Information of spin space group $P\ce{^{1}{\text{-}6}}\ce{^{\infty m}{1}}$ ( nSSG:174.174.1.1 )

The continuously infinite group ^∞1 is omitted.

Coordinates	Seitz symbol
a, b, c \| x, y, z	{ 1 ‖ 1 \| 0 }
-b, a-b, c \| x, y, z	{ 1 ‖ 3⁺₀₀₁ \| 0 }
-a+b, -a, c \| x, y, z	{ 1 ‖ 3^-₀₀₁ \| 0 }
-a+b, -a, -c \| x, y, z	{ 1 ‖ -6⁺₀₀₁ \| 0 }
a, b, -c \| x, y, z	{ 1 ‖ m₀₀₁ \| 0 }
-b, a-b, -c \| x, y, z	{ 1 ‖ -6^-₀₀₁ \| 0 }
a, b, c \| -x, y, z	{ m ‖ 1 \| 0 }
-b, a-b, c \| -x, y, z	{ m ‖ 3⁺₀₀₁ \| 0 }
-a+b, -a, c \| -x, y, z	{ m ‖ 3^-₀₀₁ \| 0 }
-a+b, -a, -c \| -x, y, z	{ m ‖ -6⁺₀₀₁ \| 0 }
a, b, -c \| -x, y, z	{ m ‖ m₀₀₁ \| 0 }
-b, a-b, -c \| -x, y, z	{ m ‖ -6^-₀₀₁ \| 0 }

WP	Site symmetry	Representative
1a	$\ce{^{1}{-6}}..\ce{^{\infty m}{1}} $	(0,0,0 \|0,0,z)
1b	$\ce{^{1}{-6}}..\ce{^{\infty m}{1}} $	(0,0,1/2 \|0,0,z)
1c	$\ce{^{1}{-6}}..\ce{^{\infty m}{1}} $	(1/3,2/3,0 \|0,0,z)
1d	$\ce{^{1}{-6}}..\ce{^{\infty m}{1}} $	(1/3,2/3,1/2 \|0,0,z)
1e	$\ce{^{1}{-6}}..\ce{^{\infty m}{1}} $	(2/3,1/3,0 \|0,0,z)
1f	$\ce{^{1}{-6}}..\ce{^{\infty m}{1}} $	(2/3,1/3,1/2 \|0,0,z)
2g	$\ce{^{1}{3}}..\ce{^{\infty m}{1}} $	(0,0,c \|0,0,z)
2h	$\ce{^{1}{3}}..\ce{^{\infty m}{1}} $	(1/3,2/3,c \|0,0,z)
2i	$\ce{^{1}{3}}..\ce{^{\infty m}{1}} $	(2/3,1/3,c \|0,0,z)
3j	$\ce{^{1}{m}}..\ce{^{\infty m}{1}} $	(a,b,0 \|0,0,z)
3k	$\ce{^{1}{m}}..\ce{^{\infty m}{1}} $	(a,b,1/2 \|0,0,z)
6l	$\ce{^{1}{1}}\ce{^{\infty m}{1}} $	(a,b,c \|0,0,z)

