Information of spin space group $P{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}{4}_2{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{c}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$ ( nSSG:101.101.1.1 )

General Positions

The continuously infinite group ^∞1 is omitted.

Coordinates	Seitz symbol
a, b, c | x, y, z	{ 1 ‖ 1 | 0 }
-b, a, c+1/2 | x, y, z	{ 1 ‖ 4+001 | 0 0 1/2 }
b, -a, c+1/2 | x, y, z	{ 1 ‖ 4-001 | 0 0 1/2 }
-a, -b, c | x, y, z	{ 1 ‖ 2001 | 0 }
-a, b, c+1/2 | x, y, z	{ 1 ‖ m100 | 0 0 1/2 }
a, -b, c+1/2 | x, y, z	{ 1 ‖ m010 | 0 0 1/2 }
-b, -a, c | x, y, z	{ 1 ‖ m110 | 0 }
b, a, c | x, y, z	{ 1 ‖ m1-10 | 0 }
a, b, c | -x, y, z	{ m ‖ 1 | 0 }
-b, a, c+1/2 | -x, y, z	{ m ‖ 4+001 | 0 0 1/2 }
b, -a, c+1/2 | -x, y, z	{ m ‖ 4-001 | 0 0 1/2 }
-a, -b, c | -x, y, z	{ m ‖ 2001 | 0 }
-a, b, c+1/2 | -x, y, z	{ m ‖ m100 | 0 0 1/2 }
a, -b, c+1/2 | -x, y, z	{ m ‖ m010 | 0 0 1/2 }
-b, -a, c | -x, y, z	{ m ‖ m110 | 0 }
b, a, c | -x, y, z	{ m ‖ m1-10 | 0 }

Wyckoff Positions

WP	Site symmetry	Representative
2a	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,c |0,0,z)
2b	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/2,1/2,c |0,0,z)
4c	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,1/2,c |0,0,z)
4d	$..{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,a,c |0,0,z)
8e	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,b,c |0,0,z)

Spin Brillouin Zone & k-little co-groups

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

Spin Brillouin Zone

Band Representations (Magnon)

2a

k-vector	A1↑G(2)
A:(1/2,1/2,1/2)	$A_1^S{A}_3^S(2)$
Γ:(0,0,0)	${\Gamma }_1^S(1)\oplus {\Gamma }_3^S(1)$
M:(1/2,1/2,0)	$M_1^S(1)\oplus M_3^S(1)$
Z:(0,0,1/2)	$Z_1^S{Z}_3^S(2)$
R:(0,1/2,1/2)	$R_1^S{R}_2^S(2)$
X:(0,1/2,0)	$X_1^S(1)\oplus X_2^S(1)$
Λ:(0,0,w)	${\Lambda }_1^S(1)\oplus {\Lambda }_3^S(1)$
V:(1/2,1/2,w)	$V_1^S(1)\oplus V_3^S(1)$
Δ:(0,v,0)	${\Delta }_1^S(1)\oplus {\Delta }_2^S(1)$
S:(u,u,1/2)	$2S_1^S(1)$
Σ:(u,u,0)	$2{\Sigma }_1^S(1)$
T:(u,1/2,1/2)	$T_1^S{T}_2^S(2)$
U:(0,v,1/2)	$U_1^S{U}_2^S(2)$
W:(0,1/2,w)	$W_1^S(1)\oplus W_2^S(1)$
Y:(u,1/2,0)	$Y_1^S(1)\oplus Y_2^S(1)$
B:(0,v,w)	$B_1^S(1)\oplus B_2^S(1)$
C:(u,u,w)	$2C_1^S(1)$
D:(u,v,0)	$2D_1^S(1)$
E:(u,v,1/2)	$2E_1^S(1)$
F:(u,1/2,w)	$F_1^S(1)\oplus F_2^S(1)$
GP:(u,v,w)	$2G{P}_1^S(1)$

