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+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, 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+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 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 2a | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,0 |0,0,z) |
| 2b | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/2,0,0 |0,0,z) |
| 2c | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,1/2 |0,0,z) |
| 2d | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,1/2,0 |0,0,z) |
| 4e | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,0,0 |0,0,z) |
| 4f | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,0,1/2 |0,0,z) |
| 4g | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (0,b,0 |0,0,z) |
| 4h | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (1/2,b,0 |0,0,z) |
| 4i | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,c |0,0,z) |
| 4j | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,1/2,c |0,0,z) |
| 8k | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c |0,0,z) |
| Wavevector-k | Little co-group |
|---|---|
| Γ:(0,0,0) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| X:(1,1,1) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| R:(1/2,0,1/2) | $\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| S:(0,1/2,1/2) | $\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| T:(1/2,1/2,0) | $\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| W:(1/2,1/2,1/2) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $ \ce{^{m}{2}}\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| Λ:(0,0,w) | $\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| A:(0,v,w) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| B:(u,0,w) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| C:(u,v,0) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| D:(u,1/2,1/2) | $\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| P:(1/2,1/2,w) | $\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| Q:(1/2,v,1/2) | $\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| GP:(u,v,w) | $\ce{^{1}{1}}\ce{^{\infty}{1}} $ |
| Γ:(0,0,0) | $\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| X:(1,1,1) | $\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| R:(1/2,0,1/2) | $\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ |
| S:(0,1/2,1/2) | $\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ |
| T:(1/2,1/2,0) | $\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| W:(1/2,1/2,1/2) | $\ce{^{2}{2}}\ce{^{2}{2}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $ \ce{^{-1}{2}}\ce{^{2}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| Λ:(0,0,w) | $\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $\ce{^{2}{2}}\ce{^{-1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| A:(0,v,w) | $\ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| B:(u,0,w) | $\ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| C:(u,v,0) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| D:(u,1/2,1/2) | $\ce{^{2}{2}}\ce{^{\infty}{1}} $ |
| P:(1/2,1/2,w) | $\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| Q:(1/2,v,1/2) | $\ce{^{2}{2}}\ce{^{\infty}{1}} $ |
| GP:(u,v,w) | $\ce{^{1}{1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
| k-vector | A↑G(1) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1) $ |
| X:(1,1,1) | $X_{1}^{S}(1) $ |
| R:(1/2,0,1/2) | $R_{1}^{S}(1) $ |
| S:(0,1/2,1/2) | $S_{1}^{S}(1) $ |
