The continuously infinite group ∞1 is omitted.
| Coordinates | Seitz symbol |
|---|---|
| a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
| -b, a, c+1/2 | x, y, z | { 1 ‖ 4+001 | 0 0 1/2 } |
| b, -a, c+1/2 | x, y, z | { 1 ‖ 4-001 | 0 0 1/2 } |
| 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 } |
| b, a, -c+1/2 | x, y, z | { 1 ‖ 2110 | 0 0 1/2 } |
| -b, -a, -c+1/2 | x, y, z | { 1 ‖ 21-10 | 0 0 1/2 } |
| a, b, c+1/2 | -x, -y, -z | { -1 ‖ 1 | 0 0 1/2 } |
| -b, a, c | -x, -y, -z | { -1 ‖ 4+001 | 0 } |
| b, -a, c | -x, -y, -z | { -1 ‖ 4-001 | 0 } |
| a, -b, -c+1/2 | -x, -y, -z | { -1 ‖ 2100 | 0 0 1/2 } |
| -a, b, -c+1/2 | -x, -y, -z | { -1 ‖ 2010 | 0 0 1/2 } |
| -a, -b, c+1/2 | -x, -y, -z | { -1 ‖ 2001 | 0 0 1/2 } |
| b, a, -c | -x, -y, -z | { -1 ‖ 2110 | 0 } |
| -b, -a, -c | -x, -y, -z | { -1 ‖ 21-10 | 0 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| -b, a, c+1/2 | -x, y, z | { m ‖ 4+001 | 0 0 1/2 } |
| b, -a, c+1/2 | -x, y, z | { m ‖ 4-001 | 0 0 1/2 } |
| 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 } |
| b, a, -c+1/2 | -x, y, z | { m ‖ 2110 | 0 0 1/2 } |
| -b, -a, -c+1/2 | -x, y, z | { m ‖ 21-10 | 0 0 1/2 } |
| a, b, c+1/2 | x, -y, -z | { 2 ‖ 1 | 0 0 1/2 } |
| -b, a, c | x, -y, -z | { 2 ‖ 4+001 | 0 } |
| b, -a, c | x, -y, -z | { 2 ‖ 4-001 | 0 } |
| a, -b, -c+1/2 | x, -y, -z | { 2 ‖ 2100 | 0 0 1/2 } |
| -a, b, -c+1/2 | x, -y, -z | { 2 ‖ 2010 | 0 0 1/2 } |
| -a, -b, c+1/2 | x, -y, -z | { 2 ‖ 2001 | 0 0 1/2 } |
| b, a, -c | x, -y, -z | { 2 ‖ 2110 | 0 } |
| -b, -a, -c | x, -y, -z | { 2 ‖ 21-10 | 0 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 2a | $\ce{^{-1}{4}}\ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
| 2b | $\ce{^{-1}{4}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,1/4 | 0,0,0) |
| 2c | $\ce{^{-1}{4}}\ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/2,1/2,0 | 0,0,0) |
| 2d | $\ce{^{-1}{4}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/2,1/2,1/4 | 0,0,0) |
| 4e | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (1/2,0,0 | 0,0,z) |
| 4f | $\ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (1/2,0,1/4 | 0,0,0) |
| 4g | $\ce{^{-1}{4}}..\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,0) |
| 4h | $\ce{^{-1}{4}}..\ce{^{\infty m}{1}} $ | (1/2,1/2,c | 0,0,0) |
