Information of spin space group $P_b{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{c}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{c}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{a}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$ ( nSSG:54.54.2.1 )

General Positions

The continuously infinite group ^∞1 is omitted.

Coordinates	Seitz symbol
a, b, c | x, y, z	{ 1 ‖ 1 | 0 }
a+1/2, -b, -c+1/2 | x, y, z	{ 1 ‖ 2100 | 1/2 0 1/2 }
-a, b, -c+1/2 | x, y, z	{ 1 ‖ 2010 | 0 0 1/2 }
-a+1/2, -b, c | x, y, z	{ 1 ‖ 2001 | 1/2 0 0 }
-a, -b, -c | x, y, z	{ 1 ‖ -1 | 0 }
-a+1/2, b, c+1/2 | x, y, z	{ 1 ‖ m100 | 1/2 0 1/2 }
a, -b, c+1/2 | x, y, z	{ 1 ‖ m010 | 0 0 1/2 }
a+1/2, b, -c | x, y, z	{ 1 ‖ m001 | 1/2 0 0 }
a, b+1/2, c | -x, -y, -z	{ -1 ‖ 1 | 0 1/2 0 }
a+1/2, -b+1/2, -c+1/2 | -x, -y, -z	{ -1 ‖ 2100 | 1/2 1/2 1/2 }
-a, b+1/2, -c+1/2 | -x, -y, -z	{ -1 ‖ 2010 | 0 1/2 1/2 }
-a+1/2, -b+1/2, c | -x, -y, -z	{ -1 ‖ 2001 | 1/2 1/2 0 }
-a, -b+1/2, -c | -x, -y, -z	{ -1 ‖ -1 | 0 1/2 0 }
-a+1/2, b+1/2, c+1/2 | -x, -y, -z	{ -1 ‖ m100 | 1/2 1/2 1/2 }
a, -b+1/2, c+1/2 | -x, -y, -z	{ -1 ‖ m010 | 0 1/2 1/2 }
a+1/2, b+1/2, -c | -x, -y, -z	{ -1 ‖ m001 | 1/2 1/2 0 }
a, b, c | -x, y, z	{ m ‖ 1 | 0 }
a+1/2, -b, -c+1/2 | -x, y, z	{ m ‖ 2100 | 1/2 0 1/2 }
-a, b, -c+1/2 | -x, y, z	{ m ‖ 2010 | 0 0 1/2 }
-a+1/2, -b, c | -x, y, z	{ m ‖ 2001 | 1/2 0 0 }
-a, -b, -c | -x, y, z	{ m ‖ -1 | 0 }
-a+1/2, b, c+1/2 | -x, y, z	{ m ‖ m100 | 1/2 0 1/2 }
a, -b, c+1/2 | -x, y, z	{ m ‖ m010 | 0 0 1/2 }
a+1/2, b, -c | -x, y, z	{ m ‖ m001 | 1/2 0 0 }
a, b+1/2, c | x, -y, -z	{ 2 ‖ 1 | 0 1/2 0 }
a+1/2, -b+1/2, -c+1/2 | x, -y, -z	{ 2 ‖ 2100 | 1/2 1/2 1/2 }
-a, b+1/2, -c+1/2 | x, -y, -z	{ 2 ‖ 2010 | 0 1/2 1/2 }
-a+1/2, -b+1/2, c | x, -y, -z	{ 2 ‖ 2001 | 1/2 1/2 0 }
-a, -b+1/2, -c | x, -y, -z	{ 2 ‖ -1 | 0 1/2 0 }
-a+1/2, b+1/2, c+1/2 | x, -y, -z	{ 2 ‖ m100 | 1/2 1/2 1/2 }
a, -b+1/2, c+1/2 | x, -y, -z	{ 2 ‖ m010 | 0 1/2 1/2 }
a+1/2, b+1/2, -c | x, -y, -z	{ 2 ‖ m001 | 1/2 1/2 0 }

Wyckoff Positions

WP	Site symmetry	Representative
8a	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{-1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,0 | 0,0,z)
8b	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{-1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,1/4,0 | 0,0,0)
8c	$.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,b,1/4 | 0,0,z)
8d	$..{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/4,0,c | 0,0,z)
8e	$..{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/4,1/4,c | 0,0,0)
16f	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,b,c | 0,0,z)

