Information of spin space group $P\ce{^{1}{m}}\ce{^{1}{\text{-}3}}\ce{^{1}{m}}\ce{^{\text{-}1}{(1/2 \ 1/2 \ 1/2)}}\ce{^{\infty m}{1}}$ ( nSSG:221.229.2.1 )

General Positions

The continuously infinite group ^∞1 is omitted.

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

Wyckoff Positions

WP	Site symmetry	Representative
2a	$\ce{^{1}{m}}\ce{^{1}{-3}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $	(0,0,0 | 0,0,z)
6b	$\ce{^{1}{4}}/\ce{^{1}{m}}\ce{^{1}{m}}.\ce{^{1}{m}}\ce{^{\infty m}{1}} $	(0,1/2,1/2 | 0,0,z)
8c	$.\ce{^{-1}{-3}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $	(1/4,1/4,1/4 | 0,0,0)
12d	$\ce{^{-1}{-4}}\ce{^{1}{m}}.\ce{^{-1}{2}}\ce{^{\infty m}{1}} $	(1/4,0,1/2 | 0,0,0)
12e	$\ce{^{1}{4}}\ce{^{1}{m}}.\ce{^{1}{m}}\ce{^{\infty m}{1}} $	(a,0,0 | 0,0,z)
16f	$.\ce{^{1}{3}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $	(a,a,a | 0,0,z)
24g	$\ce{^{1}{2}}\ce{^{1}{m}}\ce{^{1}{m}}..\ce{^{\infty m}{1}} $	(a,0,1/2 | 0,0,z)
24h	$\ce{^{1}{m}}.\ce{^{1}{2}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $	(0,b,b | 0,0,z)
48i	$..\ce{^{-1}{2}}\ce{^{\infty m}{1}} $	(1/4,b,-b+1/2 | 0,0,0)
48j	$\ce{^{1}{m}}..\ce{^{\infty m}{1}} $	(0,b,c | 0,0,z)
48k	$..\ce{^{1}{m}}\ce{^{\infty m}{1}} $	(a,a,c | 0,0,z)
96l	$\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}{m}}\ce{^{1}{-3}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $
R:(1/2,1/2,1/2)	$\ce{^{1}{m}}\ce{^{1}{-3}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $
M:(1/2,1/2,0)	$\ce{^{1}{4/}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $
X:(0,1/2,0)	$\ce{^{1}{4/}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $
Δ:(0,v,0)	$\ce{^{1}{4/}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $
T:(1/2,1/2,w)	$\ce{^{1}{4/}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $
Λ:(u,u,u)	$\ce{^{m}{-3}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $
S:(u,1/2,u)	$\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $
Σ:(u,u,0)	$\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $
Z:(u,1/2,0)	$\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $
A:(u,v,0)	$\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $
B:(u,1/2,w)	$\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $
C:(u,u,w)	$\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $
GP:(u,v,w)	$\ce{^{m}{-1}}\ce{^{\infty 2}{1}} $

Spin Brillouin Zone

Band Representations (Magnon)

2a

k-vector	A1g↑G(2)
Γ:(0,0,0)	$Γ_{1}^{S,+}(2) $
R:(1/2,1/2,1/2)	$R_{1}^{S,+}(2) $
M:(1/2,1/2,0)	$M_{1}^{S,+}(2) $
X:(0,1/2,0)	$X_{1}^{S,+}(2) $
Δ:(0,v,0)	$Δ_{1}^{S}(2) $
T:(1/2,1/2,w)	$T_{1}^{S}(2) $
Λ:(u,u,u)	$Λ_{1}^{S}(2) $
S:(u,1/2,u)	$S_{1}^{S}(2) $
Σ:(u,u,0)	$Σ_{1}^{S}(2) $
Z:(u,1/2,0)	$Z_{1}^{S}(2) $
A:(u,v,0)	$A_{1}^{S}(2) $
B:(u,1/2,w)	$B_{1}^{S}(2) $
C:(u,u,w)	$C_{1}^{S}(2) $
GP:(u,v,w)	$GP_{1}^{S}(2) $

