Spin Space Group Information

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+1/2, b, -c \| x, y, z	{ 1 ‖ 2₀₁₀ \| 1/2 0 0 }
-a+1/2, -b, c \| x, y, z	{ 1 ‖ 2₀₀₁ \| 1/2 0 0 }
-a, -b, -c \| x, y, z	{ 1 ‖ -1 \| 0 }
-a, b, c \| x, y, z	{ 1 ‖ m₁₀₀ \| 0 }
a+1/2, -b, c \| x, y, z	{ 1 ‖ m₀₁₀ \| 1/2 0 0 }
a+1/2, b, -c \| x, y, z	{ 1 ‖ m₀₀₁ \| 1/2 0 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, b+1/2, -c \| x, y, z	{ 1 ‖ 2₀₁₀ \| 0 1/2 0 }
-a, -b+1/2, c \| x, y, z	{ 1 ‖ 2₀₀₁ \| 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 ‖ m₁₀₀ \| 1/2 1/2 0 }
a, -b+1/2, c \| x, y, z	{ 1 ‖ m₀₁₀ \| 0 1/2 0 }
a, b+1/2, -c \| x, y, z	{ 1 ‖ m₀₀₁ \| 0 1/2 0 }
a, b, c+1/2 \| -x, -y, -z	{ -1 ‖ 1 \| 0 0 1/2 }
a, -b, -c+1/2 \| -x, -y, -z	{ -1 ‖ 2₁₀₀ \| 0 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 }
-a, -b, -c+1/2 \| -x, -y, -z	{ -1 ‖ -1 \| 0 0 1/2 }
-a, b, c+1/2 \| -x, -y, -z	{ -1 ‖ m₁₀₀ \| 0 0 1/2 }
a+1/2, -b, c+1/2 \| -x, -y, -z	{ -1 ‖ m₀₁₀ \| 1/2 0 1/2 }
a+1/2, b, -c+1/2 \| -x, -y, -z	{ -1 ‖ m₀₀₁ \| 1/2 0 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, -b+1/2, -c+1/2 \| -x, -y, -z	{ -1 ‖ 2₁₀₀ \| 1/2 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 }
-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+1/2 \| -x, -y, -z	{ -1 ‖ m₁₀₀ \| 1/2 1/2 1/2 }
a, -b+1/2, c+1/2 \| -x, -y, -z	{ -1 ‖ m₀₁₀ \| 0 1/2 1/2 }
a, b+1/2, -c+1/2 \| -x, -y, -z	{ -1 ‖ m₀₀₁ \| 0 1/2 1/2 }
a, b, c \| -x, y, z	{ m ‖ 1 \| 0 }
a, -b, -c \| -x, y, z	{ m ‖ 2₁₀₀ \| 0 }
-a+1/2, b, -c \| -x, y, z	{ m ‖ 2₀₁₀ \| 1/2 0 0 }
-a+1/2, -b, c \| -x, y, z	{ m ‖ 2₀₀₁ \| 1/2 0 0 }
-a, -b, -c \| -x, y, z	{ m ‖ -1 \| 0 }
-a, b, c \| -x, y, z	{ m ‖ m₁₀₀ \| 0 }
a+1/2, -b, c \| -x, y, z	{ m ‖ m₀₁₀ \| 1/2 0 0 }
a+1/2, b, -c \| -x, y, z	{ m ‖ m₀₀₁ \| 1/2 0 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, b+1/2, -c \| -x, y, z	{ m ‖ 2₀₁₀ \| 0 1/2 0 }
-a, -b+1/2, c \| -x, y, z	{ m ‖ 2₀₀₁ \| 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 ‖ m₁₀₀ \| 1/2 1/2 0 }
a, -b+1/2, c \| -x, y, z	{ m ‖ m₀₁₀ \| 0 1/2 0 }
a, b+1/2, -c \| -x, y, z	{ m ‖ m₀₀₁ \| 0 1/2 0 }
a, b, c+1/2 \| x, -y, -z	{ 2 ‖ 1 \| 0 0 1/2 }
a, -b, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₁₀₀ \| 0 0 1/2 }
-a+1/2, b, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₀₁₀ \| 1/2 0 1/2 }
-a+1/2, -b, c+1/2 \| x, -y, -z	{ 2 ‖ 2₀₀₁ \| 1/2 0 1/2 }
-a, -b, -c+1/2 \| x, -y, -z	{ 2 ‖ -1 \| 0 0 1/2 }
-a, b, c+1/2 \| x, -y, -z	{ 2 ‖ m₁₀₀ \| 0 0 1/2 }
a+1/2, -b, c+1/2 \| x, -y, -z	{ 2 ‖ m₀₁₀ \| 1/2 0 1/2 }
a+1/2, b, -c+1/2 \| x, -y, -z	{ 2 ‖ m₀₀₁ \| 1/2 0 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, -b+1/2, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₁₀₀ \| 1/2 1/2 1/2 }
-a, b+1/2, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₀₁₀ \| 0 1/2 1/2 }
-a, -b+1/2, c+1/2 \| x, -y, -z	{ 2 ‖ 2₀₀₁ \| 0 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, b+1/2, c+1/2 \| x, -y, -z	{ 2 ‖ m₁₀₀ \| 1/2 1/2 1/2 }
a, -b+1/2, c+1/2 \| x, -y, -z	{ 2 ‖ m₀₁₀ \| 0 1/2 1/2 }
a, b+1/2, -c+1/2 \| x, -y, -z	{ 2 ‖ m₀₀₁ \| 0 1/2 1/2 }