Spin Brillouin Zone & k-little co-groups

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

Spin Brillouin Zone

Band Representations (Magnon)

8a

k-vector	Ag↑G(8)
Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_2^{S,+}(2)\oplus {\Gamma }_3^{S,+}(2)\oplus {\Gamma }_4^{S,+}(2)$
R:(1/2,1/2,1/2)	$R_1^S{R}_2^S(8)$
S:(1/2,1/2,0)	$S_1^S(4)\oplus S_2^S(4)$
T:(0,1/2,1/2)	$T_1^S(4)\oplus T_2^S(4)$
U:(1/2,0,1/2)	$U_1^S{U}_2^S(8)$
X:(1/2,0,0)	$X_1^S(4)\oplus X_2^S(4)$
Y:(0,1/2,0)	$Y_1^{S,+}(2)\oplus Y_2^{S,+}(2)\oplus Y_3^{S,+}(2)\oplus Y_4^{S,+}(2)$
Z:(0,0,1/2)	$Z_1^S(4)\oplus Z_2^S(4)$
A:(u,0,1/2)	$2A_1^S(4)$
B:(0,v,1/2)	$2B_1^S(4)$
C:(u,1/2,0)	$C_1^S(2)\oplus C_2^S(2)\oplus C_3^S(2)\oplus C_4^S(2)$
D:(1/2,v,0)	$2D_1^S(4)$
Δ:(0,v,0)	${\Delta }_1^S(2)\oplus {\Delta }_2^S(2)\oplus {\Delta }_3^S(2)\oplus {\Delta }_4^S(2)$
E:(u,1/2,1/2)	$2E_1^S(4)$
G:(1/2,0,w)	$G_1^S{G}_4^S(4)\oplus G_2^S{G}_3^S(4)$
H:(0,1/2,w)	$H_1^S(2)\oplus H_2^S(2)\oplus H_3^S(2)\oplus H_4^S(2)$
Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_2^S(2)\oplus {\Lambda }_3^S(2)\oplus {\Lambda }_4^S(2)$
P:(1/2,v,1/2)	$P_1^S{P}_4^S(4)\oplus P_2^S{P}_3^S(4)$
Q:(1/2,1/2,w)	$Q_1^S{Q}_4^S(4)\oplus Q_2^S{Q}_3^S(4)$
Σ:(u,0,0)	${\Sigma }_1^S(2)\oplus {\Sigma }_2^S(2)\oplus {\Sigma }_3^S(2)\oplus {\Sigma }_4^S(2)$
K:(0,v,w)	$2K_1^S(2)\oplus 2K_2^S(2)$
L:(1/2,v,w)	$2L_1^S{L}_2^S(4)$
M:(u,0,w)	$2M_1^S(2)\oplus 2M_2^S(2)$
N:(u,1/2,w)	$2N_1^S(2)\oplus 2N_2^S(2)$
V:(u,v,0)	$2V_1^S(2)\oplus 2V_2^S(2)$
W:(u,v,1/2)	$2W_1^S(2)\oplus 2W_2^S(2)$
GP:(u,v,w)	$4G{P}_1^S(2)$