6b

k-vector	A1g↑G(6)
Γ:(0,0,0)	$Γ_{1}^{S,+}(2)⊕Γ_{3}^{S,+}(4) $
R:(1/2,1/2,1/2)	$R_{5}^{S,+}(6) $
M:(1/2,1/2,0)	$M_{4}^{S,+}(2)⊕M_{5}^{S,-}(4) $
X:(0,1/2,0)	$X_{1}^{S,+}(2)⊕X_{3}^{S,-}(2)⊕X_{4}^{S,-}(2) $
Δ:(0,v,0)	$2Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2) $
T:(1/2,1/2,w)	$T_{3}^{S}(2)⊕T_{5}^{S}(4) $
Λ:(u,u,u)	$Λ_{1}^{S}(2)⊕Λ_{3}^{S}(4) $
S:(u,1/2,u)	$S_{1}^{S}(2)⊕S_{3}^{S}(2)⊕S_{4}^{S}(2) $
Σ:(u,u,0)	$2Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2) $
Z:(u,1/2,0)	$Z_{1}^{S}(2)⊕2Z_{4}^{S}(2) $
A:(u,v,0)	$3A_{1}^{S}(2) $
B:(u,1/2,w)	$B_{1}^{S}(2)⊕2B_{2}^{S}(2) $
C:(u,u,w)	$2C_{1}^{S}(2)⊕C_{2}^{S}(2) $
GP:(u,v,w)	$3GP_{1}^{S}(2) $

12e

k-vector	A1↑G(12)
Γ:(0,0,0)	$Γ_{1}^{S,+}(2)⊕Γ_{3}^{S,+}(4)⊕Γ_{4}^{S,-}(6) $
R:(1/2,1/2,1/2)	$R_{1}^{S,+}(2)⊕R_{3}^{S,+}(4)⊕R_{4}^{S,-}(6) $
M:(1/2,1/2,0)	$2M_{1}^{S,+}(2)⊕M_{2}^{S,+}(2)⊕M_{3}^{S,-}(2)⊕M_{5}^{S,-}(4) $
X:(0,1/2,0)	$2X_{1}^{S,+}(2)⊕X_{2}^{S,+}(2)⊕X_{3}^{S,-}(2)⊕X_{5}^{S,-}(4) $
Δ:(0,v,0)	$3Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2)⊕Δ_{5}^{S}(4) $
T:(1/2,1/2,w)	$3T_{1}^{S}(2)⊕T_{2}^{S}(2)⊕T_{5}^{S}(4) $
Λ:(u,u,u)	$2Λ_{1}^{S}(2)⊕2Λ_{3}^{S}(4) $
S:(u,1/2,u)	$3S_{1}^{S}(2)⊕2S_{2}^{S}(2)⊕S_{3}^{S}(2) $
Σ:(u,u,0)	$3Σ_{1}^{S}(2)⊕2Σ_{2}^{S}(2)⊕Σ_{3}^{S}(2) $
Z:(u,1/2,0)	$4Z_{1}^{S}(2)⊕Z_{3}^{S}(2)⊕Z_{4}^{S}(2) $
A:(u,v,0)	$5A_{1}^{S}(2)⊕A_{2}^{S}(2) $
B:(u,1/2,w)	$5B_{1}^{S}(2)⊕B_{2}^{S}(2) $
C:(u,u,w)	$4C_{1}^{S}(2)⊕2C_{2}^{S}(2) $
GP:(u,v,w)	$6GP_{1}^{S}(2) $

