The continuously infinite group ∞1 is omitted.
| Coordinates | Seitz symbol |
|---|---|
| a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
| a+1/2, -b, -c | x, y, z | { 1 ‖ 2100 | 1/2 0 0 } |
| a, -b, c | x, y, z | { 1 ‖ m010 | 0 } |
| a+1/2, b, -c | x, y, z | { 1 ‖ m001 | 1/2 0 0 } |
| -a, b, -c | -x, -y, -z | { -1 ‖ 2010 | 0 } |
| -a+1/2, -b, c | -x, -y, -z | { -1 ‖ 2001 | 1/2 0 0 } |
| -a, -b, -c | -x, -y, -z | { -1 ‖ -1 | 0 } |
| -a+1/2, b, c | -x, -y, -z | { -1 ‖ m100 | 1/2 0 0 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| a+1/2, -b, -c | -x, y, z | { m ‖ 2100 | 1/2 0 0 } |
| a, -b, c | -x, y, z | { m ‖ m010 | 0 } |
| a+1/2, b, -c | -x, y, z | { m ‖ m001 | 1/2 0 0 } |
| -a, b, -c | x, -y, -z | { 2 ‖ 2010 | 0 } |
| -a+1/2, -b, c | x, -y, -z | { 2 ‖ 2001 | 1/2 0 0 } |
| -a, -b, -c | x, -y, -z | { 2 ‖ -1 | 0 } |
| -a+1/2, b, c | x, -y, -z | { 2 ‖ m100 | 1/2 0 0 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 2a | $.\ce{^{-1}{2}}/\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
| 2b | $.\ce{^{-1}{2}}/\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (0,1/2,0 | 0,0,0) |
| 2c | $.\ce{^{-1}{2}}/\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,0) |
| 2d | $.\ce{^{-1}{2}}/\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (0,1/2,1/2 | 0,0,0) |
| 2e | $\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/4,0,c | 0,0,0) |
| 2f | $\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/4,1/2,c | 0,0,0) |
| 4g | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (0,b,0 | 0,0,0) |
| 4h | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (0,b,1/2 | 0,0,0) |
| 4i | $.\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (a,0,c | 0,0,z) |
| 4j | $.\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (a,1/2,c | 0,0,z) |
| 4k | $\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (1/4,b,c | 0,0,0) |
| 8l | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
| Wavevector-k | Little co-group |
|---|---|
| Γ:(0,0,0) | $ \ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| R:(1/2,1/2,1/2) | $ \ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| S:(1/2,1/2,0) | $ \ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| T:(0,1/2,1/2) | $ \ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| U:(1/2,0,1/2) | $ \ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| X:(1/2,0,0) | $ \ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| Y:(0,1/2,0) | $ \ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| Z:(0,0,1/2) | $ \ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| A:(u,0,1/2) | $ \ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| B:(0,v,1/2) | $ \ce{^{2}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| C:(u,1/2,0) | $ \ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| D:(1/2,v,0) | $ \ce{^{2}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $ \ce{^{2}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| E:(u,1/2,1/2) | $ \ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| G:(1/2,0,w) | $ \ce{^{2}{m}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| H:(0,1/2,w) | $ \ce{^{2}{m}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| Λ:(0,0,w) | $ \ce{^{2}{m}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| P:(1/2,v,1/2) | $ \ce{^{2}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Q:(1/2,1/2,w) | $ \ce{^{2}{m}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $ \ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| K:(0,v,w) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| L:(1/2,v,w) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| M:(u,0,w) | $ \ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| N:(u,1/2,w) | $ \ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| V:(u,v,0) | $ \ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| W:(u,v,1/2) | $ \ce{^{-1}{2/}}\ce{^{1}{m}}\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_{3}^{S}(2) $ |
| R:(1/2,-1/2,-1/2) | R:(1/2,1/2,1/2) | $R_{1}^{S}R_{3}^{S}(4) $ |
| S:(1/2,-1/2,0) | U:(1/2,0,1/2) | $(S)U_{1}^{S}U_{3}^{S}(4) $ |
| T:(0,-1/2,-1/2) | S:(1/2,1/2,0) | $(T)S_{1}^{S}(2)⊕(T)S_{3}^{S}(2) $ |
| U:(1/2,0,-1/2) | T:(0,1/2,1/2) | $(U)T_{1}^{S}T_{3}^{S}(4) $ |
| X:(1/2,0,0) | Z:(0,0,1/2) | $(X)Z_{1}^{S}Z_{3}^{S}(4) $ |
| Y:(0,-1/2,0) | X:(1/2,0,0) | $(Y)X_{1}^{S}(2)⊕(Y)X_{3}^{S}(2) $ |
| Z:(0,0,-1/2) | Y:(0,1/2,0) | $(Z)Y_{1}^{S}(2)⊕(Z)Y_{3}^{S}(2) $ |
| A:(u,0,-1/2) | H:(0,1/2,u) | $(A)H_{1}^{S}(2)⊕(A)H_{3}^{S}(2) $ |
| B:(0,v,-1/2) | C:(-v,1/2,0) | $(B)C_{1}^{S}(2)⊕(B)C_{2}^{S}(2) $ |
| C:(u,-1/2,0) | G:(1/2,0,u) | $(C)G_{1}^{S}(2)⊕(C)G_{3}^{S}(2) $ |
| D:(1/2,v,0) | A:(-v,0,1/2) | $(D)A_{1}^{S}A_{2}^{S}(4) $ |
| Δ:(0,v,0) | Σ:(-v,0,0) | $(Δ)Σ_{1}^{S}(2)⊕(Δ)Σ_{2}^{S}(2) $ |
