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 } |
| c, a, b | x, y, z | { 1 ‖ 3+111 | 0 } |
| b, c, a | x, y, z | { 1 ‖ 3-111 | 0 } |
| -b, c, -a | x, y, z | { 1 ‖ 3-1-1-1 | 0 } |
| -c, -a, b | x, y, z | { 1 ‖ 3+1-1-1 | 0 } |
| -b, -c, a | x, y, z | { 1 ‖ 3--11-1 | 0 } |
| c, -a, -b | x, y, z | { 1 ‖ 3+-11-1 | 0 } |
| b, -c, -a | x, y, z | { 1 ‖ 3--1-11 | 0 } |
| -c, a, -b | x, y, z | { 1 ‖ 3+-1-11 | 0 } |
| 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 } |
| c, a, b | -x, y, z | { m ‖ 3+111 | 0 } |
| b, c, a | -x, y, z | { m ‖ 3-111 | 0 } |
| -b, c, -a | -x, y, z | { m ‖ 3-1-1-1 | 0 } |
| -c, -a, b | -x, y, z | { m ‖ 3+1-1-1 | 0 } |
| -b, -c, a | -x, y, z | { m ‖ 3--11-1 | 0 } |
| c, -a, -b | -x, y, z | { m ‖ 3+-11-1 | 0 } |
| b, -c, -a | -x, y, z | { m ‖ 3--1-11 | 0 } |
| -c, a, -b | -x, y, z | { m ‖ 3+-1-11 | 0 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 1a | $\ce{^{1}{2}}\ce{^{1}{3}}.\ce{^{\infty m}{1}} $ | (0,0,0 |0,0,z) |
| 1b | $\ce{^{1}{2}}\ce{^{1}{3}}.\ce{^{\infty m}{1}} $ | (1/2,1/2,1/2 |0,0,z) |
| 3c | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (0,1/2,1/2 |0,0,z) |
| 3d | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (1/2,0,0 |0,0,z) |
| 4e | $.\ce{^{1}{3}}.\ce{^{\infty m}{1}} $ | (a,a,a |0,0,z) |
| 6f | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,0,0 |0,0,z) |
| 6g | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,0,1/2 |0,0,z) |
| 6h | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,1/2,0 |0,0,z) |
| 6i | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,1/2,1/2 |0,0,z) |
| 12j | $\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}{3}}\ce{^{\infty m}{1}} $ |
| R:(1/2,1/2,1/2) | $\ce{^{1}{2}}\ce{^{1}{3}}\ce{^{\infty m}{1}} $ |
| M:(1/2,1/2,0) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| X:(0,1/2,0) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| Δ:(0,v,0) | $\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| T:(1/2,1/2,w) | $\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| Z:(u,1/2,0) | $\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| ZA:(1/2,u,0) | $\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| Λ:(u,u,u) | $\ce{^{1}{3}}\ce{^{\infty}{1}} $ |
| A:(u,v,0) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| B:(u,1/2,w) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| S:(u,1/2,u) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| Σ:(u,u,0) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| C:(u,u,w) | $\ce{^{1}{1}}\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) $ |