16f

k-vector	A1↑G(16)
Γ:(0,0,0)	$Γ_{1}^{S,+}(2)⊕Γ_{2}^{S,-}(2)⊕Γ_{4}^{S,-}(6)⊕Γ_{5}^{S,+}(6) $
R:(1/2,1/2,1/2)	$R_{1}^{S,+}(2)⊕R_{2}^{S,-}(2)⊕R_{4}^{S,-}(6)⊕R_{5}^{S,+}(6) $
M:(1/2,1/2,0)	$M_{1}^{S,+}(2)⊕M_{2}^{S,-}(2)⊕M_{3}^{S,-}(2)⊕M_{4}^{S,+}(2)⊕M_{5}^{S,+}(4)⊕M_{5}^{S,-}(4) $
X:(0,1/2,0)	$X_{1}^{S,+}(2)⊕X_{2}^{S,-}(2)⊕X_{3}^{S,-}(2)⊕X_{4}^{S,+}(2)⊕X_{5}^{S,+}(4)⊕X_{5}^{S,-}(4) $
Δ:(0,v,0)	$2Δ_{1}^{S}(2)⊕2Δ_{3}^{S}(2)⊕2Δ_{5}^{S}(4) $
T:(1/2,1/2,w)	$2T_{1}^{S}(2)⊕2T_{3}^{S}(2)⊕2T_{5}^{S}(4) $
Λ:(u,u,u)	$4Λ_{1}^{S}(2)⊕2Λ_{3}^{S}(4) $
S:(u,1/2,u)	$3S_{1}^{S}(2)⊕S_{2}^{S}(2)⊕3S_{3}^{S}(2)⊕S_{4}^{S}(2) $
Σ:(u,u,0)	$3Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2)⊕3Σ_{3}^{S}(2)⊕Σ_{4}^{S}(2) $
Z:(u,1/2,0)	$2Z_{1}^{S}(2)⊕2Z_{2}^{S}(2)⊕2Z_{3}^{S}(2)⊕2Z_{4}^{S}(2) $
A:(u,v,0)	$4A_{1}^{S}(2)⊕4A_{2}^{S}(2) $
B:(u,1/2,w)	$4B_{1}^{S}(2)⊕4B_{2}^{S}(2) $
C:(u,u,w)	$6C_{1}^{S}(2)⊕2C_{2}^{S}(2) $
GP:(u,v,w)	$8GP_{1}^{S}(2) $

24g

k-vector	A1↑G(24)
Γ:(0,0,0)	$Γ_{1}^{S,+}(2)⊕Γ_{2}^{S,+}(2)⊕2Γ_{3}^{S,+}(4)⊕Γ_{4}^{S,-}(6)⊕Γ_{5}^{S,-}(6) $
R:(1/2,1/2,1/2)	$R_{4}^{S,+}(6)⊕R_{4}^{S,-}(6)⊕R_{5}^{S,+}(6)⊕R_{5}^{S,-}(6) $
M:(1/2,1/2,0)	$M_{1}^{S,+}(2)⊕M_{2}^{S,+}(2)⊕M_{3}^{S,+}(2)⊕M_{4}^{S,+}(2)⊕M_{5}^{S,+}(4)⊕3M_{5}^{S,-}(4) $
X:(0,1/2,0)	$2X_{1}^{S,+}(2)⊕2X_{2}^{S,+}(2)⊕2X_{3}^{S,-}(2)⊕2X_{4}^{S,-}(2)⊕X_{5}^{S,+}(4)⊕X_{5}^{S,-}(4) $
Δ:(0,v,0)	$4Δ_{1}^{S}(2)⊕4Δ_{2}^{S}(2)⊕2Δ_{5}^{S}(4) $
T:(1/2,1/2,w)	$T_{1}^{S}(2)⊕T_{2}^{S}(2)⊕T_{3}^{S}(2)⊕T_{4}^{S}(2)⊕4T_{5}^{S}(4) $
Λ:(u,u,u)	$2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2)⊕4Λ_{3}^{S}(4) $
S:(u,1/2,u)	$3S_{1}^{S}(2)⊕3S_{2}^{S}(2)⊕3S_{3}^{S}(2)⊕3S_{4}^{S}(2) $
Σ:(u,u,0)	$5Σ_{1}^{S}(2)⊕5Σ_{2}^{S}(2)⊕Σ_{3}^{S}(2)⊕Σ_{4}^{S}(2) $
Z:(u,1/2,0)	$5Z_{1}^{S}(2)⊕Z_{2}^{S}(2)⊕Z_{3}^{S}(2)⊕5Z_{4}^{S}(2) $
A:(u,v,0)	$10A_{1}^{S}(2)⊕2A_{2}^{S}(2) $
B:(u,1/2,w)	$6B_{1}^{S}(2)⊕6B_{2}^{S}(2) $
C:(u,u,w)	$6C_{1}^{S}(2)⊕6C_{2}^{S}(2) $
GP:(u,v,w)	$12GP_{1}^{S}(2) $

