Information of spin space group $F\ce{^{\text{-}1}{\text{-}4}}\ce{^{1}{3}}\ce{^{\text{-}1}{c}}\ce{^{\infty m}{1}}$ ( nSSG:196.219.1.1 )

General Positions

The continuously infinite group ^∞1 is omitted.

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

Wyckoff Positions

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

Spin Brillouin Zone & k-little co-groups

Wavevector-k	Little co-group
Γ:(0,0,0)	$\ce{^{-1}{-4}}\ce{^{1}{3}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $
X:(0,1,0)	$\ce{^{-1}{-4}}\ce{^{1}{2}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $
L:(1/2,1/2,1/2)	$\ce{^{1}{3}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $
W:(1/2,1,0)	$\ce{^{2}{-4}}\ce{^{m}{2}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $
Δ:(0,v,0)	$\ce{^{-1}{-4}}\ce{^{m}{2}}\ce{^{2}{m}}\ce{^{\infty}{1}} $
Λ:(u,u,u)	$\ce{^{1}{3}}\ce{^{2}{m}}\ce{^{\infty}{1}} $
Q:(1/2,v,1-v)	$\ce{^{-1}{m}}\ce{^{\infty}{1}} $
Σ:(u,u,0)	$\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $
V:(u,1,0)	$\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $
A:(u,v,0)	$\ce{^{m}{2}}\ce{^{\infty}{1}} $
C:(u,u,w)	$\ce{^{2}{m}}\ce{^{\infty}{1}} $
GP:(u,v,w)	$\ce{^{1}{1}}\ce{^{\infty}{1}} $

Spin Brillouin Zone

Band Representations (Magnon)

8a

k-vector	k-vector-G↑	A↑G(2)
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S}(2) $
L:(1/2,1/2,1/2)	L:(1/2,1/2,1/2)	$L_{1}^{S}(2) $
W:(1/2,1,0)	W:(1/2,1,0)	$W_{1}^{S}(2) $
X:(0,1,0)	X:(0,1,0)	$X_{1}^{S}(2) $
Δ:(0,v,0)	Δ:(0,v,0)	$Δ_{1}^{S}(2) $
Λ:(u,u,u)	Λ:(u,u,u)	$Λ_{1}^{S}(2) $
Q:(1/2,v,1-v)	Q:(1/2,v,1-v)	$Q_{1}^{S}(2) $
Σ:(u,u,0)	Σ:(u,u,0)	$Σ_{1}^{S}(2) $
V:(u,1,0)	V:(u,1,0)	$2V_{1}^{S}(1)$	Spin Splitting
A:(u,v,0)	A:(u,v,0)	$2A_{1}^{S}(1)$	Spin Splitting
C:(u,u,w)	C:(u,u,w)	$C_{1}^{S}(2) $
GP:(u,v,w)	GP:(u,v,w)	$2GP_{1}^{S}(1)$	Spin Splitting

8b

k-vector	k-vector-G↑	A↑G(2)
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S}(2) $
L:(1/2,1/2,1/2)	L:(1/2,1/2,1/2)	$L_{1}^{S}(2) $
W:(1/2,1,0)	W:(1/2,1,0)	$W_{2}^{S}(2) $
X:(0,1,0)	X:(0,1,0)	$X_{4}^{S}(2) $
Δ:(0,v,0)	Δ:(0,v,0)	$Δ_{1}^{S}(2) $
Λ:(u,u,u)	Λ:(u,u,u)	$Λ_{1}^{S}(2) $
Q:(1/2,v,1-v)	Q:(1/2,v,1-v)	$Q_{1}^{S}(2) $
Σ:(u,u,0)	Σ:(u,u,0)	$Σ_{1}^{S}(2) $
V:(u,1,0)	V:(u,1,0)	$2V_{2}^{S}(1)$	Spin Splitting
A:(u,v,0)	A:(u,v,0)	$2A_{1}^{S}(1)$	Spin Splitting
C:(u,u,w)	C:(u,u,w)	$C_{1}^{S}(2) $
GP:(u,v,w)	GP:(u,v,w)	$2GP_{1}^{S}(1)$	Spin Splitting

32e

k-vector	k-vector-G↑	A1↑G(8)
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S}(2)⊕Γ_{4}^{S}(6) $
L:(1/2,1/2,1/2)	L:(1/2,1/2,1/2)	$2L_{1}^{S}(1)⊕2L_{2}^{S}(1)⊕4L_{3}^{S}(1) $
W:(1/2,1,0)	W:(1/2,1,0)	$2W_{1}^{S}(2)⊕2W_{2}^{S}(2) $
X:(0,1,0)	X:(0,1,0)	$X_{1}^{S}(2)⊕X_{2}^{S}(2)⊕X_{3}^{S}(2)⊕X_{4}^{S}(2) $
Δ:(0,v,0)	Δ:(0,v,0)	$2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $
Λ:(u,u,u)	Λ:(u,u,u)	$2Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2)⊕Λ_{3}^{S}(2) $
Q:(1/2,v,1-v)	Q:(1/2,v,1-v)	$4Q_{1}^{S}(2) $
Σ:(u,u,0)	Σ:(u,u,0)	$4Σ_{1}^{S}(2) $
V:(u,1,0)	V:(u,1,0)	$4V_{1}^{S}(1)⊕4V_{2}^{S}(1)$	Spin Splitting
A:(u,v,0)	A:(u,v,0)	$8A_{1}^{S}(1)$	Spin Splitting
C:(u,u,w)	C:(u,u,w)	$4C_{1}^{S}(2) $
GP:(u,v,w)	GP:(u,v,w)	$8GP_{1}^{S}(1)$	Spin Splitting

