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+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, -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+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 } |
| -b+1/2, a, c | -x, -y, -z | { -1 ‖ 4+001 | 1/2 0 0 } |
| b, -a+1/2, c | -x, -y, -z | { -1 ‖ 4-001 | 0 1/2 0 } |
| b+1/2, a+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ 2110 | 1/2 1/2 1/2 } |
| -b, -a, -c+1/2 | -x, -y, -z | { -1 ‖ 21-10 | 0 0 1/2 } |
| b+1/2, -a, -c | -x, -y, -z | { -1 ‖ -4+001 | 1/2 0 0 } |
| -b, a+1/2, -c | -x, -y, -z | { -1 ‖ -4-001 | 0 1/2 0 } |
| -b+1/2, -a+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m110 | 1/2 1/2 1/2 } |
| b, a, c+1/2 | -x, -y, -z | { -1 ‖ m1-10 | 0 0 1/2 } |
| 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+1/2, -c+1/2 | -x, y, z | { m ‖ 2010 | 0 1/2 1/2 } |
| -a+1/2, -b+1/2, c | -x, y, z | { m ‖ 2001 | 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 ‖ m100 | 1/2 0 1/2 } |
| a, -b+1/2, c+1/2 | -x, y, z | { m ‖ m010 | 0 1/2 1/2 } |
| a+1/2, b+1/2, -c | -x, y, z | { m ‖ m001 | 1/2 1/2 0 } |
| -b+1/2, a, c | x, -y, -z | { 2 ‖ 4+001 | 1/2 0 0 } |
| b, -a+1/2, c | x, -y, -z | { 2 ‖ 4-001 | 0 1/2 0 } |
| b+1/2, a+1/2, -c+1/2 | x, -y, -z | { 2 ‖ 2110 | 1/2 1/2 1/2 } |
| -b, -a, -c+1/2 | x, -y, -z | { 2 ‖ 21-10 | 0 0 1/2 } |
| b+1/2, -a, -c | x, -y, -z | { 2 ‖ -4+001 | 1/2 0 0 } |
| -b, a+1/2, -c | x, -y, -z | { 2 ‖ -4-001 | 0 1/2 0 } |
| -b+1/2, -a+1/2, c+1/2 | x, -y, -z | { 2 ‖ m110 | 1/2 1/2 1/2 } |
| b, a, c+1/2 | x, -y, -z | { 2 ‖ m1-10 | 0 0 1/2 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 4a | $\ce{^{1}{2}}.\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (3/4,1/4,1/4 | 0,0,0) |
| 4b | $\ce{^{-1}{-4}}..\ce{^{\infty m}{1}} $ | (3/4,1/4,0 | 0,0,0) |
| 4c | $\ce{^{-1}{4}}..\ce{^{\infty m}{1}} $ | (1/4,1/4,c | 0,0,0) |
| 8d | $\ce{^{1}{-1}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,z) |
| 8e | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (3/4,1/4,c | 0,0,z) |
| 8f | $..\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (a,-a,1/4 | 0,0,0) |
| 16g | $\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}{m}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| Γ:(0,0,0) | $\ce{^{-1}{4/}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| M:(1/2,1/2,0) | $\ce{^{-1}{4/}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| Z:(0,0,1/2) | $\ce{^{-1}{4/}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| R:(0,1/2,1/2) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| X:(0,1/2,0) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| Λ:(0,0,w) | $\ce{^{2}{4/}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| V:(1/2,1/2,w) | $\ce{^{2}{4/}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| S:(u,u,1/2) | $\