24h

k-vector	A1↑G(24)
Γ:(0,0,0)	$Γ_{1}^{S,+}(2)⊕Γ_{3}^{S,+}(4)⊕Γ_{4}^{S,-}(6)⊕Γ_{5}^{S,+}(6)⊕Γ_{5}^{S,-}(6) $
R:(1/2,1/2,1/2)	$R_{1}^{S,+}(2)⊕R_{3}^{S,+}(4)⊕R_{4}^{S,-}(6)⊕R_{5}^{S,+}(6)⊕R_{5}^{S,-}(6) $
M:(1/2,1/2,0)	$2M_{1}^{S,+}(2)⊕M_{2}^{S,+}(2)⊕M_{3}^{S,-}(2)⊕M_{4}^{S,+}(2)⊕M_{4}^{S,-}(2)⊕M_{5}^{S,+}(4)⊕2M_{5}^{S,-}(4) $
X:(0,1/2,0)	$2X_{1}^{S,+}(2)⊕X_{2}^{S,+}(2)⊕X_{3}^{S,-}(2)⊕X_{4}^{S,+}(2)⊕X_{4}^{S,-}(2)⊕X_{5}^{S,+}(4)⊕2X_{5}^{S,-}(4) $
Δ:(0,v,0)	$3Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2)⊕Δ_{3}^{S}(2)⊕3Δ_{5}^{S}(4) $
T:(1/2,1/2,w)	$3T_{1}^{S}(2)⊕2T_{2}^{S}(2)⊕T_{3}^{S}(2)⊕3T_{5}^{S}(4) $
Λ:(u,u,u)	$3Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2)⊕4Λ_{3}^{S}(4) $
S:(u,1/2,u)	$5S_{1}^{S}(2)⊕3S_{2}^{S}(2)⊕2S_{3}^{S}(2)⊕2S_{4}^{S}(2) $
Σ:(u,u,0)	$5Σ_{1}^{S}(2)⊕3Σ_{2}^{S}(2)⊕2Σ_{3}^{S}(2)⊕2Σ_{4}^{S}(2) $
Z:(u,1/2,0)	$5Z_{1}^{S}(2)⊕Z_{2}^{S}(2)⊕3Z_{3}^{S}(2)⊕3Z_{4}^{S}(2) $
A:(u,v,0)	$8A_{1}^{S}(2)⊕4A_{2}^{S}(2) $
B:(u,1/2,w)	$8B_{1}^{S}(2)⊕4B_{2}^{S}(2) $
C:(u,u,w)	$7C_{1}^{S}(2)⊕5C_{2}^{S}(2) $
GP:(u,v,w)	$12GP_{1}^{S}(2) $

48j

k-vector	A'↑G(48)
Γ:(0,0,0)	$Γ_{1}^{S,+}(2)⊕Γ_{2}^{S,+}(2)⊕2Γ_{3}^{S,+}(4)⊕Γ_{4}^{S,+}(6)⊕2Γ_{4}^{S,-}(6)⊕Γ_{5}^{S,+}(6)⊕2Γ_{5}^{S,-}(6) $
R:(1/2,1/2,1/2)	$R_{1}^{S,+}(2)⊕R_{2}^{S,+}(2)⊕2R_{3}^{S,+}(4)⊕R_{4}^{S,+}(6)⊕2R_{4}^{S,-}(6)⊕R_{5}^{S,+}(6)⊕2R_{5}^{S,-}(6) $
M:(1/2,1/2,0)	$3M_{1}^{S,+}(2)⊕3M_{2}^{S,+}(2)⊕M_{3}^{S,+}(2)⊕2M_{3}^{S,-}(2)⊕M_{4}^{S,+}(2)⊕2M_{4}^{S,-}(2)⊕2M_{5}^{S,+}(4)⊕4M_{5}^{S,-}(4) $
X:(0,1/2,0)	$3X_{1}^{S,+}(2)⊕3X_{2}^{S,+}(2)⊕X_{3}^{S,+}(2)⊕2X_{3}^{S,-}(2)⊕X_{4}^{S,+}(2)⊕2X_{4}^{S,-}(2)⊕2X_{5}^{S,+}(4)⊕4X_{5}^{S,-}(4) $
Δ:(0,v,0)	$5Δ_{1}^{S}(2)⊕5Δ_{2}^{S}(2)⊕Δ_{3}^{S}(2)⊕Δ_{4}^{S}(2)⊕6Δ_{5}^{S}(4) $
T:(1/2,1/2,w)	$5T_{1}^{S}(2)⊕5T_{2}^{S}(2)⊕T_{3}^{S}(2)⊕T_{4}^{S}(2)⊕6T_{5}^{S}(4) $
Λ:(u,u,u)	$4Λ_{1}^{S}(2)⊕4Λ_{2}^{S}(2)⊕8Λ_{3}^{S}(4) $
S:(u,1/2,u)	$8S_{1}^{S}(2)⊕8S_{2}^{S}(2)⊕4S_{3}^{S}(2)⊕4S_{4}^{S}(2) $
Σ:(u,u,0)	$8Σ_{1}^{S}(2)⊕8Σ_{2}^{S}(2)⊕4Σ_{3}^{S}(2)⊕4Σ_{4}^{S}(2) $
Z:(u,1/2,0)	$10Z_{1}^{S}(2)⊕2Z_{2}^{S}(2)⊕6Z_{3}^{S}(2)⊕6Z_{4}^{S}(2) $
A:(u,v,0)	$16A_{1}^{S}(2)⊕8A_{2}^{S}(2) $
B:(u,1/2,w)	$16B_{1}^{S}(2)⊕8B_{2}^{S}(2) $
C:(u,u,w)	$12C_{1}^{S}(2)⊕12C_{2}^{S}(2) $
GP:(u,v,w)	$24GP_{1}^{S}(2) $

