Information of spin space group $I{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}{4}_1/{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{a}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}\text{d}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$ ( nSSG:74.141.1.1 )

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+1/2, -c | x, y, z	{ 1 ‖ 2010 | 0 1/2 0 }
-a, -b+1/2, c | x, y, z	{ 1 ‖ 2001 | 0 1/2 0 }
-a, -b, -c | x, y, z	{ 1 ‖ -1 | 0 }
-a, b, c | x, y, z	{ 1 ‖ m100 | 0 }
a, -b+1/2, c | x, y, z	{ 1 ‖ m010 | 0 1/2 0 }
a, b+1/2, -c | x, y, z	{ 1 ‖ m001 | 0 1/2 0 }
-b+1/4, a+3/4, c+1/4 | -x, -y, -z	{ -1 ‖ 4+001 | 1/4 3/4 1/4 }
b+3/4, -a+3/4, c+1/4 | -x, -y, -z	{ -1 ‖ 4-001 | 3/4 3/4 1/4 }
b+3/4, a+1/4, -c+3/4 | -x, -y, -z	{ -1 ‖ 2110 | 3/4 1/4 3/4 }
-b+1/4, -a+1/4, -c+3/4 | -x, -y, -z	{ -1 ‖ 21-10 | 1/4 1/4 3/4 }
b+3/4, -a+1/4, -c+3/4 | -x, -y, -z	{ -1 ‖ -4+001 | 3/4 1/4 3/4 }
-b+1/4, a+1/4, -c+3/4 | -x, -y, -z	{ -1 ‖ -4-001 | 1/4 1/4 3/4 }
-b+1/4, -a+3/4, c+1/4 | -x, -y, -z	{ -1 ‖ m110 | 1/4 3/4 1/4 }
b+3/4, a+3/4, c+1/4 | -x, -y, -z	{ -1 ‖ m1-10 | 3/4 3/4 1/4 }
a+1/2, b+1/2, c+1/2 | x, y, z	{ 1 ‖ 1 | 1/2 1/2 1/2 }
a+1/2, -b+1/2, -c+1/2 | x, y, z	{ 1 ‖ 2100 | 1/2 1/2 1/2 }
-a+1/2, b, -c+1/2 | x, y, z	{ 1 ‖ 2010 | 1/2 0 1/2 }
-a+1/2, -b, c+1/2 | x, y, z	{ 1 ‖ 2001 | 1/2 0 1/2 }
-a+1/2, -b+1/2, -c+1/2 | x, y, z	{ 1 ‖ -1 | 1/2 1/2 1/2 }
-a+1/2, b+1/2, c+1/2 | x, y, z	{ 1 ‖ m100 | 1/2 1/2 1/2 }
a+1/2, -b, c+1/2 | x, y, z	{ 1 ‖ m010 | 1/2 0 1/2 }
a+1/2, b, -c+1/2 | x, y, z	{ 1 ‖ m001 | 1/2 0 1/2 }
-b+3/4, a+1/4, c+3/4 | -x, -y, -z	{ -1 ‖ 4+001 | 3/4 1/4 3/4 }
b+1/4, -a+1/4, c+3/4 | -x, -y, -z	{ -1 ‖ 4-001 | 1/4 1/4 3/4 }
b+1/4, a+3/4, -c+1/4 | -x, -y, -z	{ -1 ‖ 2110 | 1/4 3/4 1/4 }
-b+3/4, -a+3/4, -c+1/4 | -x, -y, -z	{ -1 ‖ 21-10 | 3/4 3/4 1/4 }
b+1/4, -a+3/4, -c+1/4 | -x, -y, -z	{ -1 ‖ -4+001 | 1/4 3/4 1/4 }
-b+3/4, a+3/4, -c+1/4 | -x, -y, -z	{ -1 ‖ -4-001 | 3/4 3/4 1/4 }
