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+1/2 | x, y, z | { 1 ‖ m100 | 0 0 1/2 } |
| a, -b, c+1/2 | x, y, z | { 1 ‖ m010 | 0 0 1/2 } |
| b, a, -c+1/2 | -x, -y, -z | { -1 ‖ 2110 | 0 0 1/2 } |
| -b, -a, -c+1/2 | -x, -y, -z | { -1 ‖ 21-10 | 0 0 1/2 } |
| 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 | { m ‖ 1 | 0 } |
| -a, -b, c | -x, y, z | { m ‖ 2001 | 0 } |
| -a, b, c+1/2 | -x, y, z | { m ‖ m100 | 0 0 1/2 } |
| a, -b, c+1/2 | -x, y, z | { m ‖ m010 | 0 0 1/2 } |
| b, a, -c+1/2 | x, -y, -z | { 2 ‖ 2110 | 0 0 1/2 } |
| -b, -a, -c+1/2 | x, -y, -z | { 2 ‖ 21-10 | 0 0 1/2 } |
| b, -a, -c | x, -y, -z | { 2 ‖ -4+001 | 0 } |
| -b, a, -c | x, -y, -z | { 2 ‖ -4-001 | 0 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 2a | $\ce{^{1}{2}}.\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (0,0,1/4 | 0,0,0) |
| 2b | $\ce{^{1}{2}}.\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/2,1/2,1/4 | 0,0,0) |
| 2c | $\ce{^{-1}{-4}}..\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
| 2d | $\ce{^{-1}{-4}}..\ce{^{\infty m}{1}} $ | (1/2,1/2,0 | 0,0,0) |
| 4e | $..\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (a,a,1/4 | 0,0,0) |
| 4f | $..\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (a,a,3/4 | 0,0,0) |
| 4g | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,z) |
| 4h | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (1/2,1/2,c | 0,0,z) |
| 4i | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (0,1/2,c | 0,0,z) |
| 8j | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
| Wavevector-k | Little co-group |
|---|---|
| A:(1/2,1/2,1/2) | $\ce{^{-1}{-4}}\ce{^{1}{2}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| Γ:(0,0,0) | $\ce{^{-1}{-4}}\ce{^{1}{2}}\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}} $ |
| Z:(0,0,1/2) | $\ce{^{-1}{-4}}\ce{^{1}{2}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| R:(0,1/2,1/2) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| X:(0,1/2,0) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| Λ:(0,0,w) | $\ce{^{-1}{-4}}\ce{^{m}{2}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| V:(1/2,1/2,w) | $\ce{^{-1}{-4}}\ce{^{m}{2}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| S:(u,u,1/2) | $\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| Σ:(u,u,0) | $\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| T:(u,1/2,1/2) | $\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| U:(0,v,1/2) | $\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| W:(0,1/2,w) | $\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| Y:(u,1/2,0) | $\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| B:(0,v,w) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| C:(u,u,w) | $\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| D:(u,v,0) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| E:(u,v,1/2) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| F:(u,1/2,w) | $\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(4) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2) $ | |
