The continuously infinite group ∞1 is omitted.
| Coordinates | Seitz symbol |
|---|---|
| a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
| -a, b, -c+1/2 | x, y, z | { 1 ‖ 2010 | 0 0 1/2 } |
| -a+1/2, b, c+1/2 | x, y, z | { 1 ‖ m100 | 1/2 0 1/2 } |
| a+1/2, b, -c | x, y, z | { 1 ‖ m001 | 1/2 0 0 } |
| a+1/2, -b, -c+1/2 | -x, -y, -z | { -1 ‖ 2100 | 1/2 0 1/2 } |
| -a+1/2, -b, c | -x, -y, -z | { -1 ‖ 2001 | 1/2 0 0 } |
| -a, -b, -c | -x, -y, -z | { -1 ‖ -1 | 0 } |
| a, -b, c+1/2 | -x, -y, -z | { -1 ‖ m010 | 0 0 1/2 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| -a, b, -c+1/2 | -x, y, z | { m ‖ 2010 | 0 0 1/2 } |
| -a+1/2, b, c+1/2 | -x, y, z | { m ‖ m100 | 1/2 0 1/2 } |
| a+1/2, b, -c | -x, y, z | { m ‖ m001 | 1/2 0 0 } |
| a+1/2, -b, -c+1/2 | x, -y, -z | { 2 ‖ 2100 | 1/2 0 1/2 } |
| -a+1/2, -b, c | x, -y, -z | { 2 ‖ 2001 | 1/2 0 0 } |
| -a, -b, -c | x, -y, -z | { 2 ‖ -1 | 0 } |
| a, -b, c+1/2 | x, -y, -z | { 2 ‖ m010 | 0 0 1/2 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 4a | $\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
| 4b | $\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $ | (0,1/2,0 | 0,0,0) |
| 4c | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (0,b,1/4 | 0,0,z) |
| 4d | $..\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/4,0,c | 0,0,0) |
| 4e | $..\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/4,1/2,c | 0,0,0) |
| 8f | $\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{^{m}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| B:(0,v,1/2) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| C:(u,1/2,0) | $ \ce{^{m}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| D:(1/2,v,0) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| E:(u,1/2,1/2) | $ \ce{^{m}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| G:(1/2,0,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| H:(0,1/2,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| Λ:(0,0,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| P:(1/2,v,1/2) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Q:(1/2,1/2,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $ \ce{^{m}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| K:(0,v,w) | $ \ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| L:(1/2,v,w) | $ \ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| M:(u,0,w) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| N:(u,1/2,w) | $ \ce{^{m}{2/}}\ce{^{2}{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_{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_{2}^{S}(4) $ |
| S:(1/2,1/2,0) | U:(1/2,0,1/2) | $(S)U_{1}^{S}(4) $ |
| T:(0,1/2,-1/2) | T:(0,1/2,1/2) | $T_{1}^{S}(4) $ |
| U:(1/2,0,-1/2) | S:(1/2,1/2,0) | $(U)S_{1}^{S}S_{2}^{S}(4) $ |
| X:(1/2,0,0) | X:(1/2,0,0) | $X_{1}^{S}(4) $ |
| Y:(0,1/2,0) | Z:(0,0,1/2) | $(Y)Z_{1}^{S}(2)⊕(Y)Z_{2}^{S}(2) $ |