-b+3/4, -a+1/4, c+3/4 | -x, -y, -z	{ -1 ‖ m110 | 3/4 1/4 3/4 }
b+1/4, a+1/4, c+3/4 | -x, -y, -z	{ -1 ‖ m1-10 | 1/4 1/4 3/4 }
a, b, c | -x, y, z	{ m ‖ 1 | 0 }
a, -b, -c | -x, y, z	{ m ‖ 2100 | 0 }
-a, b+1/2, -c | -x, y, z	{ m ‖ 2010 | 0 1/2 0 }
-a, -b+1/2, c | -x, y, z	{ m ‖ 2001 | 0 1/2 0 }
-a, -b, -c | -x, y, z	{ m ‖ -1 | 0 }
-a, b, c | -x, y, z	{ m ‖ m100 | 0 }
a, -b+1/2, c | -x, y, z	{ m ‖ m010 | 0 1/2 0 }
a, b+1/2, -c | -x, y, z	{ m ‖ m001 | 0 1/2 0 }
-b+1/4, a+3/4, c+1/4 | x, -y, -z	{ 2 ‖ 4+001 | 1/4 3/4 1/4 }
b+3/4, -a+3/4, c+1/4 | x, -y, -z	{ 2 ‖ 4-001 | 3/4 3/4 1/4 }
b+3/4, a+1/4, -c+3/4 | x, -y, -z	{ 2 ‖ 2110 | 3/4 1/4 3/4 }
-b+1/4, -a+1/4, -c+3/4 | x, -y, -z	{ 2 ‖ 21-10 | 1/4 1/4 3/4 }
b+3/4, -a+1/4, -c+3/4 | x, -y, -z	{ 2 ‖ -4+001 | 3/4 1/4 3/4 }
-b+1/4, a+1/4, -c+3/4 | x, -y, -z	{ 2 ‖ -4-001 | 1/4 1/4 3/4 }
-b+1/4, -a+3/4, c+1/4 | x, -y, -z	{ 2 ‖ m110 | 1/4 3/4 1/4 }
b+3/4, a+3/4, c+1/4 | x, -y, -z	{ 2 ‖ m1-10 | 3/4 3/4 1/4 }
a+1/2, b+1/2, c+1/2 | -x, y, z	{ m ‖ 1 | 1/2 1/2 1/2 }
a+1/2, -b+1/2, -c+1/2 | -x, y, z	{ m ‖ 2100 | 1/2 1/2 1/2 }
-a+1/2, b, -c+1/2 | -x, y, z	{ m ‖ 2010 | 1/2 0 1/2 }
-a+1/2, -b, c+1/2 | -x, y, z	{ m ‖ 2001 | 1/2 0 1/2 }
-a+1/2, -b+1/2, -c+1/2 | -x, y, z	{ m ‖ -1 | 1/2 1/2 1/2 }
-a+1/2, b+1/2, c+1/2 | -x, y, z	{ m ‖ m100 | 1/2 1/2 1/2 }
a+1/2, -b, c+1/2 | -x, y, z	{ m ‖ m010 | 1/2 0 1/2 }
a+1/2, b, -c+1/2 | -x, y, z	{ m ‖ m001 | 1/2 0 1/2 }
-b+3/4, a+1/4, c+3/4 | x, -y, -z	{ 2 ‖ 4+001 | 3/4 1/4 3/4 }
b+1/4, -a+1/4, c+3/4 | x, -y, -z	{ 2 ‖ 4-001 | 1/4 1/4 3/4 }
b+1/4, a+3/4, -c+1/4 | x, -y, -z	{ 2 ‖ 2110 | 1/4 3/4 1/4 }
-b+3/4, -a+3/4, -c+1/4 | x, -y, -z	{ 2 ‖ 21-10 | 3/4 3/4 1/4 }
b+1/4, -a+3/4, -c+1/4 | x, -y, -z	{ 2 ‖ -4+001 | 1/4 3/4 1/4 }
-b+3/4, a+3/4, -c+1/4 | x, -y, -z	{ 2 ‖ -4-001 | 3/4 3/4 1/4 }
-b+3/4, -a+1/4, c+3/4 | x, -y, -z	{ 2 ‖ m110 | 3/4 1/4 3/4 }
b+1/4, a+1/4, c+3/4 | x, -y, -z	{ 2 ‖ m1-10 | 1/4 1/4 3/4 }