2b

k-vector	A1↑G(2)
A:(1/2,1/2,1/2)	$A_1^S{A}_3^S(2)$
Γ:(0,0,0)	${\Gamma }_1^S(1)\oplus {\Gamma }_3^S(1)$
M:(1/2,1/2,0)	$M_1^S(1)\oplus M_3^S(1)$
Z:(0,0,1/2)	$Z_1^S{Z}_3^S(2)$
R:(0,1/2,1/2)	$R_3^S{R}_4^S(2)$
X:(0,1/2,0)	$X_3^S(1)\oplus X_4^S(1)$
Λ:(0,0,w)	${\Lambda }_1^S(1)\oplus {\Lambda }_3^S(1)$
V:(1/2,1/2,w)	$V_1^S(1)\oplus V_3^S(1)$
Δ:(0,v,0)	${\Delta }_1^S(1)\oplus {\Delta }_2^S(1)$
S:(u,u,1/2)	$2S_1^S(1)$
Σ:(u,u,0)	$2{\Sigma }_1^S(1)$
T:(u,1/2,1/2)	$T_1^S{T}_2^S(2)$
U:(0,v,1/2)	$U_1^S{U}_2^S(2)$
W:(0,1/2,w)	$W_3^S(1)\oplus W_4^S(1)$
Y:(u,1/2,0)	$Y_1^S(1)\oplus Y_2^S(1)$
B:(0,v,w)	$B_1^S(1)\oplus B_2^S(1)$
C:(u,u,w)	$2C_1^S(1)$
D:(u,v,0)	$2D_1^S(1)$
E:(u,v,1/2)	$2E_1^S(1)$
F:(u,1/2,w)	$F_1^S(1)\oplus F_2^S(1)$
GP:(u,v,w)	$2G{P}_1^S(1)$

4c

k-vector	A↑G(4)
A:(1/2,1/2,1/2)	$2A_5^S(2)$
Γ:(0,0,0)	${\Gamma }_1^S(1)\oplus {\Gamma }_2^S(1)\oplus {\Gamma }_3^S(1)\oplus {\Gamma }_4^S(1)$
M:(1/2,1/2,0)	$2M_5^S(2)$
Z:(0,0,1/2)	$Z_1^S{Z}_3^S(2)\oplus Z_2^S{Z}_4^S(2)$
R:(0,1/2,1/2)	$R_1^S{R}_2^S(2)\oplus R_3^S{R}_4^S(2)$
X:(0,1/2,0)	$X_1^S(1)\oplus X_2^S(1)\oplus X_3^S(1)\oplus X_4^S(1)$
Λ:(0,0,w)	${\Lambda }_1^S(1)\oplus {\Lambda }_2^S(1)\oplus {\Lambda }_3^S(1)\oplus {\Lambda }_4^S(1)$
V:(1/2,1/2,w)	$2V_5^S(2)$
Δ:(0,v,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_2^S(1)$
S:(u,u,1/2)	$2S_1^S(1)\oplus 2S_2^S(1)$
Σ:(u,u,0)	$2{\Sigma }_1^S(1)\oplus 2{\Sigma }_2^S(1)$
T:(u,1/2,1/2)	$2T_1^S{T}_2^S(2)$
U:(0,v,1/2)	$2U_1^S{U}_2^S(2)$
W:(0,1/2,w)	$W_1^S(1)\oplus W_2^S(1)\oplus W_3^S(1)\oplus W_4^S(1)$
Y:(u,1/2,0)	$2Y_1^S(1)\oplus 2Y_2^S(1)$
B:(0,v,w)	$2B_1^S(1)\oplus 2B_2^S(1)$
C:(u,u,w)	$2C_1^S(1)\oplus 2C_2^S(1)$
D:(u,v,0)	$4D_1^S(1)$
E:(u,v,1/2)	$4E_1^S(1)$
F:(u,1/2,w)	$2F_1^S(1)\oplus 2F_2^S(1)$
GP:(u,v,w)	$4G{P}_1^S(1)$