| E:(u,-1/2,-1/2) | Q:(1/2,1/2,u) | $(E)Q_{1}^{S}(2)⊕(E)Q_{3}^{S}(2) $ |
| G:(1/2,0,w) | B:(0,-w,1/2) | $(G)B_{1}^{S}B_{1}^{S}(4) $ |
| H:(0,-1/2,w) | D:(1/2,-w,0) | $2(H)D_{2}^{S}(2) $ |
| Λ:(0,0,w) | Δ:(0,-w,0) | $2(Λ)Δ_{1}^{S}(2) $ |
| P:(1/2,v,-1/2) | E:(-v,1/2,1/2) | $(P)E_{1}^{S}E_{2}^{S}(4) $ |
| Q:(1/2,-1/2,w) | P:(1/2,-w,1/2) | $(Q)P_{1}^{S}P_{1}^{S}(4) $ |
| Σ:(u,0,0) | Λ:(0,0,u) | $(Σ)Λ_{1}^{S}(2)⊕(Σ)Λ_{3}^{S}(2) $ |
| K:(0,v,w) | V:(-v,-w,0) | $2(K)V_{1}^{S}(2) $ |
| L:(1/2,v,w) | W:(-v,-w,1/2) | $(L)W_{1}^{S}W_{1}^{S}(4) $ |
| M:(u,0,w) | K:(0,-w,u) | $2(M)K_{1}^{S}(2) $ |
| N:(u,-1/2,w) | L:(1/2,-w,u) | $2(N)L_{1}^{S}(2) $ |
| V:(u,v,0) | M:(-v,0,u) | $(V)M_{1}^{S}(2)⊕(V)M_{2}^{S}(2) $ |
| W:(u,v,-1/2) | N:(-v,1/2,u) | $(W)N_{1}^{S}(2)⊕(W)N_{2}^{S}(2) $ |
| GP:(u,v,w) | GP:(-v,-w,u) | $2GP_{1}^{S}(2) $ |
| k-vector | k-vector-G↑ | A'↑G(4) |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{3}^{S}(2) $ |
| R:(1/2,-1/2,-1/2) | R:(1/2,1/2,1/2) | $R_{2}^{S}R_{4}^{S}(4) $ |
| S:(1/2,-1/2,0) | U:(1/2,0,1/2) | $(S)U_{2}^{S}U_{4}^{S}(4) $ |
| T:(0,-1/2,-1/2) | S:(1/2,1/2,0) | $(T)S_{2}^{S}(2)⊕(T)S_{4}^{S}(2) $ |
| U:(1/2,0,-1/2) | T:(0,1/2,1/2) | $(U)T_{1}^{S}T_{3}^{S}(4) $ |
| X:(1/2,0,0) | Z:(0,0,1/2) | $(X)Z_{1}^{S}Z_{3}^{S}(4) $ |
| Y:(0,-1/2,0) | X:(1/2,0,0) | $(Y)X_{2}^{S}(2)⊕(Y)X_{4}^{S}(2) $ |
| Z:(0,0,-1/2) | Y:(0,1/2,0) | $(Z)Y_{1}^{S}(2)⊕(Z)Y_{3}^{S}(2) $ |
| A:(u,0,-1/2) | H:(0,1/2,u) | $(A)H_{1}^{S}(2)⊕(A)H_{3}^{S}(2) $ |
| B:(0,v,-1/2) | C:(-v,1/2,0) | $(B)C_{1}^{S}(2)⊕(B)C_{2}^{S}(2) $ |
| C:(u,-1/2,0) | G:(1/2,0,u) | $(C)G_{2}^{S}(2)⊕(C)G_{4}^{S}(2) $ |
| D:(1/2,v,0) | A:(-v,0,1/2) | $(D)A_{1}^{S}A_{2}^{S}(4) $ |
| Δ:(0,v,0) | Σ:(-v,0,0) | $(Δ)Σ_{1}^{S}(2)⊕(Δ)Σ_{2}^{S}(2) $ |
| E:(u,-1/2,-1/2) | Q:(1/2,1/2,u) | $(E)Q_{2}^{S}(2)⊕(E)Q_{4}^{S}(2) $ |
| G:(1/2,0,w) | B:(0,-w,1/2) | $(G)B_{1}^{S}B_{1}^{S}(4) $ |
| H:(0,-1/2,w) | D:(1/2,-w,0) | $2(H)D_{2}^{S}(2) $ |
| Λ:(0,0,w) | Δ:(0,-w,0) | $2(Λ)Δ_{1}^{S}(2) $ |
| P:(1/2,v,-1/2) | E:(-v,1/2,1/2) | $(P)E_{1}^{S}E_{2}^{S}(4) $ |
| Q:(1/2,-1/2,w) | P:(1/2,-w,1/2) | $(Q)P_{2}^{S}P_{2}^{S}(4) $ |
| Σ:(u,0,0) | Λ:(0,0,u) | $(Σ)Λ_{1}^{S}(2)⊕(Σ)Λ_{3}^{S}(2) $ |
| K:(0,v,w) | V:(-v,-w,0) | $2(K)V_{1}^{S}(2) $ |
| L:(1/2,v,w) | W:(-v,-w,1/2) | $(L)W_{1}^{S}W_{1}^{S}(4) $ |
| M:(u,0,w) | K:(0,-w,u) | $2(M)K_{1}^{S}(2) $ |
| N:(u,-1/2,w) | L:(1/2,-w,u) | $2(N)L_{2}^{S}(2) $ |