Wavevector-k	Little co-group
A:(0,0,1/2)	$\ce{^{1}{-6}}\ce{^{\infty m}{1}} $
Γ:(0,0,0)	$\ce{^{1}{-6}}\ce{^{\infty m}{1}} $
H:(1/3,1/3,1/2)	$\ce{^{1}{-6}}\ce{^{\infty}{1}} $
K:(1/3,1/3,0)	$\ce{^{1}{-6}}\ce{^{\infty}{1}} $
L:(1/2,0,1/2)	$\ce{^{1}{m}}\ce{^{\infty m}{1}} $
M:(1/2,0,0)	$\ce{^{1}{m}}\ce{^{\infty m}{1}} $
Δ:(0,0,w)	$\ce{^{m}{-6}}\ce{^{\infty}{1}} $
P:(1/3,1/3,w)	$\ce{^{1}{3}}\ce{^{\infty}{1}} $
Λ:(u,u,0)	$\ce{^{1}{m}}\ce{^{\infty}{1}} $
Σ:(u,0,0)	$\ce{^{1}{m}}\ce{^{\infty}{1}} $
Q:(u,u,1/2)	$\ce{^{1}{m}}\ce{^{\infty}{1}} $
R:(u,0,1/2)	$\ce{^{1}{m}}\ce{^{\infty}{1}} $
U:(1/2,0,w)	$\ce{^{m}{m}}\ce{^{\infty}{1}} $
B:(u,v,0)	$\ce{^{1}{m}}\ce{^{\infty}{1}} $
C:(u,u,w)	$\ce{^{1}{1}}\ce{^{\infty}{1}} $
D:(u,0,w)	$\ce{^{1}{1}}\ce{^{\infty}{1}} $
E:(u,v,1/2)	$\ce{^{1}{m}}\ce{^{\infty}{1}} $
GP:(u,v,w)	$\ce{^{1}{1}}\ce{^{\infty}{1}} $

Spin Brillouin Zone

Spin Brilliouin Zone

k-vector	A'↑G(1)
A:(0,0,1/2)	$A_{1}^{S}(1) $
Γ:(0,0,0)	$Γ_{1}^{S}(1) $
H:(1/3,1/3,1/2)	$H_{1}^{S}(1) $
K:(1/3,1/3,0)	$K_{1}^{S}(1) $
L:(1/2,0,1/2)	$L_{1}^{S}(1) $
M:(1/2,0,0)	$M_{1}^{S}(1) $
Δ:(0,0,w)	$Δ_{1}^{S}(1) $
P:(1/3,1/3,w)	$P_{1}^{S}(1) $
Λ:(u,u,0)	$Λ_{1}^{S}(1) $
Σ:(u,0,0)	$Σ_{1}^{S}(1) $
Q:(u,u,1/2)	$Q_{1}^{S}(1) $
R:(u,0,1/2)	$R_{1}^{S}(1) $
U:(1/2,0,w)	$U_{1}^{S}(1) $
B:(u,v,0)	$B_{1}^{S}(1) $
C:(u,u,w)	$C_{1}^{S}(1) $
D:(u,0,w)	$D_{1}^{S}(1) $
E:(u,v,1/2)	$E_{1}^{S}(1) $
GP:(u,v,w)	$GP_{1}^{S}(1) $

k-vector	A'↑G(1)
A:(0,0,1/2)	$A_{2}^{S}(1) $
Γ:(0,0,0)	$Γ_{1}^{S}(1) $
H:(1/3,1/3,1/2)	$H_{2}^{S}(1) $
K:(1/3,1/3,0)	$K_{1}^{S}(1) $
L:(1/2,0,1/2)	$L_{2}^{S}(1) $
M:(1/2,0,0)	$M_{1}^{S}(1) $
Δ:(0,0,w)	$Δ_{1}^{S}(1) $
P:(1/3,1/3,w)	$P_{1}^{S}(1) $
Λ:(u,u,0)	$Λ_{1}^{S}(1) $
Σ:(u,0,0)	$Σ_{1}^{S}(1) $
Q:(u,u,1/2)	$Q_{2}^{S}(1) $
R:(u,0,1/2)	$R_{2}^{S}(1) $
U:(1/2,0,w)	$U_{1}^{S}(1) $
B:(u,v,0)	$B_{1}^{S}(1) $
C:(u,u,w)	$C_{1}^{S}(1) $
D:(u,0,w)	$D_{1}^{S}(1) $
E:(u,v,1/2)	$E_{2}^{S}(1) $
GP:(u,v,w)	$GP_{1}^{S}(1) $

