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 } |
| -b, -a, c | x, y, z | { 1 ‖ m110 | 0 } |
| b, a, c | x, y, z | { 1 ‖ m1-10 | 0 } |
| -b, a, c | -x, -y, -z | { -1 ‖ 4+001 | 0 } |
| b, -a, c | -x, -y, -z | { -1 ‖ 4-001 | 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+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 ‖ 2001 | 1/2 1/2 1/2 } |
| -b+1/2, -a+1/2, c+1/2 | x, y, z | { 1 ‖ m110 | 1/2 1/2 1/2 } |
| b+1/2, a+1/2, c+1/2 | x, y, z | { 1 ‖ m1-10 | 1/2 1/2 1/2 } |
| -b+1/2, a+1/2, c+1/2 | -x, -y, -z | { -1 ‖ 4+001 | 1/2 1/2 1/2 } |
| b+1/2, -a+1/2, c+1/2 | -x, -y, -z | { -1 ‖ 4-001 | 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+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m010 | 1/2 1/2 1/2 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| -a, -b, c | -x, y, z | { m ‖ 2001 | 0 } |
| -b, -a, c | -x, y, z | { m ‖ m110 | 0 } |
| b, a, c | -x, y, z | { m ‖ m1-10 | 0 } |
| -b, a, c | x, -y, -z | { 2 ‖ 4+001 | 0 } |
| b, -a, c | x, -y, -z | { 2 ‖ 4-001 | 0 } |
| -a, b, c | x, -y, -z | { 2 ‖ m100 | 0 } |
| a, -b, c | x, -y, -z | { 2 ‖ m010 | 0 } |
| 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 ‖ 2001 | 1/2 1/2 1/2 } |
| -b+1/2, -a+1/2, c+1/2 | -x, y, z | { m ‖ m110 | 1/2 1/2 1/2 } |
| b+1/2, a+1/2, c+1/2 | -x, y, z | { m ‖ m1-10 | 1/2 1/2 1/2 } |
| -b+1/2, a+1/2, c+1/2 | x, -y, -z | { 2 ‖ 4+001 | 1/2 1/2 1/2 } |
| b+1/2, -a+1/2, c+1/2 | x, -y, -z | { 2 ‖ 4-001 | 1/2 1/2 1/2 } |
| -a+1/2, b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m100 | 1/2 1/2 1/2 } |
| a+1/2, -b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m010 | 1/2 1/2 1/2 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 2a | $\ce{^{-1}{4}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,0) |
| 4b | $\ce{^{1}{2}}\ce{^{-1}{m}}\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (0,1/2,c | 0,0,0) |
| 8c | $..\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (a,a,c | 0,0,z) |
| 8d | $.\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (a,0,c | 0,0,0) |
| 16e | $\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}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| M:(1,1,1) | $\ce{^{-1}{4}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| P:(1/2,1/2,1/2) | $\ce{^{-1}{4}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| X:(1/2,1/2,0) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| N:(1/2,0,1/2) | $\ce{^{2}{m}}\ce{^{\infty m}{1}} $ |