| R:(1/2,1/2,1/2) | $R_{1}^{S}(1) $ |
| M:(1/2,1/2,0) | $M_{1}^{S}(1) $ |
| X:(0,1/2,0) | $X_{1}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1) $ |
| T:(1/2,1/2,w) | $T_{1}^{S}(1) $ |
| Z:(u,1/2,0) | $Z_{1}^{S}(1) $ |
| ZA:(1/2,u,0) | $ZA_{1}^{S}(1) $ |
| Λ:(u,u,u) | $Λ_{1}^{S}(1) $ |
| A:(u,v,0) | $A_{1}^{S}(1) $ |
| B:(u,1/2,w) | $B_{1}^{S}(1) $ |
| S:(u,1/2,u) | $S_{1}^{S}(1) $ |
| Σ:(u,u,0) | $Σ_{1}^{S}(1) $ |
| C:(u,u,w) | $C_{1}^{S}(1) $ |
| GP:(u,v,w) | $GP_{1}^{S}(1) $ |
| k-vector | A↑G(1) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1) $ |
| R:(1/2,1/2,1/2) | $R_{1}^{S}(1) $ |
| M:(1/2,1/2,0) | $M_{2}^{S}(1) $ |
| X:(0,1/2,0) | $X_{4}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1) $ |
| T:(1/2,1/2,w) | $T_{1}^{S}(1) $ |
| Z:(u,1/2,0) | $Z_{2}^{S}(1) $ |
| ZA:(1/2,u,0) | $ZA_{2}^{S}(1) $ |
| Λ:(u,u,u) | $Λ_{1}^{S}(1) $ |
| A:(u,v,0) | $A_{1}^{S}(1) $ |
| B:(u,1/2,w) | $B_{1}^{S}(1) $ |
| S:(u,1/2,u) | $S_{1}^{S}(1) $ |
| Σ:(u,u,0) | $Σ_{1}^{S}(1) $ |
| C:(u,u,w) | $C_{1}^{S}(1) $ |
| GP:(u,v,w) | $GP_{1}^{S}(1) $ |
| k-vector | A↑G(3) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}Γ_{3}^{S}(2) $ |
| R:(1/2,1/2,1/2) | $R_{4}^{S}(3) $ |
| M:(1/2,1/2,0) | $M_{2}^{S}(1)⊕M_{3}^{S}(1)⊕M_{4}^{S}(1) $ |
| X:(0,1/2,0) | $X_{1}^{S}(1)⊕2X_{4}^{S}(1) $ |
| Δ:(0,v,0) | $3Δ_{1}^{S}(1) $ |
| T:(1/2,1/2,w) | $T_{1}^{S}(1)⊕2T_{2}^{S}(1) $ |
| Z:(u,1/2,0) | $Z_{1}^{S}(1)⊕2Z_{2}^{S}(1) $ |
| ZA:(1/2,u,0) | $ZA_{1}^{S}(1)⊕2ZA_{2}^{S}(1) $ |
| Λ:(u,u,u) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1)⊕Λ_{3}^{S}(1) $ |
| A:(u,v,0) | $3A_{1}^{S}(1) $ |
| B:(u,1/2,w) | $3B_{1}^{S}(1) $ |
| S:(u,1/2,u) | $3S_{1}^{S}(1) $ |
| Σ:(u,u,0) | $3Σ_{1}^{S}(1) $ |
| C:(u,u,w) | $3C_{1}^{S}(1) $ |
| GP:(u,v,w) | $3GP_{1}^{S}(1) $ |
| k-vector | A↑G(3) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}Γ_{3}^{S}(2) $ |
| R:(1/2,1/2,1/2) | $R_{4}^{S}(3) $ |
| M:(1/2,1/2,0) | $M_{1}^{S}(1)⊕M_{3}^{S}(1)⊕M_{4}^{S}(1) $ |
| X:(0,1/2,0) | $2X_{1}^{S}(1)⊕X_{4}^{S}(1) $ |
| Δ:(0,v,0) | $3Δ_{1}^{S}(1) $ |
| T:(1/2,1/2,w) | $T_{1}^{S}(1)⊕2T_{2}^{S}(1) $ |
| Z:(u,1/2,0) | $2Z_{1}^{S}(1)⊕Z_{2}^{S}(1) $ |
| ZA:(1/2,u,0) | $2ZA_{1}^{S}(1)⊕ZA_{2}^{S}(1) $ |
| Λ:(u,u,u) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1)⊕Λ_{3}^{S}(1) $ |