8c

k-vector	A↑G(8)
Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)\oplus {\Gamma }_4^{S,+}(2)\oplus {\Gamma }_4^{S,-}(2)$
R:(1/2,1/2,1/2)	$R_1^S{R}_2^S(8)$
S:(1/2,1/2,0)	$S_1^S(4)\oplus S_2^S(4)$
T:(0,1/2,1/2)	$T_1^S(4)\oplus T_2^S(4)$
U:(1/2,0,1/2)	$U_1^S{U}_2^S(8)$
X:(1/2,0,0)	$X_1^S(4)\oplus X_2^S(4)$
Y:(0,1/2,0)	$Y_1^{S,+}(2)\oplus Y_1^{S,-}(2)\oplus Y_4^{S,+}(2)\oplus Y_4^{S,-}(2)$
Z:(0,0,1/2)	$Z_1^S(4)\oplus Z_2^S(4)$
A:(u,0,1/2)	$2A_1^S(4)$
B:(0,v,1/2)	$2B_1^S(4)$
C:(u,1/2,0)	$C_1^S(2)\oplus C_2^S(2)\oplus C_3^S(2)\oplus C_4^S(2)$
D:(1/2,v,0)	$2D_1^S(4)$
Δ:(0,v,0)	$2{\Delta }_1^S(2)\oplus 2{\Delta }_2^S(2)$
E:(u,1/2,1/2)	$2E_1^S(4)$
G:(1/2,0,w)	$G_1^S{G}_4^S(4)\oplus G_2^S{G}_3^S(4)$
H:(0,1/2,w)	$H_1^S(2)\oplus H_2^S(2)\oplus H_3^S(2)\oplus H_4^S(2)$
Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_2^S(2)\oplus {\Lambda }_3^S(2)\oplus {\Lambda }_4^S(2)$
P:(1/2,v,1/2)	$P_1^S{P}_4^S(4)\oplus P_2^S{P}_3^S(4)$
Q:(1/2,1/2,w)	$Q_1^S{Q}_4^S(4)\oplus Q_2^S{Q}_3^S(4)$
Σ:(u,0,0)	${\Sigma }_1^S(2)\oplus {\Sigma }_2^S(2)\oplus {\Sigma }_3^S(2)\oplus {\Sigma }_4^S(2)$
K:(0,v,w)	$2K_1^S(2)\oplus 2K_2^S(2)$
L:(1/2,v,w)	$2L_1^S{L}_2^S(4)$
M:(u,0,w)	$2M_1^S(2)\oplus 2M_2^S(2)$
N:(u,1/2,w)	$2N_1^S(2)\oplus 2N_2^S(2)$
V:(u,v,0)	$2V_1^S(2)\oplus 2V_2^S(2)$
W:(u,v,1/2)	$2W_1^S(2)\oplus 2W_2^S(2)$
GP:(u,v,w)	$4G{P}_1^S(2)$

8d

k-vector	A↑G(8)
Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)\oplus {\Gamma }_2^{S,+}(2)\oplus {\Gamma }_2^{S,-}(2)$
R:(1/2,1/2,1/2)	$R_1^S{R}_2^S(8)$
S:(1/2,1/2,0)	$S_1^S(4)\oplus S_2^S(4)$
T:(0,1/2,1/2)	$2T_1^S(4)$
U:(1/2,0,1/2)	$U_1^S{U}_2^S(8)$
X:(1/2,0,0)	$X_1^S(4)\oplus X_2^S(4)$
Y:(0,1/2,0)	$Y_1^{S,+}(2)\oplus Y_1^{S,-}(2)\oplus Y_2^{S,+}(2)\oplus Y_2^{S,-}(2)$
Z:(0,0,1/2)	$2Z_1^S(4)$
A:(u,0,1/2)	$2A_1^S(4)$
B:(0,v,1/2)	$2B_1^S(4)$
C:(u,1/2,0)	$C_1^S(2)\oplus C_2^S(2)\oplus C_3^S(2)\oplus C_4^S(2)$
D:(1/2,v,0)	$2D_1^S(4)$
Δ:(0,v,0)	${\Delta }_1^S(2)\oplus {\Delta }_2^S(2)\oplus {\Delta }_3^S(2)\oplus {\Delta }_4^S(2)$
E:(u,1/2,1/2)	$2E_1^S(4)$
G:(1/2,0,w)	$G_1^S{G}_4^S(4)\oplus G_2^S{G}_3^S(4)$
H:(0,1/2,w)	$2H_1^S(2)\oplus 2H_2^S(2)$
Λ:(0,0,w)	$2{\Lambda }_1^S(2)\oplus 2{\Lambda }_2^S(2)$
P:(1/2,v,1/2)	$P_1^S{P}_4^S(4)\oplus P_2^S{P}_3^S(4)$
Q:(1/2,1/2,w)	$Q_1^S{Q}_4^S(4)\oplus Q_2^S{Q}_3^S(4)$
Σ:(u,0,0)	${\Sigma }_1^S(2)\oplus {\Sigma }_2^S(2)\oplus {\Sigma }_3^S(2)\oplus {\Sigma }_4^S(2)$
K:(0,v,w)	$2K_1^S(2)\oplus 2K_2^S(2)$
L:(1/2,v,w)	$2L_1^S{L}_2^S(4)$
M:(u,0,w)	$2M_1^S(2)\oplus 2M_2^S(2)$
N:(u,1/2,w)	$2N_1^S(2)\oplus 2N_2^S(2)$
V:(u,v,0)	$2V_1^S(2)\oplus 2V_2^S(2)$
W:(u,v,1/2)	$2W_1^S(2)\oplus 2W_2^S(2)$
GP:(u,v,w)	$4G{P}_1^S(2)$