| A:(1/2,1/2,1/2) | R:(1/2,1/2,1/2) | $(A)R_{1}^{S}R_{2}^{S}(4) $ | |
| M:(1/2,1/2,0) | S:(1/2,1/2,0) | $(M)S_{1}^{S}(2)⊕(M)S_{2}^{S}(2) $ | |
| R:(0,1/2,1/2) | T:(0,1/2,1/2) | $2 (R)T_{1}^{S}T_{2}^{S}(2)$ | Spin Splitting |
| X:(0,1/2,0) | Y:(0,1/2,0) | $2 (X)Y_{1}^{S}(1)⊕2 (X)Y_{2}^{S}(1)$ | Spin Splitting |
| Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}Z_{2}^{S}(4) $ | |
| Δ:(0,v,0) | Δ:(0,v,0) | $2Δ_{1}^{S}(1)⊕2Δ_{2}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
| S:(u,u,1/2) | W:(u,u,1/2) | $2(S)W_{1}^{S}(2) $ | |
| Σ:(u,u,0) | V:(u,u,0) | $2(Σ)V_{1}^{S}(2) $ | |
| T:(u,1/2,1/2) | E:(u,1/2,1/2) | $2(T)E_{1}^{S}E_{2}^{S}(2)$ | Spin Splitting |
| U:(0,v,1/2) | B:(0,v,1/2) | $2(U)B_{1}^{S}B_{2}^{S}(2)$ | Spin Splitting |
| V:(1/2,1/2,w) | Q:(1/2,1/2,w) | $(V)Q_{1}^{S}(2)⊕(V)Q_{2}^{S}(2) $ | |
| W:(0,1/2,w) | H:(0,1/2,w) | $2 (W)H_{1}^{S}(1)⊕2 (W)H_{2}^{S}(1)$ | Spin Splitting |
| Y:(u,1/2,0) | C:(u,1/2,0) | $2(Y)C_{1}^{S}(1)⊕2(Y)C_{2}^{S}(1)$ | Spin Splitting |
| B:(0,v,w) | K:(0,v,w) | $2(B)K_{1}^{S}(1)⊕2(B)K_{2}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | GP:(u,u,w) | $2(C)GP_{1}^{S}(2) $ | |
| D:(u,v,0) | V:(u,v,0) | $4(D)V_{1}^{S}(1)$ | Spin Splitting |
| E:(u,v,1/2) | W:(u,v,1/2) | $4(E)W_{1}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | N:(u,1/2,w) | $2(F)N_{1}^{S}(1)⊕2(F)N_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,v,w) | $4GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A↑G(4) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2) $ | |
| A:(1/2,1/2,1/2) | R:(1/2,1/2,1/2) | $(A)R_{1}^{S}R_{2}^{S}(4) $ | |
| M:(1/2,1/2,0) | S:(1/2,1/2,0) | $(M)S_{1}^{S}(2)⊕(M)S_{2}^{S}(2) $ | |
| R:(0,1/2,1/2) | T:(0,1/2,1/2) | $2 (R)T_{3}^{S}T_{4}^{S}(2)$ | Spin Splitting |
| X:(0,1/2,0) | Y:(0,1/2,0) | $2 (X)Y_{3}^{S}(1)⊕2 (X)Y_{4}^{S}(1)$ | Spin Splitting |
| Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}Z_{2}^{S}(4) $ | |
| Δ:(0,v,0) | Δ:(0,v,0) | $2Δ_{1}^{S}(1)⊕2Δ_{2}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
| S:(u,u,1/2) | W:(u,u,1/2) | $2(S)W_{1}^{S}(2) $ | |
| Σ:(u,u,0) | V:(u,u,0) | $2(Σ)V_{1}^{S}(2) $ | |
| T:(u,1/2,1/2) | E:(u,1/2,1/2) | $2(T)E_{1}^{S}E_{2}^{S}(2)$ | Spin Splitting |
| U:(0,v,1/2) | B:(0,v,1/2) | $2(U)B_{1}^{S}B_{2}^{S}(2)$ | Spin Splitting |
| V:(1/2,1/2,w) | Q:(1/2,1/2,w) | $(V)Q_{1}^{S}(2)⊕(V)Q_{2}^{S}(2) $ | |
| W:(0,1/2,w) | H:(0,1/2,w) | $2 (W)H_{3}^{S}(1)⊕2 (W)H_{4}^{S}(1)$ | Spin Splitting |
| Y:(u,1/2,0) | C:(u,1/2,0) | $2(Y)C_{1}^{S}(1)⊕2(Y)C_{2}^{S}(1)$ | Spin Splitting |
| B:(0,v,w) | K:(0,v,w) | $2(B)K_{1}^{S}(1)⊕2(B)K_{2}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | GP:(u,u,w) | $2(C)GP_{1}^{S}(2) $ | |
| D:(u,v,0) | V:(u,v,0) | $4(D)V_{1}^{S}(1)$ | Spin Splitting |
| E:(u,v,1/2) | W:(u,v,1/2) | $4(E)W_{1}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | N:(u,1/2,w) | $2(F)N_{1}^{S}(1)⊕2(F)N_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,v,w) | $4GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A↑G(4) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2) $ | |
