Information of spin space group $C{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$ ( nSSG:35.35.1.1 )

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

Wyckoff Positions

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

Spin Brillouin Zone & k-little co-groups

Wavevector-k	Little co-group
Γ:(0,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
T:(1,0,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
Y:(1,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
Z:(0,0,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
R:(1/2,1/2,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
S:(1/2,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
A:(u,0,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
B:(0,v,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Δ:(0,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
H:(1,0,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Λ:(0,0,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Σ:(u,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
D:(1/2,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
K:(0,v,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
M:(u,0,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
P:(u,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Q:(u,v,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
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(1)
Γ:(0,0,0)	${\Gamma }_1^S(1)$
T:(1,0,1/2)	$T_1^S(1)$
Y:(1,0,0)	$Y_1^S(1)$
Z:(0,0,1/2)	$Z_1^S(1)$
R:(1/2,1/2,1/2)	$R_1^S(1)$
S:(1/2,1/2,0)	$S_1^S(1)$
A:(u,0,1/2)	$A_1^S(1)$
B:(0,v,1/2)	$B_1^S(1)$
Δ:(0,v,0)	${\Delta }_1^S(1)$
H:(1,0,w)	$H_1^S(1)$
Λ:(0,0,w)	${\Lambda }_1^S(1)$
Σ:(u,0,0)	${\Sigma }_1^S(1)$
D:(1/2,1/2,w)	$D_1^S(1)$
K:(0,v,w)	$K_1^S(1)$
M:(u,0,w)	$M_1^S(1)$
P:(u,v,0)	$P_1^S(1)$
Q:(u,v,1/2)	$Q_1^S(1)$
GP:(u,v,w)	$G{P}_1^S(1)$

2b

k-vector	A1↑G(1)
Γ:(0,0,0)	${\Gamma }_1^S(1)$
T:(1,0,1/2)	$T_1^S(1)$
Y:(1,0,0)	$Y_1^S(1)$
Z:(0,0,1/2)	$Z_1^S(1)$
R:(1/2,1/2,1/2)	$R_2^S(1)$
S:(1/2,1/2,0)	$S_2^S(1)$
A:(u,0,1/2)	$A_1^S(1)$
B:(0,v,1/2)	$B_1^S(1)$
Δ:(0,v,0)	${\Delta }_1^S(1)$
H:(1,0,w)	$H_1^S(1)$
Λ:(0,0,w)	${\Lambda }_1^S(1)$
Σ:(u,0,0)	${\Sigma }_1^S(1)$
D:(1/2,1/2,w)	$D_2^S(1)$
K:(0,v,w)	$K_1^S(1)$
M:(u,0,w)	$M_1^S(1)$
P:(u,v,0)	$P_1^S(1)$
Q:(u,v,1/2)	$Q_1^S(1)$
GP:(u,v,w)	$G{P}_1^S(1)$

4c

k-vector	A↑G(2)
Γ:(0,0,0)	${\Gamma }_1^S(1)\oplus {\Gamma }_2^S(1)$
T:(1,0,1/2)	$T_3^S(1)\oplus T_4^S(1)$
Y:(1,0,0)	$Y_3^S(1)\oplus Y_4^S(1)$
Z:(0,0,1/2)	$Z_1^S(1)\oplus Z_2^S(1)$
R:(1/2,1/2,1/2)	$R_1^S(1)\oplus R_2^S(1)$
S:(1/2,1/2,0)	$S_1^S(1)\oplus S_2^S(1)$
A:(u,0,1/2)	$A_1^S(1)\oplus A_2^S(1)$
B:(0,v,1/2)	$B_1^S(1)\oplus B_2^S(1)$
Δ:(0,v,0)	${\Delta }_1^S(1)\oplus {\Delta }_2^S(1)$
H:(1,0,w)	$H_3^S(1)\oplus H_4^S(1)$
Λ:(0,0,w)	${\Lambda }_1^S(1)\oplus {\Lambda }_2^S(1)$
Σ:(u,0,0)	${\Sigma }_1^S(1)\oplus {\Sigma }_2^S(1)$
D:(1/2,1/2,w)	$D_1^S(1)\oplus D_2^S(1)$
K:(0,v,w)	$K_1^S(1)\oplus K_2^S(1)$
M:(u,0,w)	$M_1^S(1)\oplus M_2^S(1)$
P:(u,v,0)	$2P_1^S(1)$
Q:(u,v,1/2)	$2Q_1^S(1)$
GP:(u,v,w)	$2G{P}_1^S(1)$