| 8i | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (0,1/2,c | 0,0,z) |
| 8j | $..\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (a,a,0 | 0,0,0) |
| 8k | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (a,a,1/4 | 0,0,z) |
| 8l | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (a,0,0 | 0,0,z) |
| 8m | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (a,1/2,1/4 | 0,0,0) |
| 8n | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (a,0,1/4 | 0,0,0) |
| 8o | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (a,1/2,0 | 0,0,z) |
| 16p | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
| Wavevector-k | Little co-group |
|---|---|
| A:(1/2,1/2,1/2) | $\ce{^{1}{4}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty /mm}{1}} $ |
| Γ:(0,0,0) | $\ce{^{1}{4}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty /mm}{1}} $ |
| M:(1/2,1/2,0) | $\ce{^{1}{4}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty /mm}{1}} $ |
| Z:(0,0,1/2) | $\ce{^{1}{4}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty /mm}{1}} $ |
| R:(0,1/2,1/2) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty /mm}{1}} $ |
| X:(0,1/2,0) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty /mm}{1}} $ |
| Λ:(0,0,w) | $\ce{^{1}{4}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
| V:(1/2,1/2,w) | $\ce{^{1}{4}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
| Δ:(0,v,0) | $\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
| S:(u,u,1/2) | $\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
| Σ:(u,u,0) | $\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
| T:(u,1/2,1/2) | $\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
| U:(0,v,1/2) | $\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
| W:(0,1/2,w) | $\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{\infty 2}{1}} $ |
| Y:(u,1/2,0) | $\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
| B:(0,v,w) | $\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
| C:(u,u,w) | $\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
| D:(u,v,0) | $\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
| E:(u,v,1/2) | $\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
| F:(u,1/2,w) | $\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
