Information of spin space group $P\ce{^{1}{\text{-}4}}\ce{^{1}{3}}\ce{^{1}{n}}\ce{^{\infty m}{1}}$ ( nSSG:218.218.1.1 )

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, 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	{ m ‖ -4+100 | 1/2 1/2 1/2 }
-a+1/2, -c+1/2, b+1/2 | -x, y, z	{ m ‖ -4-100 | 1/2 1/2 1/2 }
-c+1/2, -b+1/2, a+1/2 | -x, y, z	{ m ‖ -4+010 | 1/2 1/2 1/2 }
c+1/2, -b+1/2, -a+1/2 | -x, y, z	{ m ‖ -4-010 | 1/2 1/2 1/2 }
b+1/2, -a+1/2, -c+1/2 | -x, y, z	{ m ‖ -4+001 | 1/2 1/2 1/2 }
-b+1/2, a+1/2, -c+1/2 | -x, y, z	{ m ‖ -4-001 | 1/2 1/2 1/2 }
-b+1/2, -a+1/2, c+1/2 | -x, y, z	{ m ‖ m110 | 1/2 1/2 1/2 }
b+1/2, a+1/2, c+1/2 | -x, y, z	{ m ‖ m1-10 | 1/2 1/2 1/2 }
a+1/2, -c+1/2, -b+1/2 | -x, y, z	{ m ‖ m011 | 1/2 1/2 1/2 }
a+1/2, c+1/2, b+1/2 | -x, y, z	{ m ‖ m01-1 | 1/2 1/2 1/2 }
-c+1/2, b+1/2, -a+1/2 | -x, y, z	{ m ‖ m101 | 1/2 1/2 1/2 }
c+1/2, b+1/2, a+1/2 | -x, y, z	{ m ‖ m-101 | 1/2 1/2 1/2 }

Wyckoff Positions

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

Spin Brillouin Zone

Band Representations (Magnon)

2a

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

6b

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

6c

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

6d

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

8e

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

12f

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

12g

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

12h

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

24i

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