k-vector	A'↑G(1)
A:(0,0,1/2)	$A_{1}^{S}(1) $
Γ:(0,0,0)	$Γ_{1}^{S}(1) $
H:(1/3,1/3,1/2)	$H_{3}^{S}(1) $
K:(1/3,1/3,0)	$K_{3}^{S}(1) $
L:(1/2,0,1/2)	$L_{1}^{S}(1) $
M:(1/2,0,0)	$M_{1}^{S}(1) $
Δ:(0,0,w)	$Δ_{1}^{S}(1) $
P:(1/3,1/3,w)	$P_{2}^{S}(1) $
Λ:(u,u,0)	$Λ_{1}^{S}(1) $
Σ:(u,0,0)	$Σ_{1}^{S}(1) $
Q:(u,u,1/2)	$Q_{1}^{S}(1) $
R:(u,0,1/2)	$R_{1}^{S}(1) $
U:(1/2,0,w)	$U_{1}^{S}(1) $
B:(u,v,0)	$B_{1}^{S}(1) $
C:(u,u,w)	$C_{1}^{S}(1) $
D:(u,0,w)	$D_{1}^{S}(1) $
E:(u,v,1/2)	$E_{1}^{S}(1) $
GP:(u,v,w)	$GP_{1}^{S}(1) $

k-vector	A'↑G(1)
A:(0,0,1/2)	$A_{2}^{S}(1) $
Γ:(0,0,0)	$Γ_{1}^{S}(1) $
H:(1/3,1/3,1/2)	$H_{4}^{S}(1) $
K:(1/3,1/3,0)	$K_{3}^{S}(1) $
L:(1/2,0,1/2)	$L_{2}^{S}(1) $
M:(1/2,0,0)	$M_{1}^{S}(1) $
Δ:(0,0,w)	$Δ_{1}^{S}(1) $
P:(1/3,1/3,w)	$P_{2}^{S}(1) $
Λ:(u,u,0)	$Λ_{1}^{S}(1) $
Σ:(u,0,0)	$Σ_{1}^{S}(1) $
Q:(u,u,1/2)	$Q_{2}^{S}(1) $
R:(u,0,1/2)	$R_{2}^{S}(1) $
U:(1/2,0,w)	$U_{1}^{S}(1) $
B:(u,v,0)	$B_{1}^{S}(1) $
C:(u,u,w)	$C_{1}^{S}(1) $
D:(u,0,w)	$D_{1}^{S}(1) $
E:(u,v,1/2)	$E_{2}^{S}(1) $
GP:(u,v,w)	$GP_{1}^{S}(1) $

k-vector	A'↑G(1)
A:(0,0,1/2)	$A_{1}^{S}(1) $
Γ:(0,0,0)	$Γ_{1}^{S}(1) $
H:(1/3,1/3,1/2)	$H_{5}^{S}(1) $
K:(1/3,1/3,0)	$K_{5}^{S}(1) $
L:(1/2,0,1/2)	$L_{1}^{S}(1) $
M:(1/2,0,0)	$M_{1}^{S}(1) $
Δ:(0,0,w)	$Δ_{1}^{S}(1) $
P:(1/3,1/3,w)	$P_{3}^{S}(1) $
Λ:(u,u,0)	$Λ_{1}^{S}(1) $
Σ:(u,0,0)	$Σ_{1}^{S}(1) $
Q:(u,u,1/2)	$Q_{1}^{S}(1) $
R:(u,0,1/2)	$R_{1}^{S}(1) $
U:(1/2,0,w)	$U_{1}^{S}(1) $
B:(u,v,0)	$B_{1}^{S}(1) $
C:(u,u,w)	$C_{1}^{S}(1) $
D:(u,0,w)	$D_{1}^{S}(1) $
E:(u,v,1/2)	$E_{1}^{S}(1) $
GP:(u,v,w)	$GP_{1}^{S}(1) $