WP	Site symmetry	Representative
8a	$_{}^{}_{}^{1} 2_{}^{}_{}^{1} 2_{}^{}_{}^{1} 2_{}^{}_{}^{\infty m} 1$	(1/4,0,0 \| 0,0,z)
8b	$_{}^{}_{}^{- 1} 2_{}^{}_{}^{- 1} 2_{}^{}_{}^{1} 2_{}^{}_{}^{\infty m} 1$	(1/4,0,1/4 \| 0,0,0)
8c	$_{}^{}_{}^{1} 2 /_{}^{}_{}^{1} m . ._{}^{}_{}^{\infty m} 1$	(0,0,0 \| 0,0,z)
8d	$_{}^{}_{}^{- 1} 2 /_{}^{}_{}^{1} m . ._{}^{}_{}^{\infty m} 1$	(0,0,1/4 \| 0,0,0)
8e	$._{}^{}_{}^{1} 2 /_{}^{}_{}^{1} m ._{}^{}_{}^{\infty m} 1$	(1/4,1/4,0 \| 0,0,z)
8f	$._{}^{}_{}^{- 1} 2 /_{}^{}_{}^{1} m ._{}^{}_{}^{\infty m} 1$	(1/4,1/4,1/4 \| 0,0,0)
8g	$_{}^{}_{}^{1} m_{}^{}_{}^{1} m_{}^{}_{}^{1} 2_{}^{}_{}^{\infty m} 1$	(0,1/4,c \| 0,0,z)
16h	$_{}^{}_{}^{1} 2 . ._{}^{}_{}^{\infty m} 1$	(a,0,0 \| 0,0,z)
16i	$_{}^{}_{}^{- 1} 2 . ._{}^{}_{}^{\infty m} 1$	(a,0,1/4 \| 0,0,0)
16j	$._{}^{}_{}^{1} 2 ._{}^{}_{}^{\infty m} 1$	(1/4,b,0 \| 0,0,z)
16k	$._{}^{}_{}^{- 1} 2 ._{}^{}_{}^{\infty m} 1$	(1/4,b,1/4 \| 0,0,0)
16l	$. ._{}^{}_{}^{1} 2_{}^{}_{}^{\infty m} 1$	(1/4,0,c \| 0,0,z)
16m	$_{}^{}_{}^{1} m . ._{}^{}_{}^{\infty m} 1$	(0,b,c \| 0,0,z)
16n	$._{}^{}_{}^{1} m ._{}^{}_{}^{\infty m} 1$	(a,1/4,c \| 0,0,z)
32o	$_{}^{}_{}^{1} 1_{}^{}_{}^{\infty m} 1$	(a,b,c \| 0,0,z)

Wavevector-k	Little co-group
Γ:(0,0,0)	$_{}^{}_{}^{1} m_{}^{}_{}^{1} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty / mm} 1$
T:(1,0,1/2)	$_{}^{}_{}^{1} m_{}^{}_{}^{1} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty / mm} 1$
Y:(1,0,0)	$_{}^{}_{}^{1} m_{}^{}_{}^{1} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty / mm} 1$
Z:(0,0,1/2)	$_{}^{}_{}^{1} m_{}^{}_{}^{1} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty / mm} 1$
R:(1/2,1/2,1/2)	$_{}^{}_{}^{1} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty / mm} 1$
S:(1/2,1/2,0)	$_{}^{}_{}^{1} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty / mm} 1$
A:(u,0,1/2)	$_{}^{}_{}^{m} m_{}^{}_{}^{1} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty 2} 1$
B:(0,v,1/2)	$_{}^{}_{}^{1} m_{}^{}_{}^{m} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty 2} 1$
Δ:(0,v,0)	$_{}^{}_{}^{1} m_{}^{}_{}^{m} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty 2} 1$
H:(1,0,w)	$_{}^{}_{}^{1} m_{}^{}_{}^{1} m_{}^{}_{}^{m} m_{}^{}_{}^{\infty 2} 1$
Λ:(0,0,w)	$_{}^{}_{}^{1} m_{}^{}_{}^{1} m_{}^{}_{}^{m} m_{}^{}_{}^{\infty 2} 1$
Σ:(u,0,0)	$_{}^{}_{}^{m} m_{}^{}_{}^{1} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty 2} 1$
D:(1/2,1/2,w)	$_{}^{}_{}^{1} 2/_{}^{}_{}^{m} m_{}^{}_{}^{\infty 2} 1$
K:(0,v,w)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty 2} 1$
M:(u,0,w)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty 2} 1$
P:(u,v,0)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty 2} 1$
Q:(u,v,1/2)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty 2} 1$
GP:(u,v,w)	$_{}^{}_{}^{m} -1_{}^{}_{}^{\infty 2} 1$

