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 ‖ 2100 | 0 0 1/2 } |
| a+1/2, -b, c | x, y, z | { 1 ‖ m010 | 1/2 0 0 } |
| a, b+1/2, -c | x, y, z | { 1 ‖ m001 | 0 1/2 0 } |
| -a+1/2, b, -c | -x, -y, -z | { -1 ‖ 2010 | 1/2 0 0 } |
| -a, -b+1/2, c | -x, -y, -z | { -1 ‖ 2001 | 0 1/2 0 } |
| -a, -b, -c | -x, -y, -z | { -1 ‖ -1 | 0 } |
| -a, b, c+1/2 | -x, -y, -z | { -1 ‖ m100 | 0 0 1/2 } |
| 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 | x, y, z | { 1 ‖ 2100 | 1/2 1/2 0 } |
| a, -b+1/2, c+1/2 | x, y, z | { 1 ‖ m010 | 0 1/2 1/2 } |
| a+1/2, b, -c+1/2 | x, y, z | { 1 ‖ m001 | 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, c+1/2 | -x, -y, -z | { -1 ‖ 2001 | 1/2 0 1/2 } |
| -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 | -x, -y, -z | { -1 ‖ m100 | 1/2 1/2 0 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| a, -b, -c+1/2 | -x, y, z | { m ‖ 2100 | 0 0 1/2 } |
| a+1/2, -b, c | -x, y, z | { m ‖ m010 | 1/2 0 0 } |
| a, b+1/2, -c | -x, y, z | { m ‖ m001 | 0 1/2 0 } |
| -a+1/2, b, -c | x, -y, -z | { 2 ‖ 2010 | 1/2 0 0 } |
| -a, -b+1/2, c | x, -y, -z | { 2 ‖ 2001 | 0 1/2 0 } |
| -a, -b, -c | x, -y, -z | { 2 ‖ -1 | 0 } |
| -a, b, c+1/2 | x, -y, -z | { 2 ‖ m100 | 0 0 1/2 } |
| 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 | -x, y, z | { m ‖ 2100 | 1/2 1/2 0 } |
| a, -b+1/2, c+1/2 | -x, y, z | { m ‖ m010 | 0 1/2 1/2 } |
| a+1/2, b, -c+1/2 | -x, y, z | { m ‖ m001 | 1/2 0 1/2 } |
| -a, b+1/2, -c+1/2 | x, -y, -z | { 2 ‖ 2010 | 0 1/2 1/2 } |
| -a+1/2, -b, c+1/2 | x, -y, -z | { 2 ‖ 2001 | 1/2 0 1/2 } |
| -a+1/2, -b+1/2, -c+1/2 | x, -y, -z | { 2 ‖ -1 | 1/2 1/2 1/2 } |
| -a+1/2, b+1/2, c | x, -y, -z | { 2 ‖ m100 | 1/2 1/2 0 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 8a | $\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
| 8b | $\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $ | (1/4,1/4,1/4 | 0,0,0) |
| 8c | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,0,1/4 | 0,0,z) |
| 8d | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (1/4,b,0 | 0,0,0) |
| 8e | $..\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (0,1/4,c | 0,0,0) |
| 16f | $\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}} $ |
| X:(1,1,1) | $\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| R:(1/2,0,1/2) | $\ce{^{2}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| S:(0,1/2,1/2) | $\ce{^{1}{2/}}\ce{^{2}{m}}\ce{^{\infty m}{1}} $ |
| T:(1/2,1/2,0) | $\ce{^{2}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| W:(1/2,1/2,1/2) | $\ce{^{-1}{m}}\ce{^{m}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $ \ce{^{2}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Λ:(0,0,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}} $ |