k-vector	A'↑G(1)
A:(0,0,1/2)	$A_{2}^{S}(1) $
Γ:(0,0,0)	$Γ_{1}^{S}(1) $
H:(1/3,1/3,1/2)	$H_{6}^{S}(1) $
K:(1/3,1/3,0)	$K_{5}^{S}(1) $
L:(1/2,0,1/2)	$L_{2}^{S}(1) $
M:(1/2,0,0)	$M_{1}^{S}(1) $
Δ:(0,0,w)	$Δ_{1}^{S}(1) $
P:(1/3,1/3,w)	$P_{3}^{S}(1) $
Λ:(u,u,0)	$Λ_{1}^{S}(1) $
Σ:(u,0,0)	$Σ_{1}^{S}(1) $
Q:(u,u,1/2)	$Q_{2}^{S}(1) $
R:(u,0,1/2)	$R_{2}^{S}(1) $
U:(1/2,0,w)	$U_{1}^{S}(1) $
B:(u,v,0)	$B_{1}^{S}(1) $
C:(u,u,w)	$C_{1}^{S}(1) $
D:(u,0,w)	$D_{1}^{S}(1) $
E:(u,v,1/2)	$E_{2}^{S}(1) $
GP:(u,v,w)	$GP_{1}^{S}(1) $

k-vector	A1↑G(2)
A:(0,0,1/2)	$A_{1}^{S}(1)⊕A_{2}^{S}(1) $
Γ:(0,0,0)	$Γ_{1}^{S}(1)⊕Γ_{2}^{S}(1) $
H:(1/3,1/3,1/2)	$H_{1}^{S}(1)⊕H_{2}^{S}(1) $
K:(1/3,1/3,0)	$K_{1}^{S}(1)⊕K_{2}^{S}(1) $
L:(1/2,0,1/2)	$L_{1}^{S}(1)⊕L_{2}^{S}(1) $
M:(1/2,0,0)	$M_{1}^{S}(1)⊕M_{2}^{S}(1) $
Δ:(0,0,w)	$2Δ_{1}^{S}(1) $
P:(1/3,1/3,w)	$2P_{1}^{S}(1) $
Λ:(u,u,0)	$Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $
Σ:(u,0,0)	$Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $
Q:(u,u,1/2)	$Q_{1}^{S}(1)⊕Q_{2}^{S}(1) $
R:(u,0,1/2)	$R_{1}^{S}(1)⊕R_{2}^{S}(1) $
U:(1/2,0,w)	$2U_{1}^{S}(1) $
B:(u,v,0)	$B_{1}^{S}(1)⊕B_{2}^{S}(1) $
C:(u,u,w)	$2C_{1}^{S}(1) $
D:(u,0,w)	$2D_{1}^{S}(1) $
E:(u,v,1/2)	$E_{1}^{S}(1)⊕E_{2}^{S}(1) $
GP:(u,v,w)	$2GP_{1}^{S}(1) $

k-vector	A1↑G(2)
A:(0,0,1/2)	$A_{1}^{S}(1)⊕A_{2}^{S}(1) $
Γ:(0,0,0)	$Γ_{1}^{S}(1)⊕Γ_{2}^{S}(1) $
H:(1/3,1/3,1/2)	$H_{3}^{S}(1)⊕H_{4}^{S}(1) $
K:(1/3,1/3,0)	$K_{3}^{S}(1)⊕K_{4}^{S}(1) $
L:(1/2,0,1/2)	$L_{1}^{S}(1)⊕L_{2}^{S}(1) $
M:(1/2,0,0)	$M_{1}^{S}(1)⊕M_{2}^{S}(1) $
Δ:(0,0,w)	$2Δ_{1}^{S}(1) $
P:(1/3,1/3,w)	$2P_{2}^{S}(1) $
Λ:(u,u,0)	$Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $
Σ:(u,0,0)	$Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $
Q:(u,u,1/2)	$Q_{1}^{S}(1)⊕Q_{2}^{S}(1) $
R:(u,0,1/2)	$R_{1}^{S}(1)⊕R_{2}^{S}(1) $
U:(1/2,0,w)	$2U_{1}^{S}(1) $
B:(u,v,0)	$B_{1}^{S}(1)⊕B_{2}^{S}(1) $
C:(u,u,w)	$2C_{1}^{S}(1) $
D:(u,0,w)	$2D_{1}^{S}(1) $
E:(u,v,1/2)	$E_{1}^{S}(1)⊕E_{2}^{S}(1) $
GP:(u,v,w)	$2GP_{1}^{S}(1) $