Spin Brillouin Zone

mmmC

k-vector	A↑G(8)
Γ:(0,0,0)	$Γ_{1}^{S, +} (2) \oplus Γ_{1}^{S, -} (2) \oplus Γ_{3}^{S, +} (2) \oplus Γ_{3}^{S, -} (2)$
T:(1,0,1/2)	$T_{1}^{S, +} (2) \oplus T_{1}^{S, -} (2) \oplus T_{3}^{S, +} (2) \oplus T_{3}^{S, -} (2)$
Y:(1,0,0)	$Y_{1}^{S, +} (2) \oplus Y_{1}^{S, -} (2) \oplus Y_{3}^{S, +} (2) \oplus Y_{3}^{S, -} (2)$
Z:(0,0,1/2)	$Z_{1}^{S, +} (2) \oplus Z_{1}^{S, -} (2) \oplus Z_{3}^{S, +} (2) \oplus Z_{3}^{S, -} (2)$
R:(1/2,1/2,1/2)	$2 R_{1}^{S} (4)$
S:(1/2,1/2,0)	$2 S_{1}^{S} (4)$
A:(u,0,1/2)	$2 A_{1}^{S} (2) \oplus 2 A_{2}^{S} (2)$
B:(0,v,1/2)	$B_{1}^{S} (2) \oplus B_{2}^{S} (2) \oplus B_{3}^{S} (2) \oplus B_{4}^{S} (2)$
Δ:(0,v,0)	$Δ_{1}^{S} (2) \oplus Δ_{2}^{S} (2) \oplus Δ_{3}^{S} (2) \oplus Δ_{4}^{S} (2)$
H:(1,0,w)	$H_{1}^{S} (2) \oplus H_{2}^{S} (2) \oplus H_{3}^{S} (2) \oplus H_{4}^{S} (2)$
Λ:(0,0,w)	$Λ_{1}^{S} (2) \oplus Λ_{2}^{S} (2) \oplus Λ_{3}^{S} (2) \oplus Λ_{4}^{S} (2)$
Σ:(u,0,0)	$2 Σ_{1}^{S} (2) \oplus 2 Σ_{2}^{S} (2)$
D:(1/2,1/2,w)	$2 D_{1}^{S} D_{2}^{S} (4)$
K:(0,v,w)	$2 K_{1}^{S} (2) \oplus 2 K_{2}^{S} (2)$
M:(u,0,w)	$2 M_{1}^{S} (2) \oplus 2 M_{2}^{S} (2)$
P:(u,v,0)	$2 P_{1}^{S} (2) \oplus 2 P_{2}^{S} (2)$
Q:(u,v,1/2)	$2 Q_{1}^{S} (2) \oplus 2 Q_{2}^{S} (2)$
GP:(u,v,w)	$4 G P_{1}^{S} (2)$

k-vector	A↑G(8)
Γ:(0,0,0)	$Γ_{1}^{S, +} (2) \oplus Γ_{1}^{S, -} (2) \oplus Γ_{4}^{S, +} (2) \oplus Γ_{4}^{S, -} (2)$
T:(1,0,1/2)	$T_{1}^{S, +} (2) \oplus T_{1}^{S, -} (2) \oplus T_{4}^{S, +} (2) \oplus T_{4}^{S, -} (2)$
Y:(1,0,0)	$Y_{1}^{S, +} (2) \oplus Y_{1}^{S, -} (2) \oplus Y_{4}^{S, +} (2) \oplus Y_{4}^{S, -} (2)$
Z:(0,0,1/2)	$Z_{1}^{S, +} (2) \oplus Z_{1}^{S, -} (2) \oplus Z_{4}^{S, +} (2) \oplus Z_{4}^{S, -} (2)$
R:(1/2,1/2,1/2)	$2 R_{1}^{S} (4)$
S:(1/2,1/2,0)	$2 S_{1}^{S} (4)$
A:(u,0,1/2)	$A_{1}^{S} (2) \oplus A_{2}^{S} (2) \oplus A_{3}^{S} (2) \oplus A_{4}^{S} (2)$
B:(0,v,1/2)	$2 B_{1}^{S} (2) \oplus 2 B_{2}^{S} (2)$
Δ:(0,v,0)	$2 Δ_{1}^{S} (2) \oplus 2 Δ_{2}^{S} (2)$
H:(1,0,w)	$H_{1}^{S} (2) \oplus H_{2}^{S} (2) \oplus H_{3}^{S} (2) \oplus H_{4}^{S} (2)$
Λ:(0,0,w)	$Λ_{1}^{S} (2) \oplus Λ_{2}^{S} (2) \oplus Λ_{3}^{S} (2) \oplus Λ_{4}^{S} (2)$
Σ:(u,0,0)	$Σ_{1}^{S} (2) \oplus Σ_{2}^{S} (2) \oplus Σ_{3}^{S} (2) \oplus Σ_{4}^{S} (2)$
D:(1/2,1/2,w)	$2 D_{1}^{S} D_{2}^{S} (4)$
K:(0,v,w)	$2 K_{1}^{S} (2) \oplus 2 K_{2}^{S} (2)$
M:(u,0,w)	$2 M_{1}^{S} (2) \oplus 2 M_{2}^{S} (2)$
P:(u,v,0)	$2 P_{1}^{S} (2) \oplus 2 P_{2}^{S} (2)$
Q:(u,v,1/2)	$2 Q_{1}^{S} (2) \oplus 2 Q_{2}^{S} (2)$
GP:(u,v,w)	$4 G P_{1}^{S} (2)$