| A:(1/2,1/2,1/2) | R:(1/2,1/2,1/2) | $(A)R_{3}^{S}R_{4}^{S}(4) $ | |
| M:(1/2,1/2,0) | S:(1/2,1/2,0) | $(M)S_{3}^{S}(2)⊕(M)S_{4}^{S}(2) $ | |
| R:(0,1/2,1/2) | T:(0,1/2,1/2) | $2 (R)T_{3}^{S}T_{4}^{S}(2)$ | Spin Splitting |
| X:(0,1/2,0) | Y:(0,1/2,0) | $2 (X)Y_{3}^{S}(1)⊕2 (X)Y_{4}^{S}(1)$ | Spin Splitting |
| Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}Z_{2}^{S}(4) $ | |
| Δ:(0,v,0) | Δ:(0,v,0) | $2Δ_{1}^{S}(1)⊕2Δ_{2}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
| S:(u,u,1/2) | W:(u,u,1/2) | $2(S)W_{1}^{S}(2) $ | |
| Σ:(u,u,0) | V:(u,u,0) | $2(Σ)V_{1}^{S}(2) $ | |
| T:(u,1/2,1/2) | E:(u,1/2,1/2) | $2(T)E_{1}^{S}E_{2}^{S}(2)$ | Spin Splitting |
| U:(0,v,1/2) | B:(0,v,1/2) | $2(U)B_{1}^{S}B_{2}^{S}(2)$ | Spin Splitting |
| V:(1/2,1/2,w) | Q:(1/2,1/2,w) | $(V)Q_{3}^{S}(2)⊕(V)Q_{4}^{S}(2) $ | |
| W:(0,1/2,w) | H:(0,1/2,w) | $2 (W)H_{3}^{S}(1)⊕2 (W)H_{4}^{S}(1)$ | Spin Splitting |
| Y:(u,1/2,0) | C:(u,1/2,0) | $2(Y)C_{1}^{S}(1)⊕2(Y)C_{2}^{S}(1)$ | Spin Splitting |
| B:(0,v,w) | K:(0,v,w) | $2(B)K_{1}^{S}(1)⊕2(B)K_{2}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | GP:(u,u,w) | $2(C)GP_{1}^{S}(2) $ | |
| D:(u,v,0) | V:(u,v,0) | $4(D)V_{1}^{S}(1)$ | Spin Splitting |
| E:(u,v,1/2) | W:(u,v,1/2) | $4(E)W_{1}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | N:(u,1/2,w) | $2(F)N_{1}^{S}(1)⊕2(F)N_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,v,w) | $4GP_{1}^{S}(1)$ | Spin Splitting |
| 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) $ | |
| A:(1/2,1/2,1/2) | R:(1/2,1/2,1/2) | $(A)R_{1}^{S}R_{2}^{S}(4)⊕(A)R_{3}^{S}R_{4}^{S}(4) $ | |
| M:(1/2,1/2,0) | S:(1/2,1/2,0) | $(M)S_{1}^{S}(2)⊕(M)S_{2}^{S}(2)⊕(M)S_{3}^{S}(2)⊕(M)S_{4}^{S}(2) $ | |
| R:(0,1/2,1/2) | T:(0,1/2,1/2) | $2 (R)T_{1}^{S}T_{2}^{S}(2)⊕2 (R)T_{3}^{S}T_{4}^{S}(2)$ | Spin Splitting |
| X:(0,1/2,0) | Y:(0,1/2,0) | $2(X)Y_{1}^{S}(1)⊕2(X)Y_{2}^{S}(1)⊕2(X)Y_{3}^{S}(1)⊕2(X)Y_{4}^{S}(1)$ | Spin Splitting |
| Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}Z_{2}^{S}(4)⊕Z_{3}^{S}Z_{4}^{S}(4) $ | |
| Δ:(0,v,0) | Δ:(0,v,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) $ | |
| S:(u,u,1/2) | W:(u,u,1/2) | $4(S)W_{1}^{S}(2) $ | |
| Σ:(u,u,0) | V:(u,u,0) | $4(Σ)V_{1}^{S}(2) $ | |
| T:(u,1/2,1/2) | E:(u,1/2,1/2) | $4(T)E_{1}^{S}E_{2}^{S}(2)$ | Spin Splitting |
| U:(0,v,1/2) | B:(0,v,1/2) | $4(U)B_{1}^{S}B_{2}^{S}(2)$ | Spin Splitting |
| V:(1/2,1/2,w) | Q:(1/2,1/2,w) | $(V)Q_{1}^{S}(2)⊕(V)Q_{2}^{S}(2)⊕(V)Q_{3}^{S}(2)⊕(V)Q_{4}^{S}(2) $ | |
| W:(0,1/2,w) | H:(0,1/2,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,1/2,0) | C:(u,1/2,0) | $4(Y)C_{1}^{S}(1)⊕4(Y)C_{2}^{S}(1)$ | Spin Splitting |
| B:(0,v,w) | K:(0,v,w) | $4(B)K_{1}^{S}(1)⊕4(B)K_{2}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | GP:(u,u,w) | $4(C)GP_{1}^{S}(2) $ | |
| D:(u,v,0) | V:(u,v,0) | $8(D)V_{1}^{S}(1)$ | Spin Splitting |
| E:(u,v,1/2) | W:(u,v,1/2) | $8(E)W_{1}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | N:(u,1/2,w) | $4(F)N_{1}^{S}(1)⊕4(F)N_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,v,w) | $8GP_{1}^{S}(1)$ | Spin Splitting |