48k

k-vector	A'↑G(48)
Γ:(0,0,0)	$Γ_{1}^{S,+}(2)⊕Γ_{2}^{S,-}(2)⊕Γ_{3}^{S,+}(4)⊕Γ_{3}^{S,-}(4)⊕Γ_{4}^{S,+}(6)⊕2Γ_{4}^{S,-}(6)⊕2Γ_{5}^{S,+}(6)⊕Γ_{5}^{S,-}(6) $
R:(1/2,1/2,1/2)	$R_{1}^{S,+}(2)⊕R_{2}^{S,-}(2)⊕R_{3}^{S,+}(4)⊕R_{3}^{S,-}(4)⊕R_{4}^{S,+}(6)⊕2R_{4}^{S,-}(6)⊕2R_{5}^{S,+}(6)⊕R_{5}^{S,-}(6) $
M:(1/2,1/2,0)	$2M_{1}^{S,+}(2)⊕M_{1}^{S,-}(2)⊕M_{2}^{S,+}(2)⊕2M_{2}^{S,-}(2)⊕M_{3}^{S,+}(2)⊕2M_{3}^{S,-}(2)⊕2M_{4}^{S,+}(2)⊕M_{4}^{S,-}(2)⊕3M_{5}^{S,+}(4)⊕3M_{5}^{S,-}(4) $
X:(0,1/2,0)	$2X_{1}^{S,+}(2)⊕X_{1}^{S,-}(2)⊕X_{2}^{S,+}(2)⊕2X_{2}^{S,-}(2)⊕X_{3}^{S,+}(2)⊕2X_{3}^{S,-}(2)⊕2X_{4}^{S,+}(2)⊕X_{4}^{S,-}(2)⊕3X_{5}^{S,+}(4)⊕3X_{5}^{S,-}(4) $
Δ:(0,v,0)	$4Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2)⊕4Δ_{3}^{S}(2)⊕2Δ_{4}^{S}(2)⊕6Δ_{5}^{S}(4) $
T:(1/2,1/2,w)	$4T_{1}^{S}(2)⊕2T_{2}^{S}(2)⊕4T_{3}^{S}(2)⊕2T_{4}^{S}(2)⊕6T_{5}^{S}(4) $
Λ:(u,u,u)	$6Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2)⊕8Λ_{3}^{S}(4) $
S:(u,1/2,u)	$7S_{1}^{S}(2)⊕5S_{2}^{S}(2)⊕7S_{3}^{S}(2)⊕5S_{4}^{S}(2) $
Σ:(u,u,0)	$7Σ_{1}^{S}(2)⊕5Σ_{2}^{S}(2)⊕7Σ_{3}^{S}(2)⊕5Σ_{4}^{S}(2) $
Z:(u,1/2,0)	$6Z_{1}^{S}(2)⊕6Z_{2}^{S}(2)⊕6Z_{3}^{S}(2)⊕6Z_{4}^{S}(2) $
A:(u,v,0)	$12A_{1}^{S}(2)⊕12A_{2}^{S}(2) $
B:(u,1/2,w)	$12B_{1}^{S}(2)⊕12B_{2}^{S}(2) $
C:(u,u,w)	$14C_{1}^{S}(2)⊕10C_{2}^{S}(2) $
GP:(u,v,w)	$24GP_{1}^{S}(2) $