k-vector	A↑G(8)
Γ:(0,0,0)	$Γ_{1}^{S, +} (2) \oplus Γ_{1}^{S, -} (2) \oplus Γ_{2}^{S, +} (2) \oplus Γ_{2}^{S, -} (2)$
T:(1,0,1/2)	$T_{1}^{S, +} (2) \oplus T_{1}^{S, -} (2) \oplus T_{2}^{S, +} (2) \oplus T_{2}^{S, -} (2)$
Y:(1,0,0)	$Y_{1}^{S, +} (2) \oplus Y_{1}^{S, -} (2) \oplus Y_{2}^{S, +} (2) \oplus Y_{2}^{S, -} (2)$
Z:(0,0,1/2)	$Z_{1}^{S, +} (2) \oplus Z_{1}^{S, -} (2) \oplus Z_{2}^{S, +} (2) \oplus Z_{2}^{S, -} (2)$
R:(1/2,1/2,1/2)	$2 R_{1}^{S} (4)$
S:(1/2,1/2,0)	$2 S_{1}^{S} (4)$
A:(u,0,1/2)	$A_{1}^{S} (2) \oplus A_{2}^{S} (2) \oplus A_{3}^{S} (2) \oplus A_{4}^{S} (2)$
B:(0,v,1/2)	$B_{1}^{S} (2) \oplus B_{2}^{S} (2) \oplus B_{3}^{S} (2) \oplus B_{4}^{S} (2)$
Δ:(0,v,0)	$Δ_{1}^{S} (2) \oplus Δ_{2}^{S} (2) \oplus Δ_{3}^{S} (2) \oplus Δ_{4}^{S} (2)$
H:(1,0,w)	$2 H_{1}^{S} (2) \oplus 2 H_{2}^{S} (2)$
Λ:(0,0,w)	$2 Λ_{1}^{S} (2) \oplus 2 Λ_{2}^{S} (2)$
Σ:(u,0,0)	$Σ_{1}^{S} (2) \oplus Σ_{2}^{S} (2) \oplus Σ_{3}^{S} (2) \oplus Σ_{4}^{S} (2)$
D:(1/2,1/2,w)	$2 D_{1}^{S} D_{2}^{S} (4)$
K:(0,v,w)	$2 K_{1}^{S} (2) \oplus 2 K_{2}^{S} (2)$
M:(u,0,w)	$2 M_{1}^{S} (2) \oplus 2 M_{2}^{S} (2)$
P:(u,v,0)	$2 P_{1}^{S} (2) \oplus 2 P_{2}^{S} (2)$
Q:(u,v,1/2)	$2 Q_{1}^{S} (2) \oplus 2 Q_{2}^{S} (2)$
GP:(u,v,w)	$4 G P_{1}^{S} (2)$