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Σ:(u,u,0) | $\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| T:(u,1/2,1/2) | $\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| U:(0,v,1/2) | $\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| W:(0,1/2,w) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| Y:(u,1/2,0) | $\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| B:(0,v,w) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| C:(u,u,w) | $\ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| D:(u,v,0) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| E:(u,v,1/2) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| F:(u,1/2,w) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| GP:(u,v,w) | $\ce{^{m}{-1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
| k-vector | k-vector-G↑ | Ag↑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}(4)⊕(M)S_{2}^{S}(4) $ | |
| R:(0,1/2,1/2) | T:(0,1/2,1/2) | $2 (R)T_{1}^{S}T_{2}^{S}(4)$ | Spin Splitting |
| X:(0,1/2,0) | Y:(0,1/2,0) | $2 (X)Y_{1}^{S}(2)⊕2 (X)Y_{2}^{S}(2)$ | Spin Splitting |
| Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}(4)⊕Z_{2}^{S}(4) $ | |
| Δ:(0,v,0) | Δ:(0,v,0) | $2Δ_{1}^{S}(1)⊕2Δ_{2}^{S}(1)⊕2Δ_{3}^{S}(1)⊕2Δ_{4}^{S}(1)$ | 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) | $2(S)W_{1}^{S}(2)⊕2 (S)W_{2}^{S}(2) $ | |
| Σ:(u,u,0) | V:(u,u,0) | $2(Σ)V_{1}^{S}(2)⊕2(Σ)V_{2}^{S}(2) $ | |
| T:(u,1/2,1/2) | E:(u,1/2,1/2) | $2 (T)E_{1}^{S}E_{4}^{S}(2)⊕2 (T)E_{2}^{S}E_{3}^{S}(2)$ | Spin Splitting |
| U:(0,v,1/2) | B:(0,v,1/2) | $4(U)B_{1}^{S}(2)$ | Spin Splitting |
| V:(1/2,1/2,w) | Q:(1/2,1/2,w) | $(V)Q_{1}^{S}Q_{2}^{S}(4)⊕(V)Q_{3}^{S}Q_{4}^{S}(4) $ | |
| W:(0,1/2,w) | H:(0,1/2,w) | $2(W)H_{1}^{S}H_{3}^{S}(2)⊕2(W)H_{2}^{S}H_{4}^{S}(2)$ | Spin Splitting |
| Y:(u,1/2,0) | C:(u,1/2,0) | $4(Y)C_{1}^{S}(2)$ | 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) | $4(D)V_{1}^{S}(1)⊕4(D)V_{2}^{S}(1)$ | Spin Splitting |
| E:(u,v,1/2) | W:(u,v,1/2) | $4(E)W_{1}^{S}(1)⊕4(E)W_{2}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | N:(u,1/2,w) | $4(F)N_{1}^{S}N_{2}^{S}(2)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,v,w) | $8GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A↑G(8) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2)⊕Γ_{2}^{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)⊕(A)R_{3}^{S,-}R_{4}^{S,-}(4) $ | |
| M:(1/2,1/2,0) | S:(1/2,1/2,0) | $2(M)S_{2}^{S}(4) $ | |
| R:(0,1/2,1/2) | T:(0,1/2,1/2) | $2 (R)T_{1}^{S}T_{2}^{S}(4)$ | Spin Splitting |
| X:(0,1/2,0) | Y:(0,1/2,0) | $2 (X)Y_{1}^{S}(2)⊕2 (X)Y_{2}^{S}(2)$ | Spin Splitting |
| Z:(0,0,1/2) | Z:(0,0,1/2) | $2 Z_{1}^{S}(4) $ | |
| Δ:(0,v,0) | Δ:(0,v,0) | $2Δ_{1}^{S}(1)⊕2Δ_{2}^{S}(1)⊕2Δ_{3}^{S}(1)⊕2Δ_{4}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,0,w) | $2 Λ_{1}^{S}(2)⊕2 Λ_{2}^{S}(2) $ | |