16f

k-vector	A↑G(16)
Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)\oplus {\Gamma }_2^{S,+}(2)\oplus {\Gamma }_2^{S,-}(2)\oplus {\Gamma }_3^{S,+}(2)\oplus {\Gamma }_3^{S,-}(2)\oplus {\Gamma }_4^{S,+}(2)\oplus {\Gamma }_4^{S,-}(2)$
R:(1/2,1/2,1/2)	$2R_1^S{R}_2^S(8)$
S:(1/2,1/2,0)	$2S_1^S(4)\oplus 2S_2^S(4)$
T:(0,1/2,1/2)	$2T_1^S(4)\oplus 2T_2^S(4)$
U:(1/2,0,1/2)	$2U_1^S{U}_2^S(8)$
X:(1/2,0,0)	$2X_1^S(4)\oplus 2X_2^S(4)$
Y:(0,1/2,0)	$Y_1^{S,+}(2)\oplus Y_1^{S,-}(2)\oplus Y_2^{S,+}(2)\oplus Y_2^{S,-}(2)\oplus Y_3^{S,+}(2)\oplus Y_3^{S,-}(2)\oplus Y_4^{S,+}(2)\oplus Y_4^{S,-}(2)$
Z:(0,0,1/2)	$2Z_1^S(4)\oplus 2Z_2^S(4)$
A:(u,0,1/2)	$4A_1^S(4)$
B:(0,v,1/2)	$4B_1^S(4)$
C:(u,1/2,0)	$2C_1^S(2)\oplus 2C_2^S(2)\oplus 2C_3^S(2)\oplus 2C_4^S(2)$
D:(1/2,v,0)	$4D_1^S(4)$
Δ:(0,v,0)	$2{\Delta }_1^S(2)\oplus 2{\Delta }_2^S(2)\oplus 2{\Delta }_3^S(2)\oplus 2{\Delta }_4^S(2)$
E:(u,1/2,1/2)	$4E_1^S(4)$
G:(1/2,0,w)	$2G_1^S{G}_4^S(4)\oplus 2G_2^S{G}_3^S(4)$
H:(0,1/2,w)	$2H_1^S(2)\oplus 2H_2^S(2)\oplus 2H_3^S(2)\oplus 2H_4^S(2)$
Λ:(0,0,w)	$2{\Lambda }_1^S(2)\oplus 2{\Lambda }_2^S(2)\oplus 2{\Lambda }_3^S(2)\oplus 2{\Lambda }_4^S(2)$
P:(1/2,v,1/2)	$2P_1^S{P}_4^S(4)\oplus 2P_2^S{P}_3^S(4)$
Q:(1/2,1/2,w)	$2Q_1^S{Q}_4^S(4)\oplus 2Q_2^S{Q}_3^S(4)$
Σ:(u,0,0)	$2{\Sigma }_1^S(2)\oplus 2{\Sigma }_2^S(2)\oplus 2{\Sigma }_3^S(2)\oplus 2{\Sigma }_4^S(2)$
K:(0,v,w)	$4K_1^S(2)\oplus 4K_2^S(2)$
L:(1/2,v,w)	$4L_1^S{L}_2^S(4)$
M:(u,0,w)	$4M_1^S(2)\oplus 4M_2^S(2)$
N:(u,1/2,w)	$4N_1^S(2)\oplus 4N_2^S(2)$
V:(u,v,0)	$4V_1^S(2)\oplus 4V_2^S(2)$
W:(u,v,1/2)	$4W_1^S(2)\oplus 4W_2^S(2)$
GP:(u,v,w)	$8G{P}_1^S(2)$