k-vector	A'↑G(8)
Γ:(0,0,0)	$Γ_{1}^{S, +} (2) \oplus Γ_{2}^{S, -} (2) \oplus Γ_{3}^{S, +} (2) \oplus Γ_{4}^{S, -} (2)$
T:(1,0,1/2)	$T_{1}^{S, +} (2) \oplus T_{2}^{S, -} (2) \oplus T_{3}^{S, +} (2) \oplus T_{4}^{S, -} (2)$
Y:(1,0,0)	$Y_{1}^{S, +} (2) \oplus Y_{2}^{S, -} (2) \oplus Y_{3}^{S, +} (2) \oplus Y_{4}^{S, -} (2)$
Z:(0,0,1/2)	$Z_{1}^{S, +} (2) \oplus Z_{2}^{S, -} (2) \oplus Z_{3}^{S, +} (2) \oplus Z_{4}^{S, -} (2)$
R:(1/2,1/2,1/2)	$2 R_{1}^{S} (4)$
S:(1/2,1/2,0)	$2 S_{1}^{S} (4)$
A:(u,0,1/2)	$A_{1}^{S} (2) \oplus A_{2}^{S} (2) \oplus A_{3}^{S} (2) \oplus A_{4}^{S} (2)$
B:(0,v,1/2)	$2 B_{1}^{S} (2) \oplus 2 B_{3}^{S} (2)$
Δ:(0,v,0)	$2 Δ_{1}^{S} (2) \oplus 2 Δ_{3}^{S} (2)$
H:(1,0,w)	$2 H_{1}^{S} (2) \oplus 2 H_{3}^{S} (2)$
Λ:(0,0,w)	$2 Λ_{1}^{S} (2) \oplus 2 Λ_{3}^{S} (2)$
Σ:(u,0,0)	$Σ_{1}^{S} (2) \oplus Σ_{2}^{S} (2) \oplus Σ_{3}^{S} (2) \oplus Σ_{4}^{S} (2)$
D:(1/2,1/2,w)	$2 D_{1}^{S} D_{2}^{S} (4)$
K:(0,v,w)	$4 K_{1}^{S} (2)$
M:(u,0,w)	$2 M_{1}^{S} (2) \oplus 2 M_{2}^{S} (2)$
P:(u,v,0)	$2 P_{1}^{S} (2) \oplus 2 P_{2}^{S} (2)$
Q:(u,v,1/2)	$2 Q_{1}^{S} (2) \oplus 2 Q_{2}^{S} (2)$
GP:(u,v,w)	$4 G P_{1}^{S} (2)$

k-vector	A'↑G(8)
Γ:(0,0,0)	$Γ_{1}^{S, +} (2) \oplus Γ_{2}^{S, -} (2) \oplus Γ_{3}^{S, -} (2) \oplus Γ_{4}^{S, +} (2)$
T:(1,0,1/2)	$T_{1}^{S, -} (2) \oplus T_{2}^{S, +} (2) \oplus T_{3}^{S, +} (2) \oplus T_{4}^{S, -} (2)$
Y:(1,0,0)	$Y_{1}^{S, -} (2) \oplus Y_{2}^{S, +} (2) \oplus Y_{3}^{S, +} (2) \oplus Y_{4}^{S, -} (2)$
Z:(0,0,1/2)	$Z_{1}^{S, +} (2) \oplus Z_{2}^{S, -} (2) \oplus Z_{3}^{S, -} (2) \oplus Z_{4}^{S, +} (2)$
R:(1/2,1/2,1/2)	$2 R_{1}^{S} (4)$
S:(1/2,1/2,0)	$2 S_{1}^{S} (4)$
A:(u,0,1/2)	$2 A_{1}^{S} (2) \oplus 2 A_{3}^{S} (2)$
B:(0,v,1/2)	$B_{1}^{S} (2) \oplus B_{2}^{S} (2) \oplus B_{3}^{S} (2) \oplus B_{4}^{S} (2)$
Δ:(0,v,0)	$Δ_{1}^{S} (2) \oplus Δ_{2}^{S} (2) \oplus Δ_{3}^{S} (2) \oplus Δ_{4}^{S} (2)$
H:(1,0,w)	$2 H_{2}^{S} (2) \oplus 2 H_{3}^{S} (2)$
Λ:(0,0,w)	$2 Λ_{1}^{S} (2) \oplus 2 Λ_{4}^{S} (2)$
Σ:(u,0,0)	$2 Σ_{1}^{S} (2) \oplus 2 Σ_{3}^{S} (2)$
D:(1/2,1/2,w)	$2 D_{1}^{S} D_{2}^{S} (4)$
K:(0,v,w)	$2 K_{1}^{S} (2) \oplus 2 K_{2}^{S} (2)$
M:(u,0,w)	$4 M_{1}^{S} (2)$
P:(u,v,0)	$2 P_{1}^{S} (2) \oplus 2 P_{2}^{S} (2)$
Q:(u,v,1/2)	$2 Q_{1}^{S} (2) \oplus 2 Q_{2}^{S} (2)$
GP:(u,v,w)	$4 G P_{1}^{S} (2)$

