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, c, -b | -x, -y, -z | { -1 ‖ -4+100 | 0 } |
-a, -c, b | -x, -y, -z | { -1 ‖ -4-100 | 0 } |
-c, -b, a | -x, -y, -z | { -1 ‖ -4+010 | 0 } |
c, -b, -a | -x, -y, -z | { -1 ‖ -4-010 | 0 } |
b, -a, -c | -x, -y, -z | { -1 ‖ -4+001 | 0 } |
-b, a, -c | -x, -y, -z | { -1 ‖ -4-001 | 0 } |
-b, -a, c | -x, -y, -z | { -1 ‖ m110 | 0 } |
b, a, c | -x, -y, -z | { -1 ‖ m1-10 | 0 } |
a, -c, -b | -x, -y, -z | { -1 ‖ m011 | 0 } |
a, c, b | -x, -y, -z | { -1 ‖ m01-1 | 0 } |
-c, b, -a | -x, -y, -z | { -1 ‖ m101 | 0 } |
c, b, a | -x, -y, -z | { -1 ‖ m-101 | 0 } |
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, c, -b | x, -y, -z | { 2 ‖ -4+100 | 0 } |
-a, -c, b | x, -y, -z | { 2 ‖ -4-100 | 0 } |
-c, -b, a | x, -y, -z | { 2 ‖ -4+010 | 0 } |
c, -b, -a | x, -y, -z | { 2 ‖ -4-010 | 0 } |
b, -a, -c | x, -y, -z | { 2 ‖ -4+001 | 0 } |
-b, a, -c | x, -y, -z | { 2 ‖ -4-001 | 0 } |
-b, -a, c | x, -y, -z | { 2 ‖ m110 | 0 } |
b, a, c | x, -y, -z | { 2 ‖ m1-10 | 0 } |
a, -c, -b | x, -y, -z | { 2 ‖ m011 | 0 } |
a, c, b | x, -y, -z | { 2 ‖ m01-1 | 0 } |
-c, b, -a | x, -y, -z | { 2 ‖ m101 | 0 } |
c, b, a | x, -y, -z | { 2 ‖ m-101 | 0 } |
WP | Site symmetry | Representative |
---|---|---|
1a | $\ce{^{-1}{-4}}\ce{^{1}{3}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
1b | $\ce{^{-1}{-4}}\ce{^{1}{3}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (1/2,1/2,1/2 | 0,0,0) |
3c | $\ce{^{-1}{-4}}\ce{^{1}{2}}.\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (0,1/2,1/2 | 0,0,0) |
3d | $\ce{^{-1}{-4}}\ce{^{1}{2}}.\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (1/2,0,0 | 0,0,0) |
4e | $.\ce{^{1}{3}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (a,a,a | 0,0,0) |
6f | $\ce{^{1}{2}}.\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (a,0,0 | 0,0,0) |
6g | $\ce{^{1}{2}}.\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (a,1/2,1/2 | 0,0,0) |
12h | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,1/2,0 | 0,0,z) |
12i | $..\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (a,a,c | 0,0,0) |
24j | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
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{^{-1}{-4}}\ce{^{m}{2}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
T:(1/2,1/2,w) | $\ce{^{-1}{-4}}\ce{^{m}{2}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