| A:(0,v,w) | $\ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| B:(u,0,w) | $\ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| C:(u,v,0) | $\ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| D:(u,1/2,1/2) | $\ce{^{1}{2/}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
| P:(1/2,1/2,w) | $\ce{^{2}{2/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| Q:(1/2,v,1/2) | $\ce{^{2}{2/}}\ce{^{m}{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) $ | |
| R:(-1/2,0,1/2) | R:(1/2,0,1/2) | $R_{1}^{S}R_{2}^{S}(4) $ | |
| S:(0,1/2,1/2) | T:(1/2,1/2,0) | $2(S)T_{1}^{S}(2) $ | |
| T:(-1/2,1/2,0) | S:(0,1/2,1/2) | $(T)S_{1}^{S}S_{2}^{S}(4) $ | |
| W:(-1/2,1/2,1/2) | W:(1/2,1/2,1/2) | $W_{1}^{S}W_{1}^{S}(4) $ | |
| X:(-1,1,1) | X:(1,1,1) | $X_{1}^{S}(2)⊕X_{2}^{S}(2) $ | |
| D:(u,1/2,1/2) | P:(1/2,1/2,-u) | $2(D)P_{1}^{S}(2) $ | |
| Δ:(0,v,0) | Δ:(0,v,0) | $Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2) $ | |
| Λ:(0,0,w) | Σ:(w,0,0) | $(Λ)Σ_{1}^{S}(2)⊕(Λ)Σ_{2}^{S}(2) $ | |
| P:(-1/2,1/2,1+w) | D:(1+w,1/2,1/2) | $(P)D_{1}^{S}D_{1}^{S}(4) $ | |
| Q:(-1/2,1+v,1/2) | Q:(1/2,1+v,1/2) | $Q_{1}^{S}Q_{1}^{S}(4) $ | |
| Σ:(u,0,0) | Λ:(0,0,-u) | $(Σ)Λ_{1}^{S}(2)⊕(Σ)Λ_{2}^{S}(2) $ | |
| A:(0,v,w) | C:(w,v,0) | $2(A)C_{1}^{S}(2) $ | |
| B:(u,0,w) | B:(w,0,-u) | $B_{1}^{S}(2)⊕B_{2}^{S}(2) $ | |
| C:(u,v,0) | A:(0,v,-u) | $(C)A_{1}^{S}(2)⊕(C)A_{2}^{S}(2) $ | |
| GP:(u,v,w) | GP:(w,v,-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:(-1/2,0,1/2) | R:(1/2,0,1/2) | $2R_{1}^{S}R_{2}^{S}(4) $ | |
| S:(0,1/2,1/2) | T:(1/2,1/2,0) | $2(S)T_{1}^{S}(2)⊕2(S)T_{2}^{S}(2) $ | |
| T:(-1/2,1/2,0) | S:(0,1/2,1/2) | $2(T)S_{1}^{S}S_{2}^{S}(4) $ | |
| W:(-1/2,1/2,1/2) | W:(1/2,1/2,1/2) | $W_{1}^{S}W_{1}^{S}(4)⊕W_{2}^{S}W_{2}^{S}(4) $ | |
| X:(-1,1,1) | X:(1,1,1) | $X_{1}^{S}(2)⊕X_{2}^{S}(2)⊕X_{3}^{S}(2)⊕X_{4}^{S}(2) $ | |
| D:(u,1/2,1/2) | P:(1/2,1/2,-u) | $2(D)P_{1}^{S}(2)⊕2(D)P_{2}^{S}(2) $ | |
| Δ:(0,v,0) | Δ:(0,v,0) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $ | |
| Λ:(0,0,w) | Σ:(w,0,0) | $2(Λ)Σ_{1}^{S}(2)⊕2(Λ)Σ_{2}^{S}(2) $ | |
| P:(-1/2,1/2,1+w) | D:(1+w,1/2,1/2) | $2(P)D_{1}^{S}D_{1}^{S}(4) $ | |
| Q:(-1/2,1+v,1/2) | Q:(1/2,1+v,1/2) | $2Q_{1}^{S}Q_{1}^{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) $ | |
| A:(0,v,w) | C:(w,v,0) | $4(A)C_{1}^{S}(2) $ | |
| B:(u,0,w) | B:(w,0,-u) | $2B_{1}^{S}(2)⊕2B_{2}^{S}(2) $ | |
| C:(u,v,0) | A:(0,v,-u) | $2(C)A_{1}^{S}(2)⊕2(C)A_{2}^{S}(2) $ | |
| GP:(u,v,w) | GP:(w,v,-u) | $4GP_{1}^{S}(2) $ |