| V:(u,v,0) | M:(-v,0,u) | $(V)M_{1}^{S}(2)⊕(V)M_{2}^{S}(2) $ |
| W:(u,v,-1/2) | N:(-v,1/2,u) | $(W)N_{1}^{S}(2)⊕(W)N_{2}^{S}(2) $ |
| GP:(u,v,w) | GP:(-v,-w,u) | $2GP_{1}^{S}(2) $ |
| 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) $ |
| R:(1/2,-1/2,-1/2) | R:(1/2,1/2,1/2) | $R_{1}^{S}R_{3}^{S}(4)⊕R_{2}^{S}R_{4}^{S}(4) $ |
| S:(1/2,-1/2,0) | U:(1/2,0,1/2) | $(S)U_{1}^{S}U_{3}^{S}(4)⊕(S)U_{2}^{S}U_{4}^{S}(4) $ |
| T:(0,-1/2,-1/2) | S:(1/2,1/2,0) | $(T)S_{1}^{S}(2)⊕(T)S_{2}^{S}(2)⊕(T)S_{3}^{S}(2)⊕(T)S_{4}^{S}(2) $ |
| U:(1/2,0,-1/2) | T:(0,1/2,1/2) | $(U)T_{1}^{S}T_{3}^{S}(4)⊕(U)T_{2}^{S}T_{4}^{S}(4) $ |
| X:(1/2,0,0) | Z:(0,0,1/2) | $(X)Z_{1}^{S}Z_{3}^{S}(4)⊕(X)Z_{2}^{S}Z_{4}^{S}(2) $ |
| Y:(0,-1/2,0) | X:(1/2,0,0) | $(Y)X_{1}^{S}(2)⊕(Y)X_{2}^{S}(2)⊕(Y)X_{3}^{S}(2)⊕(Y)X_{4}^{S}(2) $ |
| Z:(0,0,-1/2) | Y:(0,1/2,0) | $(Z)Y_{1}^{S}(2)⊕(Z)Y_{2}^{S}(2)⊕(Z)Y_{3}^{S}(2)⊕(Z)Y_{4}^{S}(2) $ |
| A:(u,0,-1/2) | H:(0,1/2,u) | $(A)H_{1}^{S}(2)⊕(A)H_{2}^{S}(2)⊕(A)H_{3}^{S}(2)⊕(A)H_{4}^{S}(2) $ |
| B:(0,v,-1/2) | C:(-v,1/2,0) | $2 (B)C_{1}^{S}(2)⊕2 (B)C_{2}^{S}(2) $ |
| C:(u,-1/2,0) | G:(1/2,0,u) | $(C)G_{1}^{S}(2)⊕(C)G_{2}^{S}(2)⊕(C)G_{3}^{S}(2)⊕(C)G_{4}^{S}(2) $ |
| D:(1/2,v,0) | A:(-v,0,1/2) | $2 (D)A_{1}^{S}A_{2}^{S}(4) $ |
| Δ:(0,v,0) | Σ:(-v,0,0) | $2 (Δ)Σ_{1}^{S}(2)⊕2 (Δ)Σ_{2}^{S}(2) $ |
| E:(u,-1/2,-1/2) | Q:(1/2,1/2,u) | $(E)Q_{1}^{S}(2)⊕(E)Q_{2}^{S}(2)⊕(E)Q_{3}^{S}(2)⊕(E)Q_{4}^{S}(2) $ |
| G:(1/2,0,w) | B:(0,-w,1/2) | $(G)B_{1}^{S}B_{1}^{S}(4)⊕(G)B_{2}^{S}B_{2}^{S}(4) $ |
| H:(0,-1/2,w) | D:(1/2,-w,0) | $2(H)D_{1}^{S}(2)⊕2(H)D_{2}^{S}(2) $ |
| Λ:(0,0,w) | Δ:(0,-w,0) | $2(Λ)Δ_{1}^{S}(2)⊕2(Λ)Δ_{2}^{S}(2) $ |
| P:(1/2,v,-1/2) | E:(-v,1/2,1/2) | $2 (P)E_{1}^{S}E_{2}^{S}(4) $ |
| Q:(1/2,-1/2,w) | P:(1/2,-w,1/2) | $(Q)P_{1}^{S}P_{1}^{S}(4)⊕(Q)P_{2}^{S}P_{2}^{S}(4) $ |
| Σ:(u,0,0) | Λ:(0,0,u) | $(Σ)Λ_{1}^{S}(2)⊕(Σ)Λ_{2}^{S}(2)⊕(Σ)Λ_{3}^{S}(2)⊕(Σ)Λ_{4}^{S}(2) $ |
| K:(0,v,w) | V:(-v,-w,0) | $4(K)V_{1}^{S}(2) $ |
| L:(1/2,v,w) | W:(-v,-w,1/2) | $2 (L)W_{1}^{S}W_{1}^{S}(4) $ |
| M:(u,0,w) | K:(0,-w,u) | $2(M)K_{1}^{S}(2)⊕2(M)K_{2}^{S}(2) $ |
| N:(u,-1/2,w) | L:(1/2,-w,u) | $2(N)L_{1}^{S}(2)⊕2(N)L_{2}^{S}(2) $ |
| V:(u,v,0) | M:(-v,0,u) | $2 (V)M_{1}^{S}(2)⊕2 (V)M_{2}^{S}(2) $ |
| W:(u,v,-1/2) | N:(-v,1/2,u) | $2 (W)N_{1}^{S}(2)⊕2 (W)N_{2}^{S}(2) $ |
| GP:(u,v,w) | GP:(-v,-w,u) | $4GP_{1}^{S}(2) $ |
| $ $ |