| Λ:(0,0,w) | $\ce{^{2}{4}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Δ:(u,u,0) | $\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| Q:(1/2,v,1/2) | $\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| W:(1/2,1/2,w) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| Y:(u,1-u,0) | $\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| A:(u,u,w) | $\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| B:(u,0,w) | $\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| C:(u,v,0) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| GP:(u,v,w) | $\ce{^{1}{1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
| k-vector | k-vector-G↑ | A↑G(8) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2)⊕Γ_{3}^{S}(2)⊕Γ_{4}^{S}(2) $ | |
| M:(0,0,1) | Z:(0,0,1) | $(M)Z_{1}^{S}(2)⊕(M)Z_{2}^{S}(2)⊕(M)Z_{3}^{S}(2)⊕(M)Z_{4}^{S}(2) $ | |
| N:(1/2,0,1/2) | L:(1/2,1/2,1/2) | $4(N)L_{1}^{S}(2) $ | |
| P:(1/2,1/2,1/2) | H:(0,1,1/2) | $(P)H_{1}^{S}(2)⊕(P)H_{2}^{S}(2)⊕(P)H_{3}^{S}(2)⊕(P)H_{4}^{S}(2) $ | |
| X:(1/2,1/2,0) | Y:(0,1,0) | $2 (X)Y_{1}^{S}(1)⊕2 (X)Y_{2}^{S}(1)⊕2 (X)Y_{3}^{S}(1)⊕2 (X)Y_{4}^{S}(1)$ | Spin Splitting |
| Δ:(u,u,0) | Δ:(0,2*u,0) | $4Δ_{1}^{S}(1)⊕4Δ_{2}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2)⊕Λ_{3}^{S}(2)⊕Λ_{4}^{S}(2) $ | |
| Q:(1/2,v,1/2) | GP:(1/2-v,1/2+v,1/2) | $4(Q)GP_{1}^{S}(2) $ | |
| Σ:(u,0,0) | M:(u,u,0) | $4(Σ)M_{1}^{S}(2) $ | |
| W:(1/2,1/2,w) | H:(0,1,w) | $2 (W)H_{1}^{S}(1)⊕2 (W)H_{2}^{S}(1)⊕2 (W)H_{3}^{S}(1)⊕2 (W)H_{4}^{S}(1)$ | Spin Splitting |
| Y:(u,-u,1) | A:(2*u,0,1) | $4(Y)A_{1}^{S}(2)⊕4(Y)A_{2}^{S}(1)$ | Spin Splitting |
| A:(u,u,w) | E:(0,2*u,w) | $4(A)E_{1}^{S}(2)⊕4(A)E_{2}^{S}(1)$ | Spin Splitting |
| B:(u,0,w) | GP:(u,u,w) | $4(B)GP_{1}^{S}(2)$ | Spin Splitting |
| C:(u,v,0) | M:(u-v,u+v,0) | $8(C)M_{1}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u-v,u+v,w) | $8GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A'↑G(4) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{3}^{S}(2) $ | |
| M:(0,0,1) | Z:(0,0,1) | $(M)Z_{1}^{S}(2)⊕(M)Z_{3}^{S}(2) $ | |
| N:(1/2,0,1/2) | L:(1/2,1/2,1/2) | $2(N)L_{1}^{S}(2) $ | |
| P:(1/2,1/2,1/2) | H:(0,1,1/2) | $(P)H_{1}^{S}(2)⊕(P)H_{3}^{S}(2) $ | |
| X:(1/2,1/2,0) | Y:(0,1,0) | $2 (X)Y_{1}^{S}(1) ⊕2 (X)Y_{3}^{S}(1)$ | Spin Splitting |
| Δ:(u,u,0) | Δ:(0,2*u,0) | $4Δ_{1}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{3}^{S}(2) $ | |
| Q:(1/2,v,1/2) | GP:(1/2-v,1/2+v,1/2) | $2(Q)GP_{1}^{S}(2) $ | |
| Σ:(u,0,0) | M:(u,u,0) | $2(Σ)M_{1}^{S}(2) $ | |
| W:(1/2,1/2,w) | H:(0,1,w) | $2 (W)H_{1}^{S}(1)⊕2 (W)H_{3}^{S}(1)$ | Spin Splitting |
| Y:(u,-u,1) | A:(2*u,0,1) | $2 (Y)A_{1}^{S}(1)⊕2 (Y)A_{2}^{S}(1)$ | Spin Splitting |
| A:(u,u,w) | E:(0,2*u,w) | $4(A)E_{1}^{S}(1)$ | Spin Splitting |
| B:(u,0,w) | GP:(u,u,w) | $2(B)GP_{1}^{S}(2) $ | |
| C:(u,v,0) | M:(u-v,u+v,0) | $4(C)M_{1}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u-v,u+v,w) | $4GP_{1}^{S}(1)$ | Spin Splitting |