| GP:(u,v,w) | $\ce{^{1}{1}}\ce{^{\infty 2}{1}} $ |
Spin Brillouin Zone
| k-vector | A↑G(4) |
| A:(1/2,1/2,1/2) | $A_{1}^{S}(2)⊕A_{2}^{S}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2) $ |
| M:(1/2,1/2,0) | $M_{5}^{S}(4) $ |
| Z:(0,0,1/2) | $Z_{5}^{S}(4) $ |
| R:(0,1/2,1/2) | $R_{1}^{S}(2)⊕R_{3}^{S}(2) $ |
| X:(0,1/2,0) | $X_{1}^{S}(2)⊕X_{4}^{S}(2) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ |
| V:(1/2,1/2,w) | $V_{3}^{S}(2)⊕V_{4}^{S}(2) $ |
| Δ:(0,v,0) | $2Δ_{1}^{S}(2) $ |
| S:(u,u,1/2) | $S_{1}^{S}(2)⊕S_{2}^{S}(2) $ |
| Σ:(u,u,0) | $Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2) $ |
| T:(u,1/2,1/2) | $2T_{1}^{S}(2) $ |
| U:(0,v,1/2) | $U_{1}^{S}(2)⊕U_{2}^{S}(2) $ |
| W:(0,1/2,w) | $W_{1}^{S}(2)⊕W_{2}^{S}(2) $ |
| Y:(u,1/2,0) | $Y_{1}^{S}(2)⊕Y_{2}^{S}(2) $ |
| B:(0,v,w) | $2B_{1}^{S}(2) $ |
| C:(u,u,w) | $2C_{1}^{S}(2) $ |
| D:(u,v,0) | $2D_{1}^{S}(2) $ |
| E:(u,v,1/2) | $2E_{1}^{S}(2) $ |
| F:(u,1/2,w) | $2F_{1}^{S}(2) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(2) $ |
| k-vector | A↑G(8) |
| A:(1/2,1/2,1/2) | $A_{1}^{S}(2)⊕A_{2}^{S}(2)⊕A_{3}^{S}(2)⊕A_{4}^{S}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2)⊕Γ_{3}^{S}(2)⊕Γ_{4}^{S}(2) $ |
| M:(1/2,1/2,0) | $2M_{5}^{S}(4) $ |
| Z:(0,0,1/2) | $2Z_{5}^{S}(4) $ |
| R:(0,1/2,1/2) | $R_{1}^{S}(2)⊕R_{2}^{S}(2)⊕R_{3}^{S}(2)⊕R_{4}^{S}(2) $ |
| X:(0,1/2,0) | $X_{1}^{S}(2)⊕X_{2}^{S}(2)⊕X_{3}^{S}(2)⊕X_{4}^{S}(2) $ |
| Λ:(0,0,w) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2) $ |
| V:(1/2,1/2,w) | $2V_{3}^{S}(2)⊕2V_{4}^{S}(2) $ |
| Δ:(0,v,0) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $ |
| S:(u,u,1/2) | $2S_{1}^{S}(2)⊕2S_{2}^{S}(2) $ |
| Σ:(u,u,0) | $2Σ_{1}^{S}(2)⊕2Σ_{2}^{S}(2) $ |
| T:(u,1/2,1/2) | $2T_{1}^{S}(2)⊕2T_{2}^{S}(2) $ |
| U:(0,v,1/2) | $2U_{1}^{S}(2)⊕2U_{2}^{S}(2) $ |
| W:(0,1/2,w) | $2W_{1}^{S}(2)⊕2W_{2}^{S}(2) $ |
| Y:(u,1/2,0) | $2Y_{1}^{S}(2)⊕2Y_{2}^{S}(2) $ |
| B:(0,v,w) | $4B_{1}^{S}(2) $ |
| C:(u,u,w) | $4C_{1}^{S}(2) $ |
| D:(u,v,0) | $4D_{1}^{S}(2) $ |
| E:(u,v,1/2) | $4E_{1}^{S}(2) $ |
| F:(u,1/2,w) | $4F_{1}^{S}(2) $ |
| GP:(u,v,w) | $4GP_{1}^{S}(2) $ |
| k-vector | A↑G(8) |
| A:(1/2,1/2,1/2) | $A_{1}^{S}(2)⊕A_{4}^{S}(2)⊕A_{5}^{S}(4) $ |
| Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{4}^{S}(2)⊕Γ_{5}^{S}(4) $ |