| S:(u,u,1/2) | W:(u,u,1/2) | $2(S)W_{1}^{S}(2)⊕2 (S)W_{2}^{S}(2) $ | |
| Σ:(u,u,0) | V:(u,u,0) | $2(Σ)V_{1}^{S}(2)⊕2(Σ)V_{2}^{S}(2) $ | |
| T:(u,1/2,1/2) | E:(u,1/2,1/2) | $2 (T)E_{1}^{S}E_{4}^{S}(2)⊕2 (T)E_{2}^{S}E_{3}^{S}(2)$ | Spin Splitting |
| U:(0,v,1/2) | B:(0,v,1/2) | $4(U)B_{1}^{S}(2)$ | Spin Splitting |
| V:(1/2,1/2,w) | Q:(1/2,1/2,w) | $2(V)Q_{3}^{S}Q_{4}^{S}(4) $ | |
| W:(0,1/2,w) | H:(0,1/2,w) | $2(W)H_{1}^{S}H_{3}^{S}(2)⊕2(W)H_{2}^{S}H_{4}^{S}(2)$ | Spin Splitting |
| Y:(u,1/2,0) | C:(u,1/2,0) | $4(Y)C_{1}^{S}(2)$ | 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) | $4(D)V_{1}^{S}(1)⊕4(D)V_{2}^{S}(1)$ | Spin Splitting |
| E:(u,v,1/2) | W:(u,v,1/2) | $4(E)W_{1}^{S}(1)⊕4(E)W_{2}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | N:(u,1/2,w) | $4(F)N_{1}^{S}N_{2}^{S}(2)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,v,w) | $8GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A↑G(16) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2)⊕Γ_{2}^{S,+}(2)⊕Γ_{2}^{S,-}(2)⊕Γ_{3}^{S,+}(2)⊕Γ_{3}^{S,-}(2)⊕Γ_{4}^{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_{1}^{S,-}R_{2}^{S,-}(4)⊕(A)R_{3}^{S,+}R_{4}^{S,+}(4)⊕(A)R_{3}^{S,-}R_{4}^{S,-}(4) $ | |
| M:(1/2,1/2,0) | S:(1/2,1/2,0) | $2(M)S_{2}^{S}(4)⊕2(M)S_{2}^{S}(4) $ | |
| R:(0,1/2,1/2) | T:(0,1/2,1/2) | $4 (R)T_{1}^{S}T_{2}^{S}(4)$ | Spin Splitting |
| X:(0,1/2,0) | Y:(0,1/2,0) | $4 (X)Y_{1}^{S}(2)⊕4 (X)Y_{2}^{S}(2)$ | Spin Splitting |
| Z:(0,0,1/2) | Z:(0,0,1/2) | $2 Z_{1}^{S}(4)⊕2 Z_{2}^{S}(4) $ | |
| Δ:(0,v,0) | Δ:(0,v,0) | $4Δ_{1}^{S}(1)⊕4Δ_{2}^{S}(1)⊕4Δ_{3}^{S}(1)⊕4Δ_{4}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,0,w) | $2 Λ_{1}^{S}(2)⊕2 Λ_{2}^{S}(2)⊕2 Λ_{3}^{S}(2)⊕2 Λ_{4}^{S}(2) $ | |
| S:(u,u,1/2) | W:(u,u,1/2) | $4(S)W_{1}^{S}(2)⊕4 (S)W_{2}^{S}(2) $ | |
| Σ:(u,u,0) | V:(u,u,0) | $4(Σ)V_{1}^{S}(2)⊕4(Σ)V_{2}^{S}(2) $ | |
| T:(u,1/2,1/2) | E:(u,1/2,1/2) | $4 (T)E_{1}^{S}E_{4}^{S}(2)⊕4 (T)E_{2}^{S}E_{3}^{S}(2)$ | Spin Splitting |
| U:(0,v,1/2) | B:(0,v,1/2) | $8(U)B_{1}^{S}(2)$ | Spin Splitting |
| V:(1/2,1/2,w) | Q:(1/2,1/2,w) | $2(V)Q_{1}^{S}Q_{2}^{S}(4)⊕2(V)Q_{3}^{S}Q_{4}^{S}(4) $ | |
| W:(0,1/2,w) | H:(0,1/2,w) | $4(W)H_{1}^{S}H_{3}^{S}(2)⊕4(W)H_{2}^{S}H_{4}^{S}(2)$ | Spin Splitting |
| Y:(u,1/2,0) | C:(u,1/2,0) | $8(Y)C_{1}^{S}(2)$ | Spin Splitting |
| B:(0,v,w) | K:(0,v,w) | $8(B)K_{1}^{S}(1)⊕8(B)K_{2}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | GP:(u,u,w) | $8(C)GP_{1}^{S}(2) $ | |
| D:(u,v,0) | V:(u,v,0) | $8(D)V_{1}^{S}(1)⊕8(D)V_{2}^{S}(1)$ | Spin Splitting |
| E:(u,v,1/2) | W:(u,v,1/2) | $8(E)W_{1}^{S}(1)⊕8(E)W_{2}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | N:(u,1/2,w) | $8(F)N_{1}^{S}N_{2}^{S}(2)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,v,w) | $16GP_{1}^{S}(1)$ | Spin Splitting |