| A:(u,v,0) | $3A_{1}^{S}(1) $ |
| B:(u,1/2,w) | $3B_{1}^{S}(1) $ |
| S:(u,1/2,u) | $3S_{1}^{S}(1) $ |
| Σ:(u,u,0) | $3Σ_{1}^{S}(1) $ |
| C:(u,u,w) | $3C_{1}^{S}(1) $ |
| GP:(u,v,w) | $3GP_{1}^{S}(1) $ |
| k-vector | A1↑G(4) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{4}^{S}(3) $ |
| R:(1/2,1/2,1/2) | $R_{1}^{S}(1)⊕R_{4}^{S}(3) $ |
| M:(1/2,1/2,0) | $M_{1}^{S}(1)⊕M_{2}^{S}(1)⊕M_{3}^{S}(1)⊕M_{4}^{S}(1) $ |
| X:(0,1/2,0) | $X_{1}^{S}(1)⊕X_{2}^{S}(1)⊕X_{3}^{S}(1)⊕X_{4}^{S}(1) $ |
| Δ:(0,v,0) | $2Δ_{1}^{S}(1)⊕2Δ_{2}^{S}(1) $ |
| T:(1/2,1/2,w) | $2T_{1}^{S}(1)⊕2T_{2}^{S}(1) $ |
| Z:(u,1/2,0) | $2Z_{1}^{S}(1)⊕2Z_{2}^{S}(1) $ |
| ZA:(1/2,u,0) | $2ZA_{1}^{S}(1)⊕2ZA_{2}^{S}(1) $ |
| Λ:(u,u,u) | $2Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1)⊕Λ_{3}^{S}(1) $ |
| A:(u,v,0) | $4A_{1}^{S}(1) $ |
| B:(u,1/2,w) | $4B_{1}^{S}(1) $ |
| S:(u,1/2,u) | $4S_{1}^{S}(1) $ |
| Σ:(u,u,0) | $4Σ_{1}^{S}(1) $ |
| C:(u,u,w) | $4C_{1}^{S}(1) $ |
| GP:(u,v,w) | $4GP_{1}^{S}(1) $ |
| k-vector | A↑G(6) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}Γ_{3}^{S}(2)⊕Γ_{4}^{S}(3) $ |
| R:(1/2,1/2,1/2) | $R_{1}^{S}(1)⊕R_{2}^{S}R_{3}^{S}(2)⊕R_{4}^{S}(3) $ |
| M:(1/2,1/2,0) | $3M_{1}^{S}(1)⊕M_{2}^{S}(1)⊕M_{3}^{S}(1)⊕M_{4}^{S}(1) $ |
| X:(0,1/2,0) | $3X_{1}^{S}(1)⊕X_{2}^{S}(1)⊕X_{3}^{S}(1)⊕X_{4}^{S}(1) $ |
| Δ:(0,v,0) | $4Δ_{1}^{S}(1)⊕2Δ_{2}^{S}(1) $ |
| T:(1/2,1/2,w) | $4T_{1}^{S}(1)⊕2T_{2}^{S}(1) $ |
| Z:(u,1/2,0) | $4Z_{1}^{S}(1)⊕2Z_{2}^{S}(1) $ |
| ZA:(1/2,u,0) | $4ZA_{1}^{S}(1)⊕2ZA_{2}^{S}(1) $ |
| Λ:(u,u,u) | $2Λ_{1}^{S}(1)⊕2Λ_{2}^{S}(1)⊕2Λ_{3}^{S}(1) $ |
| A:(u,v,0) | $6A_{1}^{S}(1) $ |
| B:(u,1/2,w) | $6B_{1}^{S}(1) $ |
| S:(u,1/2,u) | $6S_{1}^{S}(1) $ |
| Σ:(u,u,0) | $6Σ_{1}^{S}(1) $ |
| C:(u,u,w) | $6C_{1}^{S}(1) $ |
| GP:(u,v,w) | $6GP_{1}^{S}(1) $ |
| k-vector | A↑G(6) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}Γ_{3}^{S}(2)⊕Γ_{4}^{S}(3) $ |
| R:(1/2,1/2,1/2) | $2R_{4}^{S}(3) $ |
| M:(1/2,1/2,0) | $M_{1}^{S}(1)⊕M_{2}^{S}(1)⊕3M_{3}^{S}(1)⊕M_{4}^{S}(1) $ |
| X:(0,1/2,0) | $2X_{1}^{S}(1)⊕2X_{3}^{S}(1)⊕2X_{4}^{S}(1) $ |
| Δ:(0,v,0) | $4Δ_{1}^{S}(1)⊕2Δ_{2}^{S}(1) $ |
| T:(1/2,1/2,w) | $2T_{1}^{S}(1)⊕4T_{2}^{S}(1) $ |
| Z:(u,1/2,0) | $4Z_{1}^{S}(1)⊕2Z_{2}^{S}(1) $ |
| ZA:(1/2,u,0) | $2ZA_{1}^{S}(1)⊕4ZA_{2}^{S}(1) $ |
| Λ:(u,u,u) | $2Λ_{1}^{S}(1)⊕2Λ_{2}^{S}(1)⊕2Λ_{3}^{S}(1) $ |
| A:(u,v,0) | $6A_{1}^{S}(1) $ |
| B:(u,1/2,w) | $6B_{1}^{S}(1) $ |
| S:(u,1/2,u) | $6S_{1}^{S}(1) $ |
| Σ:(u,u,0) | $6Σ_{1}^{S}(1) $ |