| M:(1/2,1/2,0) | $M_{1}^{S}(2)⊕M_{4}^{S}(2)⊕M_{5}^{S}(4) $ |
| Z:(0,0,1/2) | $Z_{1}^{S}(2)⊕Z_{4}^{S}(2)⊕Z_{5}^{S}(4) $ |
| R:(0,1/2,1/2) | $R_{1}^{S}(2)⊕R_{2}^{S}(2)⊕R_{3}^{S}(2)⊕R_{4}^{S}(2) $ |
| X:(0,1/2,0) | $X_{1}^{S}(2)⊕X_{2}^{S}(2)⊕X_{3}^{S}(2)⊕X_{4}^{S}(2) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2)⊕Λ_{3}^{S}(2)⊕Λ_{4}^{S}(2) $ |
| V:(1/2,1/2,w) | $V_{1}^{S}(2)⊕V_{2}^{S}(2)⊕V_{3}^{S}(2)⊕V_{4}^{S}(2) $ |
| Δ:(0,v,0) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $ |
| S:(u,u,1/2) | $3S_{1}^{S}(2)⊕S_{2}^{S}(2) $ |
| Σ:(u,u,0) | $3Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2) $ |
| T:(u,1/2,1/2) | $2T_{1}^{S}(2)⊕2T_{2}^{S}(2) $ |
| U:(0,v,1/2) | $2U_{1}^{S}(2)⊕2U_{2}^{S}(2) $ |
| W:(0,1/2,w) | $2W_{1}^{S}(2)⊕2W_{2}^{S}(2) $ |
| Y:(u,1/2,0) | $2Y_{1}^{S}(2)⊕2Y_{2}^{S}(2) $ |
| B:(0,v,w) | $4B_{1}^{S}(2) $ |
| C:(u,u,w) | $4C_{1}^{S}(2) $ |
| D:(u,v,0) | $4D_{1}^{S}(2) $ |
| E:(u,v,1/2) | $4E_{1}^{S}(2) $ |
| F:(u,1/2,w) | $4F_{1}^{S}(2) $ |
| GP:(u,v,w) | $4GP_{1}^{S}(2) $ |
| k-vector | A↑G(8) |
| A:(1/2,1/2,1/2) | $A_{1}^{S}(2)⊕A_{2}^{S}(2)⊕A_{5}^{S}(4) $ |
| Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2)⊕Γ_{5}^{S}(4) $ |
| M:(1/2,1/2,0) | $M_{1}^{S}(2)⊕M_{2}^{S}(2)⊕M_{5}^{S}(4) $ |
| Z:(0,0,1/2) | $Z_{1}^{S}(2)⊕Z_{2}^{S}(2)⊕Z_{5}^{S}(4) $ |
| R:(0,1/2,1/2) | $R_{1}^{S}(2)⊕R_{2}^{S}(2)⊕2R_{3}^{S}(2) $ |
| X:(0,1/2,0) | $2X_{1}^{S}(2)⊕X_{3}^{S}(2)⊕X_{4}^{S}(2) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2)⊕Λ_{3}^{S}(2)⊕Λ_{4}^{S}(2) $ |
| V:(1/2,1/2,w) | $V_{1}^{S}(2)⊕V_{2}^{S}(2)⊕V_{3}^{S}(2)⊕V_{4}^{S}(2) $ |
| Δ:(0,v,0) | $3Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2) $ |
| S:(u,u,1/2) | $2S_{1}^{S}(2)⊕2S_{2}^{S}(2) $ |
| Σ:(u,u,0) | $2Σ_{1}^{S}(2)⊕2Σ_{2}^{S}(2) $ |
| T:(u,1/2,1/2) | $3T_{1}^{S}(2)⊕T_{2}^{S}(2) $ |
| U:(0,v,1/2) | $U_{1}^{S}(2)⊕3U_{2}^{S}(2) $ |
| W:(0,1/2,w) | $2W_{1}^{S}(2)⊕2W_{2}^{S}(2) $ |
| Y:(u,1/2,0) | $3Y_{1}^{S}(2)⊕Y_{2}^{S}(2) $ |
| B:(0,v,w) | $4B_{1}^{S}(2) $ |
| C:(u,u,w) | $4C_{1}^{S}(2) $ |
| D:(u,v,0) | $4D_{1}^{S}(2) $ |
| E:(u,v,1/2) | $4E_{1}^{S}(2) $ |
| F:(u,1/2,w) | $4F_{1}^{S}(2) $ |
| GP:(u,v,w) | $4GP_{1}^{S}(2) $ |
| k-vector | A↑G(8) |
| A:(1/2,1/2,1/2) | $A_{3}^{S}(2)⊕A_{4}^{S}(2)⊕A_{5}^{S}(4) $ |
| Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2)⊕Γ_{5}^{S}(4) $ |