4d

k-vector	A'↑G(4)
A:(1/2,1/2,1/2)	$A_1^S{A}_3^S(2)\oplus A_5^S(2)$
Γ:(0,0,0)	${\Gamma }_1^S(1)\oplus {\Gamma }_3^S(1)\oplus {\Gamma }_5^S(2)$
M:(1/2,1/2,0)	$M_1^S(1)\oplus M_3^S(1)\oplus M_5^S(2)$
Z:(0,0,1/2)	$Z_1^S{Z}_3^S(2)\oplus Z_5^S(2)$
R:(0,1/2,1/2)	$R_1^S{R}_2^S(2)\oplus R_3^S{R}_4^S(2)$
X:(0,1/2,0)	$X_1^S(1)\oplus X_2^S(1)\oplus X_3^S(1)\oplus X_4^S(1)$
Λ:(0,0,w)	${\Lambda }_1^S(1)\oplus {\Lambda }_3^S(1)\oplus {\Lambda }_5^S(2)$
V:(1/2,1/2,w)	$V_1^S(1)\oplus V_3^S(1)\oplus V_5^S(2)$
Δ:(0,v,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_2^S(1)$
S:(u,u,1/2)	$3S_1^S(1)\oplus S_2^S(1)$
Σ:(u,u,0)	$3{\Sigma }_1^S(1)\oplus {\Sigma }_2^S(1)$
T:(u,1/2,1/2)	$2T_1^S{T}_2^S(2)$
U:(0,v,1/2)	$2U_1^S{U}_2^S(2)$
W:(0,1/2,w)	$W_1^S(1)\oplus W_2^S(1)\oplus W_3^S(1)\oplus W_4^S(1)$
Y:(u,1/2,0)	$2Y_1^S(1)\oplus 2Y_2^S(1)$
B:(0,v,w)	$2B_1^S(1)\oplus 2B_2^S(1)$
C:(u,u,w)	$3C_1^S(1)\oplus C_2^S(1)$
D:(u,v,0)	$4D_1^S(1)$
E:(u,v,1/2)	$4E_1^S(1)$
F:(u,1/2,w)	$2F_1^S(1)\oplus 2F_2^S(1)$
GP:(u,v,w)	$4G{P}_1^S(1)$

8e

k-vector	A↑G(8)
A:(1/2,1/2,1/2)	$A_1^S{A}_3^S(2)\oplus A_2^S{A}_4^S(2)\oplus 2A_5^S(2)$
Γ:(0,0,0)	${\Gamma }_1^S(1)\oplus {\Gamma }_2^S(1)\oplus {\Gamma }_3^S(1)\oplus {\Gamma }_4^S(1)\oplus 2{\Gamma }_5^S(2)$
M:(1/2,1/2,0)	$M_1^S(1)\oplus M_2^S(1)\oplus M_3^S(1)\oplus M_4^S(1)\oplus 2M_5^S(2)$
Z:(0,0,1/2)	$Z_1^S{Z}_3^S(2)\oplus Z_2^S{Z}_4^S(2)\oplus 2Z_5^S(2)$
R:(0,1/2,1/2)	$2R_1^S{R}_2^S(2)\oplus 2R_3^S{R}_4^S(2)$
X:(0,1/2,0)	$2X_1^S(1)\oplus 2X_2^S(1)\oplus 2X_3^S(1)\oplus 2X_4^S(1)$
Λ:(0,0,w)	${\Lambda }_1^S(1)\oplus {\Lambda }_2^S(1)\oplus {\Lambda }_3^S(1)\oplus {\Lambda }_4^S(1)\oplus 2{\Lambda }_5^S(2)$
V:(1/2,1/2,w)	$V_1^S(1)\oplus V_2^S(1)\oplus V_3^S(1)\oplus V_4^S(1)\oplus 2V_5^S(2)$
Δ:(0,v,0)	$4{\Delta }_1^S(1)\oplus 4{\Delta }_2^S(1)$
S:(u,u,1/2)	$4S_1^S(1)\oplus 4S_2^S(1)$
Σ:(u,u,0)	$4{\Sigma }_1^S(1)\oplus 4{\Sigma }_2^S(1)$
T:(u,1/2,1/2)	$4T_1^S{T}_2^S(2)$
U:(0,v,1/2)	$4U_1^S{U}_2^S(2)$
W:(0,1/2,w)	$2W_1^S(1)\oplus 2W_2^S(1)\oplus 2W_3^S(1)\oplus 2W_4^S(1)$
Y:(u,1/2,0)	$4Y_1^S(1)\oplus 4Y_2^S(1)$
B:(0,v,w)	$4B_1^S(1)\oplus 4B_2^S(1)$
C:(u,u,w)	$4C_1^S(1)\oplus 4C_2^S(1)$
D:(u,v,0)	$8D_1^S(1)$
E:(u,v,1/2)	$8E_1^S(1)$
F:(u,1/2,w)	$4F_1^S(1)\oplus 4F_2^S(1)$
GP:(u,v,w)	$8G{P}_1^S(1)$