Wyckoff Positions

WP	Site symmetry	Representative
4a	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{-4}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,3/4,1/8 | 0,0,0)
4b	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{-4}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,1/4,3/8 | 0,0,0)
8c	$.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}/{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,0 | 0,0,z)
8d	$.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}/{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,1/2 | 0,0,z)
8e	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,1/4,c | 0,0,z)
16f	$.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,0,0 | 0,0,z)
16g	$..{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,a+1/4,7/8 | 0,0,0)
16h	$.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,b,c | 0,0,z)
32i	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,b,c | 0,0,z)

Spin Brillouin Zone & k-little co-groups

Wavevector-k	Little co-group
Γ:(0,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
M:(1,1,1)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
P:(1/2,1/2,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
X:(1/2,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
N:(1/2,0,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
Λ:(0,0,w)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Δ:(u,u,0)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Q:(1/2,v,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Σ:(u,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
W:(1/2,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Y:(u,1-u,0)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
A:(u,u,w)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
B:(u,0,w)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
C:(u,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
GP:(u,v,w)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{-1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$

Spin Brillouin Zone

Band Representations (Magnon)

8c

k-vector	k-vector-G↑	Ag↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_3^{S,+}(2)$
M:(1,1,1)	X:(1,1,1)	$(M)X_1^{S,+}(2)\oplus (M)X_3^{S,+}(2)$
N:(1/2,0,1/2)	R:(1/2,0,1/2)	$2(N)R_1^{S,+}(1)\oplus 2(N)R_2^{S,+}(1)$	Spin Splitting
P:(1/2,1/2,1/2)	W:(1/2,1/2,1/2)	$(P)W_1^S(4)$
X:(1/2,1/2,0)	T:(1/2,1/2,0)	$(X)T_1^S(4)$
Δ:(u,u,0)	C:(u,u,0)	$(\Delta )C_1^S(2)\oplus (\Delta )C_2^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_3^S(2)$
Q:(1/2,v,1/2)	Q:(1/2,v,1/2)	$2Q_1^S(1)\oplus 2Q_2^S(1)$	Spin Splitting
Σ:(u,0,0)	Σ:(u,0,0)	$2{\Sigma }_1^S(1)\oplus 2{\Sigma }_2^S(1)$	Spin Splitting
W:(1/2,1/2,w)	P:(1/2,1/2,w)	$(W)P_1^S(W)P_2^S(4)$
Y:(u,1-u,0)	C:(u,1-u,0)	$(Y)C_1^S(2)\oplus (Y)C_2^S(2)$
A:(u,u,w)	GP:(u,u,w)	$2(A)G{P}_1^S(2)$
B:(u,0,w)	B:(u,0,w)	$2B_1^S(1)\oplus 2B_2^S(1)$	Spin Splitting
C:(u,v,0)	C:(u,v,0)	$2C_1^S(1)\oplus 2C_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u,v,w)	$4G{P}_1^S(1)$	Spin Splitting

8d

k-vector	k-vector-G↑	Ag↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_3^{S,+}(2)$
M:(1,1,1)	X:(1,1,1)	$(M)X_1^{S,+}(2)\oplus (M)X_3^{S,+}(2)$
N:(1/2,0,1/2)	R:(1/2,0,1/2)	$2(N)R_1^{S,-}(1)\oplus 2(N)R_2^{S,-}(1)$	Spin Splitting
P:(1/2,1/2,1/2)	W:(1/2,1/2,1/2)	$(P)W_1^S(4)$
X:(1/2,1/2,0)	T:(1/2,1/2,0)	$(X)T_1^S(4)$
Δ:(u,u,0)	C:(u,u,0)	$(\Delta )C_1^S(2)\oplus (\Delta )C_2^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_3^S(2)$
Q:(1/2,v,1/2)	Q:(1/2,v,1/2)	$2Q_1^S(1)\oplus 2Q_2^S(1)$	Spin Splitting
Σ:(u,0,0)	Σ:(u,0,0)	$2{\Sigma }_1^S(1)\oplus 2{\Sigma }_2^S(1)$	Spin Splitting
W:(1/2,1/2,w)	P:(1/2,1/2,w)	$(W)P_1^S(W)P_2^S(4)$
Y:(u,1-u,0)	C:(u,1-u,0)	$(Y)C_1^S(2)\oplus (Y)C_2^S(2)$
A:(u,u,w)	GP:(u,u,w)	$2(A)G{P}_1^S(2)$
B:(u,0,w)	B:(u,0,w)	$2B_1^S(1)\oplus 2B_2^S(1)$	Spin Splitting
C:(u,v,0)	C:(u,v,0)	$2C_1^S(1)\oplus 2C_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u,v,w)	$4G{P}_1^S(1)$	Spin Splitting