| M:(1/2,1/2,0) | $M_{3}^{S}(2)⊕M_{4}^{S}(2)⊕M_{5}^{S}(4) $ |
| Z:(0,0,1/2) | $Z_{1}^{S}(2)⊕Z_{2}^{S}(2)⊕Z_{5}^{S}(4) $ |
| R:(0,1/2,1/2) | $2R_{2}^{S}(2)⊕R_{3}^{S}(2)⊕R_{4}^{S}(2) $ |
| X:(0,1/2,0) | $X_{1}^{S}(2)⊕X_{2}^{S}(2)⊕2X_{4}^{S}(2) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2)⊕Λ_{3}^{S}(2)⊕Λ_{4}^{S}(2) $ |
| V:(1/2,1/2,w) | $V_{1}^{S}(2)⊕V_{2}^{S}(2)⊕V_{3}^{S}(2)⊕V_{4}^{S}(2) $ |
| Δ:(0,v,0) | $3Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2) $ |
| S:(u,u,1/2) | $2S_{1}^{S}(2)⊕2S_{2}^{S}(2) $ |
| Σ:(u,u,0) | $2Σ_{1}^{S}(2)⊕2Σ_{2}^{S}(2) $ |
| T:(u,1/2,1/2) | $T_{1}^{S}(2)⊕3T_{2}^{S}(2) $ |
| U:(0,v,1/2) | $U_{1}^{S}(2)⊕3U_{2}^{S}(2) $ |
| W:(0,1/2,w) | $2W_{1}^{S}(2)⊕2W_{2}^{S}(2) $ |
| Y:(u,1/2,0) | $Y_{1}^{S}(2)⊕3Y_{2}^{S}(2) $ |
| B:(0,v,w) | $4B_{1}^{S}(2) $ |
| C:(u,u,w) | $4C_{1}^{S}(2) $ |
| D:(u,v,0) | $4D_{1}^{S}(2) $ |
| E:(u,v,1/2) | $4E_{1}^{S}(2) $ |
| F:(u,1/2,w) | $4F_{1}^{S}(2) $ |
| GP:(u,v,w) | $4GP_{1}^{S}(2) $ |
| k-vector | A↑G(16) |
| A:(1/2,1/2,1/2) | $A_{1}^{S}(2)⊕A_{2}^{S}(2)⊕A_{3}^{S}(2)⊕A_{4}^{S}(2)⊕2A_{5}^{S}(4) $ |
| Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2)⊕Γ_{3}^{S}(2)⊕Γ_{4}^{S}(2)⊕2Γ_{5}^{S}(4) $ |
| M:(1/2,1/2,0) | $M_{1}^{S}(2)⊕M_{2}^{S}(2)⊕M_{3}^{S}(2)⊕M_{4}^{S}(2)⊕2M_{5}^{S}(4) $ |
| Z:(0,0,1/2) | $Z_{1}^{S}(2)⊕Z_{2}^{S}(2)⊕Z_{3}^{S}(2)⊕Z_{4}^{S}(2)⊕2Z_{5}^{S}(4) $ |
| R:(0,1/2,1/2) | $2R_{1}^{S}(2)⊕2R_{2}^{S}(2)⊕2R_{3}^{S}(2)⊕2R_{4}^{S}(2) $ |
| X:(0,1/2,0) | $2X_{1}^{S}(2)⊕2X_{2}^{S}(2)⊕2X_{3}^{S}(2)⊕2X_{4}^{S}(2) $ |
| Λ:(0,0,w) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2)⊕2Λ_{3}^{S}(2)⊕2Λ_{4}^{S}(2) $ |
| V:(1/2,1/2,w) | $2V_{1}^{S}(2)⊕2V_{2}^{S}(2)⊕2V_{3}^{S}(2)⊕2V_{4}^{S}(2) $ |
| Δ:(0,v,0) | $4Δ_{1}^{S}(2)⊕4Δ_{2}^{S}(2) $ |
| S:(u,u,1/2) | $4S_{1}^{S}(2)⊕4S_{2}^{S}(2) $ |
| Σ:(u,u,0) | $4Σ_{1}^{S}(2)⊕4Σ_{2}^{S}(2) $ |
| T:(u,1/2,1/2) | $4T_{1}^{S}(2)⊕4T_{2}^{S}(2) $ |
| U:(0,v,1/2) | $4U_{1}^{S}(2)⊕4U_{2}^{S}(2) $ |
| W:(0,1/2,w) | $4W_{1}^{S}(2)⊕4W_{2}^{S}(2) $ |
| Y:(u,1/2,0) | $4Y_{1}^{S}(2)⊕4Y_{2}^{S}(2) $ |
| B:(0,v,w) | $8B_{1}^{S}(2) $ |
| C:(u,u,w) | $8C_{1}^{S}(2) $ |
| D:(u,v,0) | $8D_{1}^{S}(2) $ |
| E:(u,v,1/2) | $8E_{1}^{S}(2) $ |
| F:(u,1/2,w) | $8F_{1}^{S}(2) $ |
| GP:(u,v,w) | $8GP_{1}^{S}(2) $ |