Spin Space Group Information

The continuously infinite group ^∞1 is omitted.

Coordinates	Seitz symbol
a, b, c \| x, y, z	{ 1 ‖ 1 \| 0 }
-a+1/2, -b+1/2, c \| x, y, z	{ 1 ‖ 2₀₀₁ \| 1/2 1/2 0 }
b, a, -c \| x, y, z	{ 1 ‖ 2₁₁₀ \| 0 }
-b+1/2, -a+1/2, -c \| x, y, z	{ 1 ‖ 2_1-10 \| 1/2 1/2 0 }
-a, -b, -c \| x, y, z	{ 1 ‖ -1 \| 0 }
a+1/2, b+1/2, -c \| x, y, z	{ 1 ‖ m₀₀₁ \| 1/2 1/2 0 }
-b, -a, c \| x, y, z	{ 1 ‖ m₁₁₀ \| 0 }
b+1/2, a+1/2, c \| x, y, z	{ 1 ‖ m_1-10 \| 1/2 1/2 0 }
-b+1/2, a, c+1/2 \| -x, -y, -z	{ -1 ‖ 4⁺₀₀₁ \| 1/2 0 1/2 }
b, -a+1/2, c+1/2 \| -x, -y, -z	{ -1 ‖ 4^-₀₀₁ \| 0 1/2 1/2 }
a, -b+1/2, -c+1/2 \| -x, -y, -z	{ -1 ‖ 2₁₀₀ \| 0 1/2 1/2 }
-a+1/2, b, -c+1/2 \| -x, -y, -z	{ -1 ‖ 2₀₁₀ \| 1/2 0 1/2 }
b+1/2, -a, -c+1/2 \| -x, -y, -z	{ -1 ‖ -4⁺₀₀₁ \| 1/2 0 1/2 }
-b, a+1/2, -c+1/2 \| -x, -y, -z	{ -1 ‖ -4^-₀₀₁ \| 0 1/2 1/2 }
-a, b+1/2, c+1/2 \| -x, -y, -z	{ -1 ‖ m₁₀₀ \| 0 1/2 1/2 }
a+1/2, -b, c+1/2 \| -x, -y, -z	{ -1 ‖ m₀₁₀ \| 1/2 0 1/2 }
a, b, c \| -x, y, z	{ m ‖ 1 \| 0 }
-a+1/2, -b+1/2, c \| -x, y, z	{ m ‖ 2₀₀₁ \| 1/2 1/2 0 }
b, a, -c \| -x, y, z	{ m ‖ 2₁₁₀ \| 0 }
-b+1/2, -a+1/2, -c \| -x, y, z	{ m ‖ 2_1-10 \| 1/2 1/2 0 }
-a, -b, -c \| -x, y, z	{ m ‖ -1 \| 0 }
a+1/2, b+1/2, -c \| -x, y, z	{ m ‖ m₀₀₁ \| 1/2 1/2 0 }
-b, -a, c \| -x, y, z	{ m ‖ m₁₁₀ \| 0 }
b+1/2, a+1/2, c \| -x, y, z	{ m ‖ m_1-10 \| 1/2 1/2 0 }
-b+1/2, a, c+1/2 \| x, -y, -z	{ 2 ‖ 4⁺₀₀₁ \| 1/2 0 1/2 }
b, -a+1/2, c+1/2 \| x, -y, -z	{ 2 ‖ 4^-₀₀₁ \| 0 1/2 1/2 }
a, -b+1/2, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₁₀₀ \| 0 1/2 1/2 }
-a+1/2, b, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₀₁₀ \| 1/2 0 1/2 }
b+1/2, -a, -c+1/2 \| x, -y, -z	{ 2 ‖ -4⁺₀₀₁ \| 1/2 0 1/2 }
-b, a+1/2, -c+1/2 \| x, -y, -z	{ 2 ‖ -4^-₀₀₁ \| 0 1/2 1/2 }
-a, b+1/2, c+1/2 \| x, -y, -z	{ 2 ‖ m₁₀₀ \| 0 1/2 1/2 }
a+1/2, -b, c+1/2 \| x, -y, -z	{ 2 ‖ m₀₁₀ \| 1/2 0 1/2 }