k-vector	A↑G(16)
Γ:(0,0,0)	$Γ_{1}^{S, +} (2) \oplus Γ_{1}^{S, -} (2) \oplus Γ_{2}^{S, +} (2) \oplus Γ_{2}^{S, -} (2) \oplus Γ_{3}^{S, +} (2) \oplus Γ_{3}^{S, -} (2) \oplus Γ_{4}^{S, +} (2) \oplus Γ_{4}^{S, -} (2)$
T:(1,0,1/2)	$T_{1}^{S, +} (2) \oplus T_{1}^{S, -} (2) \oplus T_{2}^{S, +} (2) \oplus T_{2}^{S, -} (2) \oplus T_{3}^{S, +} (2) \oplus T_{3}^{S, -} (2) \oplus T_{4}^{S, +} (2) \oplus T_{4}^{S, -} (2)$
Y:(1,0,0)	$Y_{1}^{S, +} (2) \oplus Y_{1}^{S, -} (2) \oplus Y_{2}^{S, +} (2) \oplus Y_{2}^{S, -} (2) \oplus Y_{3}^{S, +} (2) \oplus Y_{3}^{S, -} (2) \oplus Y_{4}^{S, +} (2) \oplus Y_{4}^{S, -} (2)$
Z:(0,0,1/2)	$Z_{1}^{S, +} (2) \oplus Z_{1}^{S, -} (2) \oplus Z_{2}^{S, +} (2) \oplus Z_{2}^{S, -} (2) \oplus Z_{3}^{S, +} (2) \oplus Z_{3}^{S, -} (2) \oplus Z_{4}^{S, +} (2) \oplus Z_{4}^{S, -} (2)$
R:(1/2,1/2,1/2)	$4 R_{1}^{S} (4)$
S:(1/2,1/2,0)	$4 S_{1}^{S} (4)$
A:(u,0,1/2)	$2 A_{1}^{S} (2) \oplus 2 A_{2}^{S} (2) \oplus 2 A_{3}^{S} (2) \oplus 2 A_{4}^{S} (2)$
B:(0,v,1/2)	$2 B_{1}^{S} (2) \oplus 2 B_{2}^{S} (2) \oplus 2 B_{3}^{S} (2) \oplus 2 B_{4}^{S} (2)$
Δ:(0,v,0)	$2 Δ_{1}^{S} (2) \oplus 2 Δ_{2}^{S} (2) \oplus 2 Δ_{3}^{S} (2) \oplus 2 Δ_{4}^{S} (2)$
H:(1,0,w)	$2 H_{1}^{S} (2) \oplus 2 H_{2}^{S} (2) \oplus 2 H_{3}^{S} (2) \oplus 2 H_{4}^{S} (2)$
Λ:(0,0,w)	$2 Λ_{1}^{S} (2) \oplus 2 Λ_{2}^{S} (2) \oplus 2 Λ_{3}^{S} (2) \oplus 2 Λ_{4}^{S} (2)$
Σ:(u,0,0)	$2 Σ_{1}^{S} (2) \oplus 2 Σ_{2}^{S} (2) \oplus 2 Σ_{3}^{S} (2) \oplus 2 Σ_{4}^{S} (2)$
D:(1/2,1/2,w)	$4 D_{1}^{S} D_{2}^{S} (4)$
K:(0,v,w)	$4 K_{1}^{S} (2) \oplus 4 K_{2}^{S} (2)$
M:(u,0,w)	$4 M_{1}^{S} (2) \oplus 4 M_{2}^{S} (2)$
P:(u,v,0)	$4 P_{1}^{S} (2) \oplus 4 P_{2}^{S} (2)$
Q:(u,v,1/2)	$4 Q_{1}^{S} (2) \oplus 4 Q_{2}^{S} (2)$
GP:(u,v,w)	$8 G P_{1}^{S} (2)$