96l

k-vector	A↑G(96)
Γ:(0,0,0)	$Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2)⊕Γ_{2}^{S,+}(2)⊕Γ_{2}^{S,-}(2)⊕2Γ_{3}^{S,+}(4)⊕2Γ_{3}^{S,-}(4)⊕3Γ_{4}^{S,+}(6)⊕3Γ_{4}^{S,-}(6)⊕3Γ_{5}^{S,+}(6)⊕3Γ_{5}^{S,-}(6) $
R:(1/2,1/2,1/2)	$R_{1}^{S,+}(2)⊕R_{1}^{S,-}(2)⊕R_{2}^{S,+}(2)⊕R_{2}^{S,-}(2)⊕2R_{3}^{S,+}(4)⊕2R_{3}^{S,-}(4)⊕3R_{4}^{S,+}(6)⊕3R_{4}^{S,-}(6)⊕3R_{5}^{S,+}(6)⊕3R_{5}^{S,-}(6) $
M:(1/2,1/2,0)	$3M_{1}^{S,+}(2)⊕3M_{1}^{S,-}(2)⊕3M_{2}^{S,+}(2)⊕3M_{2}^{S,-}(2)⊕3M_{3}^{S,+}(2)⊕3M_{3}^{S,-}(2)⊕3M_{4}^{S,+}(2)⊕3M_{4}^{S,-}(2)⊕6M_{5}^{S,+}(4)⊕6M_{5}^{S,-}(4) $
X:(0,1/2,0)	$3X_{1}^{S,+}(2)⊕3X_{1}^{S,-}(2)⊕3X_{2}^{S,+}(2)⊕3X_{2}^{S,-}(2)⊕3X_{3}^{S,+}(2)⊕3X_{3}^{S,-}(2)⊕3X_{4}^{S,+}(2)⊕3X_{4}^{S,-}(2)⊕6X_{5}^{S,+}(4)⊕6X_{5}^{S,-}(4) $
Δ:(0,v,0)	$6Δ_{1}^{S}(2)⊕6Δ_{2}^{S}(2)⊕6Δ_{3}^{S}(2)⊕6Δ_{4}^{S}(2)⊕12Δ_{5}^{S}(4) $
T:(1/2,1/2,w)	$6T_{1}^{S}(2)⊕6T_{2}^{S}(2)⊕6T_{3}^{S}(2)⊕6T_{4}^{S}(2)⊕12T_{5}^{S}(4) $
Λ:(u,u,u)	$8Λ_{1}^{S}(2)⊕8Λ_{2}^{S}(2)⊕16Λ_{3}^{S}(4) $
S:(u,1/2,u)	$12S_{1}^{S}(2)⊕12S_{2}^{S}(2)⊕12S_{3}^{S}(2)⊕12S_{4}^{S}(2) $
Σ:(u,u,0)	$12Σ_{1}^{S}(2)⊕12Σ_{2}^{S}(2)⊕12Σ_{3}^{S}(2)⊕12Σ_{4}^{S}(2) $
Z:(u,1/2,0)	$12Z_{1}^{S}(2)⊕12Z_{2}^{S}(2)⊕12Z_{3}^{S}(2)⊕12Z_{4}^{S}(2) $
A:(u,v,0)	$24A_{1}^{S}(2)⊕24A_{2}^{S}(2) $
B:(u,1/2,w)	$24B_{1}^{S}(2)⊕24B_{2}^{S}(2) $
C:(u,u,w)	$24C_{1}^{S}(2)⊕24C_{2}^{S}(2) $
GP:(u,v,w)	$48GP_{1}^{S}(2) $