Λ:(u,u,u) | $\ce{^{1}{3}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
S:(u,1/2,u) | $\ce{^{-1}{m}}\ce{^{m}{2}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
Σ:(u,u,0) | $\ce{^{2}{m}}\ce{^{-1}{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{^{2}{m}}\ce{^{\infty}{1}} $ |
GP:(u,v,w) | $\ce{^{1}{1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
k-vector | k-vector-G↑ | A↑G(24) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}Γ_{3}^{S}(4)⊕3 Γ_{4}^{S}(6) $ | |
M:(1/2,1/2,0) | M:(1/2,1/2,0) | $3 M_{1}^{S}(2)⊕3 M_{2}^{S}(2)⊕3 M_{3}^{S}(2)⊕3 M_{4}^{S}(2) $ | |
R:(1/2,1/2,1/2) | R:(1/2,1/2,1/2) | $R_{1}^{S}(2)⊕R_{2}^{S}R_{3}^{S}(4)⊕3R_{4}^{S}(6) $ | |
X:(0,1/2,0) | X:(0,1/2,0) | $3 X_{1}^{S}(2)⊕3 X_{2}^{S}(2)⊕3 X_{3}^{S}(2)⊕3 X_{4}^{S}(2) $ | |
Δ:(0,v,0) | Δ:(0,v,0) | $6Δ_{1}^{S}(2)⊕6Δ_{2}^{S}(2) $ | |
Λ:(u,u,u) | Λ:(u,u,u) | $4Λ_{1}^{S}(2)⊕4 Λ_{2}^{S}(2)⊕4 Λ_{3}^{S}(2) $ | |
S:(u,1/2,u) | S:(u,1/2,u) | $12S_{1}^{S}(2) $ | |
Σ:(u,u,0) | Σ:(u,u,0) | $12Σ_{1}^{S}(2) $ | |
T:(1/2,1/2,w) | T:(1/2,1/2,w) | $6T_{1}^{S}(2)⊕6T_{2}^{S}(2) $ | |
Z:(u,1/2,0) | Z:(u,1/2,0) | $12Z_{1}^{S}(1)⊕12Z_{2}^{S}(1)$ | Spin Splitting |
A:(u,v,0) | A:(u,v,0) | $24A_{1}^{S}(1)$ | Spin Splitting |
B:(u,1/2,w) | B:(u,1/2,w) | $24B_{1}^{S}(1)$ | Spin Splitting |
C:(u,u,w) | C:(u,u,w) | $12C_{1}^{S}(2) $ | |
GP:(u,v,w) | GP:(u,v,w) | $24GP_{1}^{S}(1)$ | Spin Splitting |
k-vector | k-vector-G↑ | A↑G(12) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}Γ_{3}^{S}(4)⊕Γ_{4}^{S}(6) $ | |
M:(1/2,1/2,0) | M:(1/2,1/2,0) | $M_{1}^{S}(2)⊕M_{2}^{S}(2)⊕M_{3}^{S}(2)⊕3 M_{4}^{S}(2) $ | |
R:(1/2,1/2,1/2) | R:(1/2,1/2,1/2) | $2 R_{4}^{S}(6) $ | |
X:(0,1/2,0) | X:(0,1/2,0) | $2 X_{1}^{S}(2)⊕2 X_{2}^{S}(2)⊕2X_{4}^{S}(2) $ | |
Δ:(0,v,0) | Δ:(0,v,0) | $4Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $ | |
Λ:(u,u,u) | Λ:(u,u,u) | $2Λ_{1}^{S}(2)⊕2 Λ_{2}^{S}(2)⊕2 Λ_{3}^{S}(2) $ | |
S:(u,1/2,u) | S:(u,1/2,u) | $6S_{1}^{S}(2) $ | |
Σ:(u,u,0) | Σ:(u,u,0) | $6Σ_{1}^{S}(2) $ | |
T:(1/2,1/2,w) | T:(1/2,1/2,w) | $2T_{1}^{S}(2)⊕4T_{2}^{S}(2) $ | |
Z:(u,1/2,0) | Z:(u,1/2,0) | $4Z_{1}^{S}(1)⊕8Z_{2}^{S}(1)$ | Spin Splitting |
A:(u,v,0) | A:(u,v,0) | $12A_{1}^{S}(1)$ | Spin Splitting |
B:(u,1/2,w) | B:(u,1/2,w) | $12B_{1}^{S}(1)$ | Spin Splitting |
C:(u,u,w) | C:(u,u,w) | $6C_{1}^{S}(2) $ | |
GP:(u,v,w) | GP:(u,v,w) | $12GP_{1}^{S}(1)$ | Spin Splitting |