| T:(1/2,1/2,0) | $T_{1}^{S}(1) $ |
| W:(1/2,1/2,1/2) | $W_{1}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1) $ |
| A:(0,v,w) | $A_{1}^{S}(1) $ |
| B:(u,0,w) | $B_{1}^{S}(1) $ |
| C:(u,v,0) | $C_{1}^{S}(1) $ |
| D:(u,1/2,1/2) | $D_{1}^{S}(1) $ |
| P:(1/2,1/2,w) | $P_{1}^{S}(1) $ |
| Q:(1/2,v,1/2) | $Q_{1}^{S}(1) $ |
| GP:(u,v,w) | $GP_{1}^{S}(1) $ |
| k-vector | A↑G(1) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1) $ |
| X:(1,1,1) | $X_{1}^{S}(1) $ |
| R:(1/2,0,1/2) | $R_{2}^{S}(1) $ |
| S:(0,1/2,1/2) | $S_{1}^{S}(1) $ |
| T:(1/2,1/2,0) | $T_{2}^{S}(1) $ |
| W:(1/2,1/2,1/2) | $W_{3}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1) $ |
| A:(0,v,w) | $A_{1}^{S}(1) $ |
| B:(u,0,w) | $B_{1}^{S}(1) $ |
| C:(u,v,0) | $C_{1}^{S}(1) $ |
| D:(u,1/2,1/2) | $D_{1}^{S}(1) $ |
| P:(1/2,1/2,w) | $P_{2}^{S}(1) $ |
| Q:(1/2,v,1/2) | $Q_{2}^{S}(1) $ |
| GP:(u,v,w) | $GP_{1}^{S}(1) $ |
| k-vector | A↑G(1) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1) $ |
| X:(1,1,1) | $X_{1}^{S}(1) $ |
| R:(1/2,0,1/2) | $R_{2}^{S}(1) $ |
| S:(0,1/2,1/2) | $S_{2}^{S}(1) $ |
| T:(1/2,1/2,0) | $T_{1}^{S}(1) $ |
| W:(1/2,1/2,1/2) | $W_{2}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1) $ |
| A:(0,v,w) | $A_{1}^{S}(1) $ |
| B:(u,0,w) | $B_{1}^{S}(1) $ |
| C:(u,v,0) | $C_{1}^{S}(1) $ |
| D:(u,1/2,1/2) | $D_{2}^{S}(1) $ |
| P:(1/2,1/2,w) | $P_{1}^{S}(1) $ |
| Q:(1/2,v,1/2) | $Q_{2}^{S}(1) $ |
| GP:(u,v,w) | $GP_{1}^{S}(1) $ |
| k-vector | A↑G(1) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1) $ |
| X:(1,1,1) | $X_{1}^{S}(1) $ |
| R:(1/2,0,1/2) | $R_{1}^{S}(1) $ |
| S:(0,1/2,1/2) | $S_{2}^{S}(1) $ |
| T:(1/2,1/2,0) | $T_{2}^{S}(1) $ |
| W:(1/2,1/2,1/2) | $W_{4}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1) $ |
| A:(0,v,w) | $A_{1}^{S}(1) $ |
| B:(u,0,w) | $B_{1}^{S}(1) $ |
| C:(u,v,0) | $C_{1}^{S}(1) $ |
| D:(u,1/2,1/2) | $D_{2}^{S}(1) $ |
| P:(1/2,1/2,w) | $P_{2}^{S}(1) $ |
| Q:(1/2,v,1/2) | $Q_{1}^{S}(1) $ |
| GP:(u,v,w) | $GP_{1}^{S}(1) $ |
| k-vector | A↑G(2) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{3}^{S}(1) $ |
| X:(1,1,1) | $X_{1}^{S}(1)⊕X_{3}^{S}(1) $ |
| R:(1/2,0,1/2) | $R_{1}^{S}(1)⊕R_{2}^{S}(1) $ |
| S:(0,1/2,1/2) | $2S_{1}^{S}(1) $ |
| T:(1/2,1/2,0) | $T_{1}^{S}(1)⊕T_{2}^{S}(1) $ |
| W:(1/2,1/2,1/2) | $W_{1}^{S}(1)⊕W_{3}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $ |
| Σ:(u,0,0) | $2Σ_{1}^{S}(1) $ |
| A:(0,v,w) | $2A_{1}^{S}(1) $ |
| B:(u,0,w) | $2B_{1}^{S}(1) $ |
| C:(u,v,0) | $2C_{1}^{S}(1) $ |
| D:(u,1/2,1/2) | $2D_{1}^{S}(1) $ |
| P:(1/2,1/2,w) | $P_{1}^{S}(1)⊕P_{2}^{S}(1) $ |
| Q:(1/2,v,1/2) | $Q_{1}^{S}(1)⊕Q_{2}^{S}(1) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
| k-vector | A↑G(2) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{3}^{S}(1) $ |
| X:(1,1,1) | $X_{1}^{S}(1)⊕X_{3}^{S}(1) $ |
| R:(1/2,0,1/2) | $R_{1}^{S}(1)⊕R_{2}^{S}(1) $ |
| S:(0,1/2,1/2) | $2S_{2}^{S}(1) $ |
| T:(1/2,1/2,0) | $T_{1}^{S}(1)⊕T_{2}^{S}(1) $ |
| W:(1/2,1/2,1/2) | $W_{2}^{S}(1)⊕W_{4}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $ |
| Σ:(u,0,0) | $2Σ_{1}^{S}(1) $ |
| A:(0,v,w) | $2A_{1}^{S}(1) $ |
| B:(u,0,w) | $2B_{1}^{S}(1) $ |
| C:(u,v,0) | $2C_{1}^{S}(1) $ |
| D:(u,1/2,1/2) | $2D_{2}^{S}(1) $ |
| P:(1/2,1/2,w) | $P_{1}^{S}(1)⊕P_{2}^{S}(1) $ |
| Q:(1/2,v,1/2) | $Q_{1}^{S}(1)⊕Q_{2}^{S}(1) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
| k-vector | A↑G(2) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{4}^{S}(1) $ |
| X:(1,1,1) | $X_{1}^{S}(1)⊕X_{4}^{S}(1) $ |
