0)	${\Gamma }_1^S(1)\oplus {\Gamma }_2^S(1)\oplus 2{\Gamma }_3^S(2)\oplus 3{\Gamma }_4^S(3)\oplus 3{\Gamma }_5^S(3)$
H:(1,1,1)	$H_1^S{H}_2^S(2)\oplus H_3^S{H}_3^S(4)\oplus 3H_4^S{H}_5^S(6)$
P:(1/2,1/2,1/2)	$2P_1^S(2)\oplus 2P_2^S(2)\oplus 4P_3^S(4)$
N:(1/2,1/2,0)	$12N_1^S(2)$
Δ:(0,v,0)	$6{\Delta }_1^S(1)\oplus 6{\Delta }_2^S(1)\oplus 6{\Delta }_3^S{\Delta }_4^S(2)$
Λ:(u,u,u)	$4{\Lambda }_1^S(1)\oplus 4{\Lambda }_2^S(1)\oplus 8{\Lambda }_3^S(2)$
D:(1/2,1/2,w)	$12D_1^S(2)$
G:(1+u,1-u,1)	$12G_1^S{G}_2^S(2)$
Σ:(u,u,0)	$12{\Sigma }_1^S(1)\oplus 12{\Sigma }_2^S(1)$
A:(u,v,0)	$24A_1^S(1)$
C:(u,u,w)	$12C_1^S(1)\oplus 12C_2^S(1)$
GP:(u,v,w)	$24G{P}_1^S(1)$

48f

k-vector	k-vector-G↑	A↑G(24)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)\oplus {\Gamma }_2^S(2)\oplus 2{\Gamma }_3^S(4)\oplus {\Gamma }_4^S(6)\oplus {\Gamma }_5^S(6)$
H:(1,1,1)	H:(1,1,1)	$2H_4^S{H}_5^S(12)$
N:(1/2,1/2,0)	N:(1/2,1/2,0)	$6N_1^S(4)$
P:(1/2,1/2,1/2)	P:(1/2,1/2,1/2)	$P_1^S(4)\oplus P_2^S(4)\oplus 2P_3^S(8)$
D:(1/2,1/2,w)	D:(1/2,1/2,w)	$6D_1^S(4)$
Δ:(0,v,0)	Δ:(0,v,0)	$4{\Delta }_1^S(2)\oplus 4{\Delta }_2^S(2)\oplus 2{\Delta }_3^S{\Delta }_4^S(4)$
G:(1+u,1-u,1)	G:(1+u,1-u,1)	$6G_1^S{G}_2^S(4)$
Λ:(u,u,u)	Λ:(u,u,u)	$2{\Lambda }_1^S(2)\oplus 2{\Lambda }_2^S(2)\oplus 4{\Lambda }_3^S(4)$
Σ:(u,u,0)	Σ:(u,u,0)	$6{\Sigma }_1^S(2)\oplus 6{\Sigma }_2^S(2)$
A:(u,v,0)	A:(u,v,0)	$12A_1^S(2)$
C:(u,u,w)	C:(u,u,w)	$6C_1^S(2)\oplus 6C_2^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$12G{P}_1^S(2)$

96h

k-vector	k-vector-G↑	A↑G(48)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)\oplus {\Gamma }_2^S(2)\oplus 2{\Gamma }_3^S(4)\oplus 3{\Gamma }_4^S(6)\oplus 3{\Gamma }_5^S(6)$
H:(1,1,1)	H:(1,1,1)	$H_1^S{H}_2^S(4)\oplus H_3^S{H}_3^S(8)\oplus 3H_4^S{H}_5^S(12)$
N:(1/2,1/2,0)	N:(1/2,1/2,0)	$12N_1^S(4)$
P:(1/2,1/2,1/2)	P:(1/2,1/2,1/2)	$2P_1^S(4)\oplus 2P_2^S(4)\oplus 4P_3^S(8)$
D:(1/2,1/2,w)	D:(1/2,1/2,w)	$12D_1^S(4)$
Δ:(0,v,0)	Δ:(0,v,0)	$6{\Delta }_1^S(2)\oplus 6{\Delta }_2^S(2)\oplus 6{\Delta }_3^S{\Delta }_4^S(4)$
G:(1+u,1-u,1)	G:(1+u,1-u,1)	$12G_1^S{G}_2^S(4)$
Λ:(u,u,u)	Λ:(u,u,u)	$4{\Lambda }_1^S(2)\oplus 4{\Lambda }_2^S(2)\oplus 8{\Lambda }_3^S(4)$
Σ:(u,u,0)	Σ:(u,u,0)	$12{\Sigma }_1^S(2)\oplus 12{\Sigma }_2^S(2)$
A:(u,v,0)	A:(u,v,0)	$24A_1^S(2)$
C:(u,u,w)	C:(u,u,w)	$12C_1^S(2)\oplus 12C_2^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$24G{P}_1^S(2)$