8e

k-vector	k-vector-G↑	A1↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_2^{S,-}(2)$
M:(1,1,1)	X:(1,1,1)	$(M)X_1^{S,+}(2)\oplus (M)X_2^{S,-}(2)$
N:(1/2,0,1/2)	R:(1/2,0,1/2)	$2(N)R_1^{S,+}(1)\oplus 2(N)R_2^{S,-}(1)$	Spin Splitting
P:(1/2,1/2,1/2)	W:(1/2,1/2,1/2)	$(P)W_1^S(4)$
X:(1/2,1/2,0)	T:(1/2,1/2,0)	$(X)T_1^S(4)$
Δ:(u,u,0)	C:(u,u,0)	$(\Delta )C_1^S(2)\oplus (\Delta )C_2^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	$2{\Lambda }_1^S(2)$
Q:(1/2,v,1/2)	Q:(1/2,v,1/2)	$2Q_1^S(1)\oplus 2Q_2^S(1)$	Spin Splitting
Σ:(u,0,0)	Σ:(u,0,0)	$2{\Sigma }_1^S(1)\oplus 2{\Sigma }_3^S(1)$	Spin Splitting
W:(1/2,1/2,w)	P:(1/2,1/2,w)	$(W)P_1^S(W)P_2^S(4)$
Y:(u,1-u,0)	C:(u,1-u,0)	$(Y)C_1^S(2)\oplus (Y)C_2^S(2)$
A:(u,u,w)	GP:(u,u,w)	$2(A)G{P}_1^S(2)$
B:(u,0,w)	B:(u,0,w)	$4B_1^S(1)$	Spin Splitting
C:(u,v,0)	C:(u,v,0)	$2C_1^S(1)\oplus 2C_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u,v,w)	$4G{P}_1^S(1)$	Spin Splitting

16f

k-vector	k-vector-G↑	A↑G(8)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)\oplus {\Gamma }_3^{S,+}(2)\oplus {\Gamma }_3^{S,-}(2)$
M:(1,1,1)	X:(1,1,1)	$(M)X_1^{S,+}(2)\oplus (M)X_1^{S,-}(2)\oplus (M)X_3^{S,+}(2)\oplus (M)X_3^{S,-}(2)$
N:(1/2,0,1/2)	R:(1/2,0,1/2)	$2(N)R_1^{S,+}(1)\oplus 2(N)R_1^{S,-}(1)\oplus 2(N)R_2^{S,+}(1)\oplus 2(N)R_2^{S,-}(1)$	Spin Splitting
P:(1/2,1/2,1/2)	W:(1/2,1/2,1/2)	$2(P)W_1^S(4)$
X:(1/2,1/2,0)	T:(1/2,1/2,0)	$2(X)T_1^S(4)$
Δ:(u,u,0)	C:(u,u,0)	$2(\Delta )C_1^S(2)\oplus 2(\Delta )C_2^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_2^S(2)\oplus {\Lambda }_3^S(2)\oplus {\Lambda }_4^S(2)$
Q:(1/2,v,1/2)	Q:(1/2,v,1/2)	$4Q_1^S(1)\oplus 4Q_2^S(1)$	Spin Splitting
Σ:(u,0,0)	Σ:(u,0,0)	$4{\Sigma }_1^S(1)\oplus 4{\Sigma }_2^S(1)$	Spin Splitting
W:(1/2,1/2,w)	P:(1/2,1/2,w)	$2(W)P_1^S(W)P_2^S(4)$
Y:(u,1-u,0)	C:(u,1-u,0)	$2(Y)C_1^S(2)\oplus 2(Y)C_2^S(2)$
A:(u,u,w)	GP:(u,u,w)	$4(A)G{P}_1^S(2)$
B:(u,0,w)	B:(u,0,w)	$4B_1^S(1)\oplus 4B_2^S(1)$	Spin Splitting
C:(u,v,0)	C:(u,v,0)	$4C_1^S(1)\oplus 4C_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u,v,w)	$8G{P}_1^S(1)$	Spin Splitting