4d

k-vector	A'↑G(2)
Γ:(0,0,0)	${\Gamma }_1^S(1)\oplus {\Gamma }_4^S(1)$
T:(1,0,1/2)	$T_1^S(1)\oplus T_4^S(1)$
Y:(1,0,0)	$Y_1^S(1)\oplus Y_4^S(1)$
Z:(0,0,1/2)	$Z_1^S(1)\oplus Z_4^S(1)$
R:(1/2,1/2,1/2)	$R_1^S(1)\oplus R_2^S(1)$
S:(1/2,1/2,0)	$S_1^S(1)\oplus S_2^S(1)$
A:(u,0,1/2)	$2A_1^S(1)$
B:(0,v,1/2)	$B_1^S(1)\oplus B_2^S(1)$
Δ:(0,v,0)	${\Delta }_1^S(1)\oplus {\Delta }_2^S(1)$
H:(1,0,w)	$H_1^S(1)\oplus H_4^S(1)$
Λ:(0,0,w)	${\Lambda }_1^S(1)\oplus {\Lambda }_4^S(1)$
Σ:(u,0,0)	$2{\Sigma }_1^S(1)$
D:(1/2,1/2,w)	$D_1^S(1)\oplus D_2^S(1)$
K:(0,v,w)	$K_1^S(1)\oplus K_2^S(1)$
M:(u,0,w)	$2M_1^S(1)$
P:(u,v,0)	$2P_1^S(1)$
Q:(u,v,1/2)	$2Q_1^S(1)$
GP:(u,v,w)	$2G{P}_1^S(1)$

4e

k-vector	A'↑G(2)
Γ:(0,0,0)	${\Gamma }_1^S(1)\oplus {\Gamma }_3^S(1)$
T:(1,0,1/2)	$T_1^S(1)\oplus T_3^S(1)$
Y:(1,0,0)	$Y_1^S(1)\oplus Y_3^S(1)$
Z:(0,0,1/2)	$Z_1^S(1)\oplus Z_3^S(1)$
R:(1/2,1/2,1/2)	$R_1^S(1)\oplus R_2^S(1)$
S:(1/2,1/2,0)	$S_1^S(1)\oplus S_2^S(1)$
A:(u,0,1/2)	$A_1^S(1)\oplus A_2^S(1)$
B:(0,v,1/2)	$2B_1^S(1)$
Δ:(0,v,0)	$2{\Delta }_1^S(1)$
H:(1,0,w)	$H_1^S(1)\oplus H_3^S(1)$
Λ:(0,0,w)	${\Lambda }_1^S(1)\oplus {\Lambda }_3^S(1)$
Σ:(u,0,0)	${\Sigma }_1^S(1)\oplus {\Sigma }_2^S(1)$
D:(1/2,1/2,w)	$D_1^S(1)\oplus D_2^S(1)$
K:(0,v,w)	$2K_1^S(1)$
M:(u,0,w)	$M_1^S(1)\oplus M_2^S(1)$
P:(u,v,0)	$2P_1^S(1)$
Q:(u,v,1/2)	$2Q_1^S(1)$
GP:(u,v,w)	$2G{P}_1^S(1)$

8f

k-vector	A↑G(4)
Γ:(0,0,0)	${\Gamma }_1^S(1)\oplus {\Gamma }_2^S(1)\oplus {\Gamma }_3^S(1)\oplus {\Gamma }_4^S(1)$
T:(1,0,1/2)	$T_1^S(1)\oplus T_2^S(1)\oplus T_3^S(1)\oplus T_4^S(1)$
Y:(1,0,0)	$Y_1^S(1)\oplus Y_2^S(1)\oplus Y_3^S(1)\oplus Y_4^S(1)$
Z:(0,0,1/2)	$Z_1^S(1)\oplus Z_2^S(1)\oplus Z_3^S(1)\oplus Z_4^S(1)$
R:(1/2,1/2,1/2)	$2R_1^S(1)\oplus 2R_2^S(1)$
S:(1/2,1/2,0)	$2S_1^S(1)\oplus 2S_2^S(1)$
A:(u,0,1/2)	$2A_1^S(1)\oplus 2A_2^S(1)$
B:(0,v,1/2)	$2B_1^S(1)\oplus 2B_2^S(1)$
Δ:(0,v,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_2^S(1)$
H:(1,0,w)	$H_1^S(1)\oplus H_2^S(1)\oplus H_3^S(1)\oplus H_4^S(1)$
Λ:(0,0,w)	${\Lambda }_1^S(1)\oplus {\Lambda }_2^S(1)\oplus {\Lambda }_3^S(1)\oplus {\Lambda }_4^S(1)$
Σ:(u,0,0)	$2{\Sigma }_1^S(1)\oplus 2{\Sigma }_2^S(1)$
D:(1/2,1/2,w)	$2D_1^S(1)\oplus 2D_2^S(1)$
K:(0,v,w)	$2K_1^S(1)\oplus 2K_2^S(1)$
M:(u,0,w)	$2M_1^S(1)\oplus 2M_2^S(1)$
P:(u,v,0)	$4P_1^S(1)$
Q:(u,v,1/2)	$4Q_1^S(1)$
GP:(u,v,w)	$4G{P}_1^S(1)$