k-vector	A1↑G(2)
A:(0,0,1/2)	$A_{1}^{S}(1)⊕A_{2}^{S}(1) $
Γ:(0,0,0)	$Γ_{1}^{S}(1)⊕Γ_{2}^{S}(1) $
H:(1/3,1/3,1/2)	$H_{5}^{S}(1)⊕H_{6}^{S}(1) $
K:(1/3,1/3,0)	$K_{5}^{S}(1)⊕K_{6}^{S}(1) $
L:(1/2,0,1/2)	$L_{1}^{S}(1)⊕L_{2}^{S}(1) $
M:(1/2,0,0)	$M_{1}^{S}(1)⊕M_{2}^{S}(1) $
Δ:(0,0,w)	$2Δ_{1}^{S}(1) $
P:(1/3,1/3,w)	$2P_{3}^{S}(1) $
Λ:(u,u,0)	$Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $
Σ:(u,0,0)	$Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $
Q:(u,u,1/2)	$Q_{1}^{S}(1)⊕Q_{2}^{S}(1) $
R:(u,0,1/2)	$R_{1}^{S}(1)⊕R_{2}^{S}(1) $
U:(1/2,0,w)	$2U_{1}^{S}(1) $
B:(u,v,0)	$B_{1}^{S}(1)⊕B_{2}^{S}(1) $
C:(u,u,w)	$2C_{1}^{S}(1) $
D:(u,0,w)	$2D_{1}^{S}(1) $
E:(u,v,1/2)	$E_{1}^{S}(1)⊕E_{2}^{S}(1) $
GP:(u,v,w)	$2GP_{1}^{S}(1) $

k-vector	A'↑G(3)
A:(0,0,1/2)	$A_{1}^{S}(1)⊕A_{3}^{S}A_{5}^{S}(2) $
Γ:(0,0,0)	$Γ_{1}^{S}(1)⊕Γ_{3}^{S}Γ_{5}^{S}(2) $
H:(1/3,1/3,1/2)	$H_{1}^{S}(1)⊕H_{3}^{S}(1)⊕H_{5}^{S}(1) $
K:(1/3,1/3,0)	$K_{1}^{S}(1)⊕K_{3}^{S}(1)⊕K_{5}^{S}(1) $
L:(1/2,0,1/2)	$3L_{1}^{S}(1) $
M:(1/2,0,0)	$3M_{1}^{S}(1) $
Δ:(0,0,w)	$Δ_{1}^{S}(1)⊕Δ_{2}^{S}Δ_{3}^{S}(2) $
P:(1/3,1/3,w)	$P_{1}^{S}(1)⊕P_{2}^{S}(1)⊕P_{3}^{S}(1) $
Λ:(u,u,0)	$3Λ_{1}^{S}(1) $
Σ:(u,0,0)	$3Σ_{1}^{S}(1) $
Q:(u,u,1/2)	$3Q_{1}^{S}(1) $
R:(u,0,1/2)	$3R_{1}^{S}(1) $
U:(1/2,0,w)	$3U_{1}^{S}(1) $
B:(u,v,0)	$3B_{1}^{S}(1) $
C:(u,u,w)	$3C_{1}^{S}(1) $
D:(u,0,w)	$3D_{1}^{S}(1) $
E:(u,v,1/2)	$3E_{1}^{S}(1) $
GP:(u,v,w)	$3GP_{1}^{S}(1) $