48f

k-vector	k-vector-G↑	A↑G(12)
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S}(2)⊕Γ_{2}^{S}Γ_{3}^{S}(4)⊕Γ_{4}^{S}(6) $
L:(1/2,1/2,1/2)	L:(1/2,1/2,1/2)	$2L_{1}^{S}(2)⊕2L_{2}^{S}L_{3}^{S}(4) $
W:(1/2,1,0)	W:(1/2,1,0)	$4W_{1}^{S}(2)⊕2W_{2}^{S}(2) $
X:(0,1,0)	X:(0,1,0)	$3 X_{1}^{S}(2)⊕X_{2}^{S}(2)⊕X_{3}^{S}(2)⊕X_{4}^{S}(2) $
Δ:(0,v,0)	Δ:(0,v,0)	$4Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $
Λ:(u,u,u)	Λ:(u,u,u)	$2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2)⊕2Λ_{3}^{S}(2) $
Q:(1/2,v,1-v)	Q:(1/2,v,1-v)	$6Q_{1}^{S}(2) $
Σ:(u,u,0)	Σ:(u,u,0)	$6Σ_{1}^{S}(2) $
V:(u,1,0)	V:(u,1,0)	$8V_{1}^{S}(1)⊕4V_{2}^{S}(1)$	Spin Splitting
A:(u,v,0)	A:(u,v,0)	$12A_{1}^{S}(1)$	Spin Splitting
C:(u,u,w)	C:(u,u,w)	$6C_{1}^{S}(2) $
GP:(u,v,w)	GP:(u,v,w)	$12GP_{1}^{S}(1)$	Spin Splitting

48g

k-vector	k-vector-G↑	A↑G(12)
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S}(2)⊕Γ_{2}^{S}Γ_{3}^{S}(4)⊕Γ_{4}^{S}(6) $
L:(1/2,1/2,1/2)	L:(1/2,1/2,1/2)	$2L_{1}^{S}(2)⊕2L_{2}^{S}L_{3}^{S}(4) $
W:(1/2,1,0)	W:(1/2,1,0)	$2W_{1}^{S}(2)⊕4W_{2}^{S}(2) $
X:(0,1,0)	X:(0,1,0)	$X_{1}^{S}(2)⊕X_{2}^{S}(2)⊕X_{3}^{S}(2)⊕3 X_{4}^{S}(2) $
Δ:(0,v,0)	Δ:(0,v,0)	$4Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $
Λ:(u,u,u)	Λ:(u,u,u)	$2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2)⊕2Λ_{3}^{S}(2) $
Q:(1/2,v,1-v)	Q:(1/2,v,1-v)	$6Q_{1}^{S}(2) $
Σ:(u,u,0)	Σ:(u,u,0)	$6Σ_{1}^{S}(2) $
V:(u,1,0)	V:(u,1,0)	$4V_{1}^{S}(1)⊕8V_{2}^{S}(1)$	Spin Splitting
A:(u,v,0)	A:(u,v,0)	$12A_{1}^{S}(1)$	Spin Splitting
C:(u,u,w)	C:(u,u,w)	$6C_{1}^{S}(2) $
GP:(u,v,w)	GP:(u,v,w)	$12GP_{1}^{S}(1)$	Spin Splitting

96h

k-vector	k-vector-G↑	A↑G(24)
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S}(2)⊕Γ_{2}^{S}Γ_{3}^{S}(4)⊕3Γ_{4}^{S}(6) $
L:(1/2,1/2,1/2)	L:(1/2,1/2,1/2)	$4L_{1}^{S}(2)⊕4L_{2}^{S}L_{3}^{S}(4) $
W:(1/2,1,0)	W:(1/2,1,0)	$6W_{1}^{S}(2)⊕6W_{2}^{S}(2) $
X:(0,1,0)	X:(0,1,0)	$3X_{1}^{S}(2)⊕3X_{2}^{S}(2)⊕3X_{3}^{S}(2)⊕3X_{4}^{S}(2) $
Δ:(0,v,0)	Δ:(0,v,0)	$6Δ_{1}^{S}(2)⊕6Δ_{2}^{S}(2) $
Λ:(u,u,u)	Λ:(u,u,u)	$4Λ_{1}^{S}(2)⊕4Λ_{2}^{S}(2)⊕4Λ_{3}^{S}(2) $
Q:(1/2,v,1-v)	Q:(1/2,v,1-v)	$12Q_{1}^{S}(2) $
Σ:(u,u,0)	Σ:(u,u,0)	$12Σ_{1}^{S}(2) $
V:(u,1,0)	V:(u,1,0)	$12V_{1}^{S}(1)⊕12V_{2}^{S}(1)$	Spin Splitting
A:(u,v,0)	A:(u,v,0)	$24A_{1}^{S}(1)$	Spin Splitting
C:(u,u,w)	C:(u,u,w)	$12C_{1}^{S}(2) $
GP:(u,v,w)	GP:(u,v,w)	$24GP_{1}^{S}(1)$	Spin Splitting