WP	Site symmetry	Representative
2a	$_{}^{}_{}^{- 1} -4_{}^{}_{}^{- 1} 2_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$	(1/4,3/4,1/4 \| 0,0,0)
2b	$_{}^{}_{}^{- 1} -4_{}^{}_{}^{- 1} 2_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$	(3/4,1/4,1/4 \| 0,0,0)
4c	$_{}^{}_{}^{1} 2_{}^{}_{}^{- 1} 2_{}^{}_{}^{- 1} 2 ._{}^{}_{}^{\infty m} 1$	(1/4,1/4,1/4 \| 0,0,0)
4d	$_{}^{}_{}^{1} 2 ._{}^{}_{}^{1} 2_{}^{}_{}^{1} 2_{}^{}_{}^{\infty m} 1$	(1/4,1/4,0 \| 0,0,z)
4e	$. ._{}^{}_{}^{1} 2 /_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$	(0,0,1/2 \| 0,0,z)
4f	$. ._{}^{}_{}^{1} 2 /_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$	(0,0,0 \| 0,0,z)
4g	$_{}^{}_{}^{1} 2 ._{}^{}_{}^{1} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$	(3/4,1/4,c \| 0,0,z)
8h	$_{}^{}_{}^{1} 2 . ._{}^{}_{}^{\infty m} 1$	(1/4,1/4,c \| 0,0,z)
8i	$._{}^{}_{}^{- 1} 2 ._{}^{}_{}^{\infty m} 1$	(a,1/4,3/4 \| 0,0,0)
8j	$._{}^{}_{}^{- 1} 2 ._{}^{}_{}^{\infty m} 1$	(a,1/4,1/4 \| 0,0,0)
8k	$. ._{}^{}_{}^{1} 2_{}^{}_{}^{\infty m} 1$	(a,a,0 \| 0,0,z)
8l	$. ._{}^{}_{}^{1} 2_{}^{}_{}^{\infty m} 1$	(a,a,1/2 \| 0,0,z)
8m	$. ._{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$	(a,-a,c \| 0,0,z)
16n	$_{}^{}_{}^{1} 1_{}^{}_{}^{\infty m} 1$	(a,b,c \| 0,0,z)

Wavevector-k	Little co-group
A:(1/2,1/2,1/2)	$_{}^{}_{}^{- 1} 4/_{}^{}_{}^{1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$
Γ:(0,0,0)	$_{}^{}_{}^{- 1} 4/_{}^{}_{}^{1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$
M:(1/2,1/2,0)	$_{}^{}_{}^{- 1} 4/_{}^{}_{}^{1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$
Z:(0,0,1/2)	$_{}^{}_{}^{- 1} 4/_{}^{}_{}^{1} m_{}^{}_{}^{- 1} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$
R:(0,1/2,1/2)	$_{}^{}_{}^{2} m_{}^{}_{}^{2} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$
X:(0,1/2,0)	$_{}^{}_{}^{2} m_{}^{}_{}^{2} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$
Λ:(0,0,w)	$_{}^{}_{}^{2} 4/_{}^{}_{}^{m} m_{}^{}_{}^{2} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
V:(1/2,1/2,w)	$_{}^{}_{}^{2} 4/_{}^{}_{}^{m} m_{}^{}_{}^{2} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
Δ:(0,v,0)	$_{}^{}_{}^{2} m_{}^{}_{}^{- 1} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
S:(u,u,1/2)	$_{}^{}_{}^{1} m_{}^{}_{}^{m} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
Σ:(u,u,0)	$_{}^{}_{}^{1} m_{}^{}_{}^{m} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
T:(u,1/2,1/2)	$_{}^{}_{}^{- 1} m_{}^{}_{}^{2} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
U:(0,v,1/2)	$_{}^{}_{}^{2} m_{}^{}_{}^{- 1} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
W:(0,1/2,w)	$_{}^{}_{}^{2} m_{}^{}_{}^{2} m_{}^{}_{}^{m} m_{}^{}_{}^{\infty} 1$
Y:(u,1/2,0)	$_{}^{}_{}^{- 1} m_{}^{}_{}^{2} m_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
B:(0,v,w)	$_{}^{}_{}^{- 1} 2/_{}^{}_{}^{2} m_{}^{}_{}^{\infty} 1$
C:(u,u,w)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
D:(u,v,0)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
E:(u,v,1/2)	$_{}^{}_{}^{m} 2/_{}^{}_{}^{1} m_{}^{}_{}^{\infty} 1$
F:(u,1/2,w)	$_{}^{}_{}^{- 1} 2/_{}^{}_{}^{2} m_{}^{}_{}^{\infty} 1$
GP:(u,v,w)	$_{}^{}_{}^{m} -1_{}^{}_{}^{\infty} 1$