Coordinates	Seitz symbol
a, b, c \| x, y, z	{ 1 ‖ 1 \| 0 }
a, -b, -c \| x, y, z	{ 1 ‖ 2₁₀₀ \| 0 }
-a+1/2, b, -c \| x, y, z	{ 1 ‖ 2₀₁₀ \| 1/2 0 0 }
-a+1/2, -b, c \| x, y, z	{ 1 ‖ 2₀₀₁ \| 1/2 0 0 }
-a, -b, -c \| x, y, z	{ 1 ‖ -1 \| 0 }
-a, b, c \| x, y, z	{ 1 ‖ m₁₀₀ \| 0 }
a+1/2, -b, c \| x, y, z	{ 1 ‖ m₀₁₀ \| 1/2 0 0 }
a+1/2, b, -c \| x, y, z	{ 1 ‖ m₀₀₁ \| 1/2 0 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, b+1/2, -c \| x, y, z	{ 1 ‖ 2₀₁₀ \| 0 1/2 0 }
-a, -b+1/2, c \| x, y, z	{ 1 ‖ 2₀₀₁ \| 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 ‖ m₁₀₀ \| 1/2 1/2 0 }
a, -b+1/2, c \| x, y, z	{ 1 ‖ m₀₁₀ \| 0 1/2 0 }
a, b+1/2, -c \| x, y, z	{ 1 ‖ m₀₀₁ \| 0 1/2 0 }
a, b, c+1/2 \| -x, -y, -z	{ -1 ‖ 1 \| 0 0 1/2 }
a, -b, -c+1/2 \| -x, -y, -z	{ -1 ‖ 2₁₀₀ \| 0 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 }
-a, -b, -c+1/2 \| -x, -y, -z	{ -1 ‖ -1 \| 0 0 1/2 }
-a, b, c+1/2 \| -x, -y, -z	{ -1 ‖ m₁₀₀ \| 0 0 1/2 }
a+1/2, -b, c+1/2 \| -x, -y, -z	{ -1 ‖ m₀₁₀ \| 1/2 0 1/2 }
a+1/2, b, -c+1/2 \| -x, -y, -z	{ -1 ‖ m₀₀₁ \| 1/2 0 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, -b+1/2, -c+1/2 \| -x, -y, -z	{ -1 ‖ 2₁₀₀ \| 1/2 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 }
-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+1/2 \| -x, -y, -z	{ -1 ‖ m₁₀₀ \| 1/2 1/2 1/2 }
a, -b+1/2, c+1/2 \| -x, -y, -z	{ -1 ‖ m₀₁₀ \| 0 1/2 1/2 }
a, b+1/2, -c+1/2 \| -x, -y, -z	{ -1 ‖ m₀₀₁ \| 0 1/2 1/2 }
a, b, c \| -x, y, z	{ m ‖ 1 \| 0 }
a, -b, -c \| -x, y, z	{ m ‖ 2₁₀₀ \| 0 }
-a+1/2, b, -c \| -x, y, z	{ m ‖ 2₀₁₀ \| 1/2 0 0 }
-a+1/2, -b, c \| -x, y, z	{ m ‖ 2₀₀₁ \| 1/2 0 0 }
-a, -b, -c \| -x, y, z	{ m ‖ -1 \| 0 }
-a, b, c \| -x, y, z	{ m ‖ m₁₀₀ \| 0 }
a+1/2, -b, c \| -x, y, z	{ m ‖ m₀₁₀ \| 1/2 0 0 }
a+1/2, b, -c \| -x, y, z	{ m ‖ m₀₀₁ \| 1/2 0 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, b+1/2, -c \| -x, y, z	{ m ‖ 2₀₁₀ \| 0 1/2 0 }
-a, -b+1/2, c \| -x, y, z	{ m ‖ 2₀₀₁ \| 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 ‖ m₁₀₀ \| 1/2 1/2 0 }
a, -b+1/2, c \| -x, y, z	{ m ‖ m₀₁₀ \| 0 1/2 0 }
a, b+1/2, -c \| -x, y, z	{ m ‖ m₀₀₁ \| 0 1/2 0 }
a, b, c+1/2 \| x, -y, -z	{ 2 ‖ 1 \| 0 0 1/2 }
a, -b, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₁₀₀ \| 0 0 1/2 }
-a+1/2, b, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₀₁₀ \| 1/2 0 1/2 }
-a+1/2, -b, c+1/2 \| x, -y, -z	{ 2 ‖ 2₀₀₁ \| 1/2 0 1/2 }
-a, -b, -c+1/2 \| x, -y, -z	{ 2 ‖ -1 \| 0 0 1/2 }
-a, b, c+1/2 \| x, -y, -z	{ 2 ‖ m₁₀₀ \| 0 0 1/2 }
a+1/2, -b, c+1/2 \| x, -y, -z	{ 2 ‖ m₀₁₀ \| 1/2 0 1/2 }
a+1/2, b, -c+1/2 \| x, -y, -z	{ 2 ‖ m₀₀₁ \| 1/2 0 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, -b+1/2, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₁₀₀ \| 1/2 1/2 1/2 }
-a, b+1/2, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₀₁₀ \| 0 1/2 1/2 }
-a, -b+1/2, c+1/2 \| x, -y, -z	{ 2 ‖ 2₀₀₁ \| 0 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, b+1/2, c+1/2 \| x, -y, -z	{ 2 ‖ m₁₀₀ \| 1/2 1/2 1/2 }
a, -b+1/2, c+1/2 \| x, -y, -z	{ 2 ‖ m₀₁₀ \| 0 1/2 1/2 }
a, b+1/2, -c+1/2 \| x, -y, -z	{ 2 ‖ m₀₀₁ \| 0 1/2 1/2 }

k-vector	A↑G(4)
Γ:(0,0,0)	$Γ_{1}^{S, +} (2) \oplus Γ_{1}^{S, -} (2)$
T:(1,0,1/2)	$T_{1}^{S, +} (2) \oplus T_{1}^{S, -} (2)$
Y:(1,0,0)	$Y_{1}^{S, +} (2) \oplus Y_{1}^{S, -} (2)$
Z:(0,0,1/2)	$Z_{1}^{S, +} (2) \oplus Z_{1}^{S, -} (2)$
R:(1/2,1/2,1/2)	$R_{1}^{S} (4)$
S:(1/2,1/2,0)	$S_{1}^{S} (4)$
A:(u,0,1/2)	$A_{1}^{S} (2) \oplus A_{2}^{S} (2)$
B:(0,v,1/2)	$B_{1}^{S} (2) \oplus B_{2}^{S} (2)$
Δ:(0,v,0)	$Δ_{1}^{S} (2) \oplus Δ_{2}^{S} (2)$
H:(1,0,w)	$H_{1}^{S} (2) \oplus H_{2}^{S} (2)$
Λ:(0,0,w)	$Λ_{1}^{S} (2) \oplus Λ_{2}^{S} (2)$
Σ:(u,0,0)	$Σ_{1}^{S} (2) \oplus Σ_{2}^{S} (2)$
D:(1/2,1/2,w)	$D_{1}^{S} D_{2}^{S} (4)$
K:(0,v,w)	$K_{1}^{S} (2) \oplus K_{2}^{S} (2)$
M:(u,0,w)	$M_{1}^{S} (2) \oplus M_{2}^{S} (2)$
P:(u,v,0)	$P_{1}^{S} (2) \oplus P_{2}^{S} (2)$
Q:(u,v,1/2)	$Q_{1}^{S} (2) \oplus Q_{2}^{S} (2)$
GP:(u,v,w)	$2 G P_{1}^{S} (2)$