16h

k-vector	k-vector-G↑	A'↑G(8)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_2^{S,-}(2)\oplus {\Gamma }_3^{S,+}(2)\oplus {\Gamma }_4^{S,-}(2)$
M:(1,1,1)	X:(1,1,1)	$(M)X_1^{S,+}(2)\oplus (M)X_2^{S,-}(2)\oplus (M)X_3^{S,+}(2)\oplus (M)X_4^{S,-}(2)$
N:(1/2,0,1/2)	R:(1/2,0,1/2)	$2(N)R_1^{S,+}(1)\oplus 2(N)R_1^{S,-}(1)\oplus 2(N)R_2^{S,+}(1)\oplus 2(N)R_2^{S,-}(1)$	Spin Splitting
P:(1/2,1/2,1/2)	W:(1/2,1/2,1/2)	$2(P)W_1^S(4)$
X:(1/2,1/2,0)	T:(1/2,1/2,0)	$2(X)T_1^S(4)$
Δ:(u,u,0)	C:(u,u,0)	$2(\Delta )C_1^S(2)\oplus 2(\Delta )C_2^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	$2{\Lambda }_1^S(2)\oplus 2{\Lambda }_3^S(2)$
Q:(1/2,v,1/2)	Q:(1/2,v,1/2)	$4Q_1^S(1)\oplus 4Q_2^S(1)$	Spin Splitting
Σ:(u,0,0)	Σ:(u,0,0)	$2{\Sigma }_1^S(1)\oplus 2{\Sigma }_2^S(1)\oplus 2{\Sigma }_3^S(1)\oplus 2{\Sigma }_4^S(1)$	Spin Splitting
W:(1/2,1/2,w)	P:(1/2,1/2,w)	$2(W)P_1^S(W)P_2^S(4)$
Y:(u,1-u,0)	C:(u,1-u,0)	$2(Y)C_1^S(2)\oplus 2(Y)C_2^S(2)$
A:(u,u,w)	GP:(u,u,w)	$4(A)G{P}_1^S(2)$
B:(u,0,w)	B:(u,0,w)	$4B_1^S(1)\oplus 4B_2^S(1)$	Spin Splitting
C:(u,v,0)	C:(u,v,0)	$4C_1^S(1)\oplus 4C_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u,v,w)	$8G{P}_1^S(1)$	Spin Splitting

32i

k-vector	k-vector-G↑	A↑G(16)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)\oplus {\Gamma }_2^{S,+}(2)\oplus {\Gamma }_2^{S,-}(2)\oplus {\Gamma }_3^{S,+}(2)\oplus {\Gamma }_3^{S,-}(2)\oplus {\Gamma }_4^{S,+}(2)\oplus {\Gamma }_4^{S,-}(2)$
M:(1,1,1)	X:(1,1,1)	$(M)X_1^{S,+}(2)\oplus (M)X_1^{S,-}(2)\oplus (M)X_2^{S,+}(2)\oplus (M)X_2^{S,-}(2)\oplus (M)X_3^{S,+}(2)\oplus (M)X_3^{S,-}(2)\oplus (M)X_4^{S,+}(2)\oplus (M)X_4^{S,-}(2)$
N:(1/2,0,1/2)	R:(1/2,0,1/2)	$4(N)R_1^{S,+}(1)\oplus 4(N)R_1^{S,-}(1)\oplus 4(N)R_2^{S,+}(1)\oplus 4(N)R_2^{S,-}(1)$	Spin Splitting
P:(1/2,1/2,1/2)	W:(1/2,1/2,1/2)	$4(P)W_1^S(4)$
X:(1/2,1/2,0)	T:(1/2,1/2,0)	$4(X)T_1^S(4)$
Δ:(u,u,0)	C:(u,u,0)	$4(\Delta )C_1^S(2)\oplus 4(\Delta )C_2^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	$2{\Lambda }_1^S(2)\oplus 2{\Lambda }_2^S(2)\oplus 2{\Lambda }_3^S(2)\oplus 2{\Lambda }_4^S(2)$
Q:(1/2,v,1/2)	Q:(1/2,v,1/2)	$8Q_1^S(1)\oplus 8Q_2^S(1)$	Spin Splitting
Σ:(u,0,0)	Σ:(u,0,0)	$4{\Sigma }_1^S(1)\oplus 4{\Sigma }_2^S(1)\oplus 4{\Sigma }_3^S(1)\oplus 4{\Sigma }_4^S(1)$	Spin Splitting
W:(1/2,1/2,w)	P:(1/2,1/2,w)	$4(W)P_1^S(W)P_2^S(4)$
Y:(u,1-u,0)	C:(u,1-u,0)	$4(Y)C_1^S(2)\oplus 4(Y)C_2^S(2)$
A:(u,u,w)	GP:(u,u,w)	$8(A)G{P}_1^S(2)$
B:(u,0,w)	B:(u,0,w)	$8B_1^S(1)\oplus 8B_2^S(1)$	Spin Splitting
C:(u,v,0)	C:(u,v,0)	$8C_1^S(1)\oplus 8C_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u,v,w)	$16G{P}_1^S(1)$	Spin Splitting