| R:(1/2,0,1/2) | $2R_{1}^{S}(1) $ |
| S:(0,1/2,1/2) | $S_{1}^{S}(1)⊕S_{2}^{S}(1) $ |
| T:(1/2,1/2,0) | $T_{1}^{S}(1)⊕T_{2}^{S}(1) $ |
| W:(1/2,1/2,1/2) | $W_{1}^{S}(1)⊕W_{4}^{S}(1) $ |
| Δ:(0,v,0) | $2Δ_{1}^{S}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
| A:(0,v,w) | $2A_{1}^{S}(1) $ |
| B:(u,0,w) | $2B_{1}^{S}(1) $ |
| C:(u,v,0) | $2C_{1}^{S}(1) $ |
| D:(u,1/2,1/2) | $D_{1}^{S}(1)⊕D_{2}^{S}(1) $ |
| P:(1/2,1/2,w) | $P_{1}^{S}(1)⊕P_{2}^{S}(1) $ |
| Q:(1/2,v,1/2) | $2Q_{1}^{S}(1) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
| k-vector | A↑G(2) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{4}^{S}(1) $ |
| X:(1,1,1) | $X_{1}^{S}(1)⊕X_{4}^{S}(1) $ |
| R:(1/2,0,1/2) | $2R_{2}^{S}(1) $ |
| S:(0,1/2,1/2) | $S_{1}^{S}(1)⊕S_{2}^{S}(1) $ |
| T:(1/2,1/2,0) | $T_{1}^{S}(1)⊕T_{2}^{S}(1) $ |
| W:(1/2,1/2,1/2) | $W_{2}^{S}(1)⊕W_{3}^{S}(1) $ |
| Δ:(0,v,0) | $2Δ_{1}^{S}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
| A:(0,v,w) | $2A_{1}^{S}(1) $ |
| B:(u,0,w) | $2B_{1}^{S}(1) $ |
| C:(u,v,0) | $2C_{1}^{S}(1) $ |
| D:(u,1/2,1/2) | $D_{1}^{S}(1)⊕D_{2}^{S}(1) $ |
| P:(1/2,1/2,w) | $P_{1}^{S}(1)⊕P_{2}^{S}(1) $ |
| Q:(1/2,v,1/2) | $2Q_{2}^{S}(1) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
| k-vector | A↑G(2) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}(1) $ |
| X:(1,1,1) | $X_{1}^{S}(1)⊕X_{2}^{S}(1) $ |
| R:(1/2,0,1/2) | $R_{1}^{S}(1)⊕R_{2}^{S}(1) $ |
| S:(0,1/2,1/2) | $S_{1}^{S}(1)⊕S_{2}^{S}(1) $ |
| T:(1/2,1/2,0) | $2T_{1}^{S}(1) $ |
| W:(1/2,1/2,1/2) | $W_{1}^{S}(1)⊕W_{2}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1) $ |
| Λ:(0,0,w) | $2Λ_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
| A:(0,v,w) | $2A_{1}^{S}(1) $ |
| B:(u,0,w) | $2B_{1}^{S}(1) $ |
| C:(u,v,0) | $2C_{1}^{S}(1) $ |
| D:(u,1/2,1/2) | $D_{1}^{S}(1)⊕D_{2}^{S}(1) $ |
| P:(1/2,1/2,w) | $2P_{1}^{S}(1) $ |
| Q:(1/2,v,1/2) | $Q_{1}^{S}(1)⊕Q_{2}^{S}(1) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
| k-vector | A↑G(2) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}(1) $ |
| X:(1,1,1) | $X_{1}^{S}(1)⊕X_{2}^{S}(1) $ |
| R:(1/2,0,1/2) | $R_{1}^{S}(1)⊕R_{2}^{S}(1) $ |
| S:(0,1/2,1/2) | $S_{1}^{S}(1)⊕S_{2}^{S}(1) $ |
| T:(1/2,1/2,0) | $2T_{2}^{S}(1) $ |
| W:(1/2,1/2,1/2) | $W_{3}^{S}(1)⊕W_{4}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1) $ |
| Λ:(0,0,w) | $2Λ_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
| A:(0,v,w) | $2A_{1}^{S}(1) $ |
| B:(u,0,w) | $2B_{1}^{S}(1) $ |
| C:(u,v,0) | $2C_{1}^{S}(1) $ |
| D:(u,1/2,1/2) | $D_{1}^{S}(1)⊕D_{2}^{S}(1) $ |
| P:(1/2,1/2,w) | $2P_{2}^{S}(1) $ |
| Q:(1/2,v,1/2) | $Q_{1}^{S}(1)⊕Q_{2}^{S}(1) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
| k-vector | A↑G(4) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}(1)⊕Γ_{3}^{S}(1)⊕Γ_{4}^{S}(1) $ |
| X:(1,1,1) | $X_{1}^{S}(1)⊕X_{2}^{S}(1)⊕X_{3}^{S}(1)⊕X_{4}^{S}(1) $ |
| R:(1/2,0,1/2) | $2R_{1}^{S}(1)⊕2R_{2}^{S}(1) $ |
| S:(0,1/2,1/2) | $2S_{1}^{S}(1)⊕2S_{2}^{S}(1) $ |
| T:(1/2,1/2,0) | $2T_{1}^{S}(1)⊕2T_{2}^{S}(1) $ |
| W:(1/2,1/2,1/2) | $W_{1}^{S}(1)⊕W_{2}^{S}(1)⊕W_{3}^{S}(1)⊕W_{4}^{S}(1) $ |
| Δ:(0,v,0) | $2Δ_{1}^{S}(1)⊕2Δ_{2}^{S}(1) $ |
| Λ:(0,0,w) | $2Λ_{1}^{S}(1)⊕2Λ_{2}^{S}(1) $ |
| Σ:(u,0,0) | $2Σ_{1}^{S}(1)⊕2Σ_{2}^{S}(1) $ |
| A:(0,v,w) | $4A_{1}^{S}(1) $ |
| B:(u,0,w) | $4B_{1}^{S}(1) $ |
| C:(u,v,0) | $4C_{1}^{S}(1) $ |
| D:(u,1/2,1/2) | $2D_{1}^{S}(1)⊕2D_{2}^{S}(1) $ |
| P:(1/2,1/2,w) | $2P_{1}^{S}(1)⊕2P_{2}^{S}(1) $ |
| Q:(1/2,v,1/2) | $2Q_{1}^{S}(1)⊕2Q_{2}^{S}(1) $ |
| GP:(u,v,w) | $4GP_{1}^{S}(1) $ |