Spin Brillouin Zone

k-vector	k-vector-G↑	A↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S, +} (2) \oplus Γ_{1}^{S, -} (2)$
A:(1/2,1/2,1/2)	T:(1,0,1/2)	$(A) T_{1}^{S, +} (2) \oplus (A) T_{1}^{S, -} (2)$
M:(1/2,1/2,0)	Y:(1,0,0)	$(M) Y_{1}^{S, +} (2) \oplus (M) Y_{1}^{S, -} (2)$
R:(0,1/2,1/2)	R:(1/2,1/2,1/2)	$R_{1}^{S} (4)$
X:(0,1/2,0)	S:(1/2,1/2,0)	$(X) S_{1}^{S} (4)$
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_{1}^{S, +} (2) \oplus Z_{1}^{S, -} (2)$
Δ:(0,v,0)	P:(v,v,0)	$(Δ) P_{1}^{S} (2) \oplus (Δ) P_{2}^{S} (2)$
Λ:(0,0,w)	Λ:(0,0,w)	$Λ_{1}^{S} (2) \oplus Λ_{2}^{S} (2)$
S:(u,u,1/2)	A:(2*u,0,1/2)	$2 (S) A_{1}^{S} (1) \oplus 2 (S) A_{2}^{S} (1)$	Spin Splitting
Σ:(u,u,0)	Σ:(2*u,0,0)	$2 Σ_{1}^{S} (1) \oplus 2 Σ_{2}^{S} (1)$	Spin Splitting
T:(u,1/2,1/2)	Q:(1/2+u,1/2-u,1/2)	$(T) Q_{1}^{S} (2) \oplus (T) Q_{2}^{S} (2)$
U:(0,v,1/2)	Q:(v,v,1/2)	$(U) Q_{1}^{S} (2) \oplus (U) Q_{2}^{S} (2)$
V:(1/2,1/2,w)	H:(1,0,w)	$(V) H_{1}^{S} (2) \oplus (V) H_{2}^{S} (2)$
W:(0,1/2,w)	D:(1/2,1/2,w)	$(W) D_{1}^{S} D_{2}^{S} (4)$
Y:(u,1/2,0)	P:(1/2+u,1/2-u,0)	$(Y) P_{1}^{S} (2) \oplus (Y) P_{2}^{S} (2)$
B:(0,v,w)	GP:(v,v,w)	$2 (B) G P_{1}^{S} (2)$
C:(u,u,w)	M:(2*u,0,w)	$2 (C) M_{1}^{S} (1) \oplus 2 (C) M_{2}^{S} (1)$	Spin Splitting
D:(u,v,0)	P:(u+v,-u+v,0)	$2 (D) P_{1}^{S} (1) \oplus 2 (D) P_{2}^{S} (1)$	Spin Splitting
E:(u,v,1/2)	Q:(u+v,-u+v,1/2)	$2 (E) Q_{1}^{S} (1) \oplus 2 (E) Q_{2}^{S} (1)$	Spin Splitting
F:(u,1/2,w)	GP:(1/2+u,1/2-u,w)	$2 (F) G P_{1}^{S} (2)$
GP:(u,v,w)	GP:(u+v,-u+v,w)	$4 G P_{1}^{S} (1)$	Spin Splitting