| C:(u,u,w) | $6C_{1}^{S}(1) $ |
| GP:(u,v,w) | $6GP_{1}^{S}(1) $ |
| k-vector | A↑G(6) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}Γ_{3}^{S}(2)⊕Γ_{4}^{S}(3) $ |
| R:(1/2,1/2,1/2) | $2R_{4}^{S}(3) $ |
| M:(1/2,1/2,0) | $M_{1}^{S}(1)⊕M_{2}^{S}(1)⊕M_{3}^{S}(1)⊕3M_{4}^{S}(1) $ |
| X:(0,1/2,0) | $2X_{1}^{S}(1)⊕2X_{2}^{S}(1)⊕2X_{4}^{S}(1) $ |
| Δ:(0,v,0) | $4Δ_{1}^{S}(1)⊕2Δ_{2}^{S}(1) $ |
| T:(1/2,1/2,w) | $2T_{1}^{S}(1)⊕4T_{2}^{S}(1) $ |
| Z:(u,1/2,0) | $2Z_{1}^{S}(1)⊕4Z_{2}^{S}(1) $ |
| ZA:(1/2,u,0) | $4ZA_{1}^{S}(1)⊕2ZA_{2}^{S}(1) $ |
| Λ:(u,u,u) | $2Λ_{1}^{S}(1)⊕2Λ_{2}^{S}(1)⊕2Λ_{3}^{S}(1) $ |
| A:(u,v,0) | $6A_{1}^{S}(1) $ |
| B:(u,1/2,w) | $6B_{1}^{S}(1) $ |
| S:(u,1/2,u) | $6S_{1}^{S}(1) $ |
| Σ:(u,u,0) | $6Σ_{1}^{S}(1) $ |
| C:(u,u,w) | $6C_{1}^{S}(1) $ |
| GP:(u,v,w) | $6GP_{1}^{S}(1) $ |
| k-vector | A↑G(6) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}Γ_{3}^{S}(2)⊕Γ_{4}^{S}(3) $ |
| R:(1/2,1/2,1/2) | $R_{1}^{S}(1)⊕R_{2}^{S}R_{3}^{S}(2)⊕R_{4}^{S}(3) $ |
| M:(1/2,1/2,0) | $M_{1}^{S}(1)⊕3M_{2}^{S}(1)⊕M_{3}^{S}(1)⊕M_{4}^{S}(1) $ |
| X:(0,1/2,0) | $X_{1}^{S}(1)⊕X_{2}^{S}(1)⊕X_{3}^{S}(1)⊕3X_{4}^{S}(1) $ |
| Δ:(0,v,0) | $4Δ_{1}^{S}(1)⊕2Δ_{2}^{S}(1) $ |
| T:(1/2,1/2,w) | $4T_{1}^{S}(1)⊕2T_{2}^{S}(1) $ |
| Z:(u,1/2,0) | $2Z_{1}^{S}(1)⊕4Z_{2}^{S}(1) $ |
| ZA:(1/2,u,0) | $2ZA_{1}^{S}(1)⊕4ZA_{2}^{S}(1) $ |
| Λ:(u,u,u) | $2Λ_{1}^{S}(1)⊕2Λ_{2}^{S}(1)⊕2Λ_{3}^{S}(1) $ |
| A:(u,v,0) | $6A_{1}^{S}(1) $ |
| B:(u,1/2,w) | $6B_{1}^{S}(1) $ |
| S:(u,1/2,u) | $6S_{1}^{S}(1) $ |
| Σ:(u,u,0) | $6Σ_{1}^{S}(1) $ |
| C:(u,u,w) | $6C_{1}^{S}(1) $ |
| GP:(u,v,w) | $6GP_{1}^{S}(1) $ |
| k-vector | A↑G(12) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}Γ_{3}^{S}(2)⊕3Γ_{4}^{S}(3) $ |
| R:(1/2,1/2,1/2) | $R_{1}^{S}(1)⊕R_{2}^{S}R_{3}^{S}(2)⊕3R_{4}^{S}(3) $ |
| M:(1/2,1/2,0) | $3M_{1}^{S}(1)⊕3M_{2}^{S}(1)⊕3M_{3}^{S}(1)⊕3M_{4}^{S}(1) $ |
| X:(0,1/2,0) | $3X_{1}^{S}(1)⊕3X_{2}^{S}(1)⊕3X_{3}^{S}(1)⊕3X_{4}^{S}(1) $ |
| Δ:(0,v,0) | $6Δ_{1}^{S}(1)⊕6Δ_{2}^{S}(1) $ |
| T:(1/2,1/2,w) | $6T_{1}^{S}(1)⊕6T_{2}^{S}(1) $ |
| Z:(u,1/2,0) | $6Z_{1}^{S}(1)⊕6Z_{2}^{S}(1) $ |
| ZA:(1/2,u,0) | $6ZA_{1}^{S}(1)⊕6ZA_{2}^{S}(1) $ |
| Λ:(u,u,u) | $4Λ_{1}^{S}(1)⊕4Λ_{2}^{S}(1)⊕4Λ_{3}^{S}(1) $ |
| A:(u,v,0) | $12A_{1}^{S}(1) $ |
| B:(u,1/2,w) | $12B_{1}^{S}(1) $ |
| S:(u,1/2,u) | $12S_{1}^{S}(1) $ |
| Σ:(u,u,0) | $12Σ_{1}^{S}(1) $ |
| C:(u,u,w) | $12C_{1}^{S}(1) $ |
| GP:(u,v,w) | $12GP_{1}^{S}(1) $ |