| Z:(0,0,-1/2) | Y:(0,1/2,0) | $(Z)Y_{1}^{S}(4) $ |
| A:(u,0,-1/2) | C:(u,1/2,0) | $(A)C_{1}^{S}C_{2}^{S}(4) $ |
| B:(0,v,-1/2) | H:(0,1/2,v) | $(B)H_{1}^{S}(4) $ |
| C:(u,1/2,0) | A:(u,0,1/2) | $(C)A_{1}^{S}(2)⊕(C)A_{2}^{S}(2) $ |
| D:(1/2,v,0) | G:(1/2,0,v) | $(D)G_{1}^{S}(4) $ |
| Δ:(0,v,0) | Λ:(0,0,v) | $(Δ)Λ_{1}^{S}(2)⊕(Δ)Λ_{2}^{S}(2) $ |
| E:(u,1/2,-1/2) | E:(u,1/2,1/2) | $E_{1}^{S}E_{2}^{S}(4) $ |
| G:(1/2,0,w) | D:(1/2,-w,0) | $(G)D_{1}^{S}D_{2}^{S}(4) $ |
| H:(0,1/2,w) | B:(0,-w,1/2) | $(H)B_{1}^{S}(2)⊕(H)B_{2}^{S}(2) $ |
| Λ:(0,0,w) | Δ:(0,-w,0) | $(Λ)Δ_{1}^{S}(2)⊕(Λ)Δ_{2}^{S}(2) $ |
| P:(1/2,v,-1/2) | Q:(1/2,1/2,v) | $(P)Q_{1}^{S}(2)⊕(P)Q_{2}^{S}(2) $ |
| Q:(1/2,1/2,w) | P:(1/2,-w,1/2) | $(Q)P_{1}^{S}P_{2}^{S}(4) $ |
| Σ:(u,0,0) | Σ:(u,0,0) | $Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2) $ |
| K:(0,v,w) | K:(0,-w,v) | $K_{1}^{S}(2)⊕K_{2}^{S}(2) $ |
| L:(1/2,v,w) | L:(1/2,-w,v) | $L_{1}^{S}(2)⊕L_{2}^{S}(2) $ |
| M:(u,0,w) | V:(u,-w,0) | $2(M)V_{1}^{S}(2) $ |
| N:(u,1/2,w) | W:(u,-w,1/2) | $2(N)W_{1}^{S}(2) $ |
| V:(u,v,0) | M:(u,0,v) | $(V)M_{1}^{S}(2)⊕(V)M_{2}^{S}(2) $ |
| W:(u,v,-1/2) | N:(u,1/2,v) | $(W)N_{1}^{S}(2)⊕(W)N_{2}^{S}(2) $ |
| GP:(u,v,w) | GP:(u,-w,v) | $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_{2}^{S}(4)⊕R_{3}^{S}R_{4}^{S}(4) $ |
| S:(1/2,1/2,0) | U:(1/2,0,1/2) | $2(S)U_{1}^{S}(4) $ |
| T:(0,1/2,-1/2) | T:(0,1/2,1/2) | $2T_{1}^{S}(4) $ |
| U:(1/2,0,-1/2) | S:(1/2,1/2,0) | $(U)S_{1}^{S}S_{2}^{S}(4)⊕(U)S_{3}^{S}S_{4}^{S}(4) $ |
| X:(1/2,0,0) | X:(1/2,0,0) | $2X_{1}^{S}(4) $ |
| Y:(0,1/2,0) | Z:(0,0,1/2) | $(Y)Z_{1}^{S}(2)⊕(Y)Z_{2}^{S}(2)⊕(Y)Z_{3}^{S}(2)⊕(Y)Z_{4}^{S}(2) $ |
| Z:(0,0,-1/2) | Y:(0,1/2,0) | $2(Z)Y_{1}^{S}(4) $ |
| A:(u,0,-1/2) | C:(u,1/2,0) | $2(A)C_{1}^{S}C_{2}^{S}(4) $ |
| B:(0,v,-1/2) | H:(0,1/2,v) | $2(B)H_{1}^{S}(4) $ |
| C:(u,1/2,0) | A:(u,0,1/2) | $2(C)A_{1}^{S}(2)⊕2(C)A_{2}^{S}(2) $ |
| D:(1/2,v,0) | G:(1/2,0,v) | $2(D)G_{1}^{S}(4) $ |
| Δ:(0,v,0) | Λ:(0,0,v) | $(Δ)Λ_{1}^{S}(2)⊕(Δ)Λ_{2}^{S}(2)⊕(Δ)Λ_{3}^{S}(2)⊕(Δ)Λ_{4}^{S}(2) $ |
| E:(u,1/2,-1/2) | E:(u,1/2,1/2) | $2E_{1}^{S}E_{2}^{S}(4) $ |
| G:(1/2,0,w) | D:(1/2,-w,0) | $2(G)D_{1}^{S}D_{2}^{S}(4) $ |
| H:(0,1/2,w) | B:(0,-w,1/2) | $2(H)B_{1}^{S}(2)⊕2(H)B_{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) | Q:(1/2,1/2,v) | $(P)Q_{1}^{S}(2)⊕(P)Q_{2}^{S}(2)⊕(P)Q_{3}^{S}(2)⊕(P)Q_{4}^{S}(2) $ |
| Q:(1/2,1/2,w) | P:(1/2,-w,1/2) | $2(Q)P_{1}^{S}P_{2}^{S}(4) $ |
| Σ:(u,0,0) | Σ:(u,0,0) | $2Σ_{1}^{S}(2)⊕2Σ_{2}^{S}(2) $ |
| K:(0,v,w) | K:(0,-w,v) | $2K_{1}^{S}(2)⊕2K_{2}^{S}(2) $ |
| L:(1/2,v,w) | L:(1/2,-w,v) | $2L_{1}^{S}(2)⊕2L_{2}^{S}(2) $ |
| M:(u,0,w) | V:(u,-w,0) | $4(M)V_{1}^{S}(2) $ |
| N:(u,1/2,w) | W:(u,-w,1/2) | $4(N)W_{1}^{S}(2) $ |
| V:(u,v,0) | M:(u,0,v) | $2(V)M_{1}^{S}(2)⊕2(V)M_{2}^{S}(2) $ |
| W:(u,v,-1/2) | N:(u,1/2,v) | $2(W)N_{1}^{S}(2)⊕2(W)N_{2}^{S}(2) $ |
| GP:(u,v,w) | GP:(u,-w,v) | $4GP_{1}^{S}(2) $ |