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

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

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

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

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

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

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

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

Coordinates	Seitz symbol
a, b, c \| x, y, z	{ 1 ‖ 1 \| 0 }
-a+1/2, -b+1/2, c \| x, y, z	{ 1 ‖ 2₀₀₁ \| 1/2 1/2 0 }
b, a, -c \| x, y, z	{ 1 ‖ 2₁₁₀ \| 0 }
-b+1/2, -a+1/2, -c \| x, y, z	{ 1 ‖ 2_1-10 \| 1/2 1/2 0 }
-a, -b, -c \| x, y, z	{ 1 ‖ -1 \| 0 }
a+1/2, b+1/2, -c \| x, y, z	{ 1 ‖ m₀₀₁ \| 1/2 1/2 0 }
-b, -a, c \| x, y, z	{ 1 ‖ m₁₁₀ \| 0 }
b+1/2, a+1/2, c \| x, y, z	{ 1 ‖ m_1-10 \| 1/2 1/2 0 }
-b+1/2, a, c+1/2 \| -x, -y, -z	{ -1 ‖ 4⁺₀₀₁ \| 1/2 0 1/2 }
b, -a+1/2, c+1/2 \| -x, -y, -z	{ -1 ‖ 4^-₀₀₁ \| 0 1/2 1/2 }
a, -b+1/2, -c+1/2 \| -x, -y, -z	{ -1 ‖ 2₁₀₀ \| 0 1/2 1/2 }
-a+1/2, b, -c+1/2 \| -x, -y, -z	{ -1 ‖ 2₀₁₀ \| 1/2 0 1/2 }
b+1/2, -a, -c+1/2 \| -x, -y, -z	{ -1 ‖ -4⁺₀₀₁ \| 1/2 0 1/2 }
-b, a+1/2, -c+1/2 \| -x, -y, -z	{ -1 ‖ -4^-₀₀₁ \| 0 1/2 1/2 }
-a, b+1/2, c+1/2 \| -x, -y, -z	{ -1 ‖ m₁₀₀ \| 0 1/2 1/2 }
a+1/2, -b, c+1/2 \| -x, -y, -z	{ -1 ‖ m₀₁₀ \| 1/2 0 1/2 }
a, b, c \| -x, y, z	{ m ‖ 1 \| 0 }
-a+1/2, -b+1/2, c \| -x, y, z	{ m ‖ 2₀₀₁ \| 1/2 1/2 0 }
b, a, -c \| -x, y, z	{ m ‖ 2₁₁₀ \| 0 }
-b+1/2, -a+1/2, -c \| -x, y, z	{ m ‖ 2_1-10 \| 1/2 1/2 0 }
-a, -b, -c \| -x, y, z	{ m ‖ -1 \| 0 }
a+1/2, b+1/2, -c \| -x, y, z	{ m ‖ m₀₀₁ \| 1/2 1/2 0 }
-b, -a, c \| -x, y, z	{ m ‖ m₁₁₀ \| 0 }
b+1/2, a+1/2, c \| -x, y, z	{ m ‖ m_1-10 \| 1/2 1/2 0 }
-b+1/2, a, c+1/2 \| x, -y, -z	{ 2 ‖ 4⁺₀₀₁ \| 1/2 0 1/2 }
b, -a+1/2, c+1/2 \| x, -y, -z	{ 2 ‖ 4^-₀₀₁ \| 0 1/2 1/2 }
a, -b+1/2, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₁₀₀ \| 0 1/2 1/2 }
-a+1/2, b, -c+1/2 \| x, -y, -z	{ 2 ‖ 2₀₁₀ \| 1/2 0 1/2 }
b+1/2, -a, -c+1/2 \| x, -y, -z	{ 2 ‖ -4⁺₀₀₁ \| 1/2 0 1/2 }
-b, a+1/2, -c+1/2 \| x, -y, -z	{ 2 ‖ -4^-₀₀₁ \| 0 1/2 1/2 }
-a, b+1/2, c+1/2 \| x, -y, -z	{ 2 ‖ m₁₀₀ \| 0 1/2 1/2 }
a+1/2, -b, c+1/2 \| x, -y, -z	{ 2 ‖ m₀₁₀ \| 1/2 0 1/2 }

Information of spin space group PA-1A22-142/A1A221nA-1A22-1nA1A221mA∞mA22∞m1 ( nSSG:67.134.1.1 )

Information of spin space group $P_{}^{}_{}^{- 1} 4_{2} /_{}^{}_{}^{1} n_{}^{}_{}^{- 1} n_{}^{}_{}^{1} m_{}^{}_{}^{\infty m} 1$ ( nSSG:67.134.1.1 )