k-vector	A'↑G(3)
A:(0,0,1/2)	$A_{2}^{S}(1)⊕A_{4}^{S}A_{6}^{S}(2) $
Γ:(0,0,0)	$Γ_{1}^{S}(1)⊕Γ_{3}^{S}Γ_{5}^{S}(2) $
H:(1/3,1/3,1/2)	$H_{2}^{S}(1)⊕H_{4}^{S}(1)⊕H_{6}^{S}(1) $
K:(1/3,1/3,0)	$K_{1}^{S}(1)⊕K_{3}^{S}(1)⊕K_{5}^{S}(1) $
L:(1/2,0,1/2)	$3L_{2}^{S}(1) $
M:(1/2,0,0)	$3M_{1}^{S}(1) $
Δ:(0,0,w)	$Δ_{1}^{S}(1)⊕Δ_{2}^{S}Δ_{3}^{S}(2) $
P:(1/3,1/3,w)	$P_{1}^{S}(1)⊕P_{2}^{S}(1)⊕P_{3}^{S}(1) $
Λ:(u,u,0)	$3Λ_{1}^{S}(1) $
Σ:(u,0,0)	$3Σ_{1}^{S}(1) $
Q:(u,u,1/2)	$3Q_{2}^{S}(1) $
R:(u,0,1/2)	$3R_{2}^{S}(1) $
U:(1/2,0,w)	$3U_{1}^{S}(1) $
B:(u,v,0)	$3B_{1}^{S}(1) $
C:(u,u,w)	$3C_{1}^{S}(1) $
D:(u,0,w)	$3D_{1}^{S}(1) $
E:(u,v,1/2)	$3E_{2}^{S}(1) $
GP:(u,v,w)	$3GP_{1}^{S}(1) $

k-vector	A↑G(6)
A:(0,0,1/2)	$A_{1}^{S}(1)⊕A_{2}^{S}(1)⊕A_{3}^{S}A_{5}^{S}(2)⊕A_{4}^{S}A_{6}^{S}(2) $
Γ:(0,0,0)	$Γ_{1}^{S}(1)⊕Γ_{2}^{S}(1)⊕Γ_{3}^{S}Γ_{5}^{S}(2)⊕Γ_{4}^{S}Γ_{6}^{S}(2) $
H:(1/3,1/3,1/2)	$H_{1}^{S}(1)⊕H_{2}^{S}(1)⊕H_{3}^{S}(1)⊕H_{4}^{S}(1)⊕H_{5}^{S}(1)⊕H_{6}^{S}(1) $
K:(1/3,1/3,0)	$K_{1}^{S}(1)⊕K_{2}^{S}(1)⊕K_{3}^{S}(1)⊕K_{4}^{S}(1)⊕K_{5}^{S}(1)⊕K_{6}^{S}(1) $
L:(1/2,0,1/2)	$3L_{1}^{S}(1)⊕3L_{2}^{S}(1) $
M:(1/2,0,0)	$3M_{1}^{S}(1)⊕3M_{2}^{S}(1) $
Δ:(0,0,w)	$2Δ_{1}^{S}(1)⊕2Δ_{2}^{S}Δ_{3}^{S}(2) $
P:(1/3,1/3,w)	$2P_{1}^{S}(1)⊕2P_{2}^{S}(1)⊕2P_{3}^{S}(1) $
Λ:(u,u,0)	$3Λ_{1}^{S}(1)⊕3Λ_{2}^{S}(1) $
Σ:(u,0,0)	$3Σ_{1}^{S}(1)⊕3Σ_{2}^{S}(1) $
Q:(u,u,1/2)	$3Q_{1}^{S}(1)⊕3Q_{2}^{S}(1) $
R:(u,0,1/2)	$3R_{1}^{S}(1)⊕3R_{2}^{S}(1) $
U:(1/2,0,w)	$6U_{1}^{S}(1) $
B:(u,v,0)	$3B_{1}^{S}(1)⊕3B_{2}^{S}(1) $
C:(u,u,w)	$6C_{1}^{S}(1) $
D:(u,0,w)	$6D_{1}^{S}(1) $
E:(u,v,1/2)	$3E_{1}^{S}(1)⊕3E_{2}^{S}(1) $
GP:(u,v,w)	$6GP_{1}^{S}(1) $