k-vector	Ag↑G(4)
Γ:(0,0,0)	$Γ_{1}^{S, +} (2) \oplus Γ_{3}^{S, +} (2)$
T:(1,0,1/2)	$T_{1}^{S, +} (2) \oplus T_{3}^{S, +} (2)$
Y:(1,0,0)	$Y_{1}^{S, +} (2) \oplus Y_{3}^{S, +} (2)$
Z:(0,0,1/2)	$Z_{1}^{S, +} (2) \oplus Z_{3}^{S, +} (2)$
R:(1/2,1/2,1/2)	$R_{1}^{S} (4)$
S:(1/2,1/2,0)	$S_{1}^{S} (4)$
A:(u,0,1/2)	$A_{1}^{S} (2) \oplus A_{2}^{S} (2)$
B:(0,v,1/2)	$B_{1}^{S} (2) \oplus B_{3}^{S} (2)$
Δ:(0,v,0)	$Δ_{1}^{S} (2) \oplus Δ_{3}^{S} (2)$
H:(1,0,w)	$H_{1}^{S} (2) \oplus H_{3}^{S} (2)$
Λ:(0,0,w)	$Λ_{1}^{S} (2) \oplus Λ_{3}^{S} (2)$
Σ:(u,0,0)	$Σ_{1}^{S} (2) \oplus Σ_{2}^{S} (2)$
D:(1/2,1/2,w)	$D_{1}^{S} D_{2}^{S} (4)$
K:(0,v,w)	$2 K_{1}^{S} (2)$
M:(u,0,w)	$M_{1}^{S} (2) \oplus M_{2}^{S} (2)$
P:(u,v,0)	$P_{1}^{S} (2) \oplus P_{2}^{S} (2)$
Q:(u,v,1/2)	$Q_{1}^{S} (2) \oplus Q_{2}^{S} (2)$
GP:(u,v,w)	$2 G P_{1}^{S} (2)$

k-vector	A1↑G(4)
Γ:(0,0,0)	$Γ_{1}^{S, +} (2) \oplus Γ_{2}^{S, -} (2)$
T:(1,0,1/2)	$T_{3}^{S, +} (2) \oplus T_{4}^{S, -} (2)$
Y:(1,0,0)	$Y_{3}^{S, +} (2) \oplus Y_{4}^{S, -} (2)$
Z:(0,0,1/2)	$Z_{1}^{S, +} (2) \oplus Z_{2}^{S, -} (2)$
R:(1/2,1/2,1/2)	$R_{1}^{S} (4)$
S:(1/2,1/2,0)	$S_{1}^{S} (4)$
A:(u,0,1/2)	$A_{1}^{S} (2) \oplus A_{3}^{S} (2)$
B:(0,v,1/2)	$B_{1}^{S} (2) \oplus B_{3}^{S} (2)$
Δ:(0,v,0)	$Δ_{1}^{S} (2) \oplus Δ_{3}^{S} (2)$
H:(1,0,w)	$2 H_{3}^{S} (2)$
Λ:(0,0,w)	$2 Λ_{1}^{S} (2)$
Σ:(u,0,0)	$Σ_{1}^{S} (2) \oplus Σ_{3}^{S} (2)$
D:(1/2,1/2,w)	$D_{1}^{S} D_{2}^{S} (4)$
K:(0,v,w)	$2 K_{1}^{S} (2)$
M:(u,0,w)	$2 M_{1}^{S} (2)$
P:(u,v,0)	$P_{1}^{S} (2) \oplus P_{2}^{S} (2)$
Q:(u,v,1/2)	$Q_{1}^{S} (2) \oplus Q_{2}^{S} (2)$
GP:(u,v,w)	$2 G P_{1}^{S} (2)$

Information of spin space group CcA1A221mA1A221mA1A221eA∞mA22∞m1 ( nSSG:67.67.2.1 )

Information of spin space group $C_{c}_{}^{}_{}^{1} m_{}^{}_{}^{1} m_{}^{}_{}^{1} e_{}^{}_{}^{\infty m} 1$ ( nSSG:67.67.2.1 )