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