The continuously infinite group ∞1 is omitted.
| Coordinates | Seitz symbol |
|---|---|
| a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
| -b, a-b, c | x, y, z | { 1 ‖ 3+001 | 0 } |
| -a+b, -a, c | x, y, z | { 1 ‖ 3-001 | 0 } |
| a-b, -b, -c | x, y, z | { 1 ‖ 2100 | 0 } |
| b, a, -c | x, y, z | { 1 ‖ 2110 | 0 } |
| -a, -a+b, -c | x, y, z | { 1 ‖ 2010 | 0 } |
| -a, -b, -c | x, y, z | { 1 ‖ -1 | 0 } |
| b, -a+b, -c | x, y, z | { 1 ‖ -3+001 | 0 } |
| a-b, a, -c | x, y, z | { 1 ‖ -3-001 | 0 } |
| -a+b, b, c | x, y, z | { 1 ‖ m100 | 0 } |
| -b, -a, c | x, y, z | { 1 ‖ m110 | 0 } |
| a, a-b, c | x, y, z | { 1 ‖ m010 | 0 } |
| a, b, c+1/2 | -x, -y, -z | { -1 ‖ 1 | 0 0 1/2 } |
| -b, a-b, c+1/2 | -x, -y, -z | { -1 ‖ 3+001 | 0 0 1/2 } |
| -a+b, -a, c+1/2 | -x, -y, -z | { -1 ‖ 3-001 | 0 0 1/2 } |
| a-b, -b, -c+1/2 | -x, -y, -z | { -1 ‖ 2100 | 0 0 1/2 } |
| b, a, -c+1/2 | -x, -y, -z | { -1 ‖ 2110 | 0 0 1/2 } |
| -a, -a+b, -c+1/2 | -x, -y, -z | { -1 ‖ 2010 | 0 0 1/2 } |
| -a, -b, -c+1/2 | -x, -y, -z | { -1 ‖ -1 | 0 0 1/2 } |
| b, -a+b, -c+1/2 | -x, -y, -z | { -1 ‖ -3+001 | 0 0 1/2 } |
| a-b, a, -c+1/2 | -x, -y, -z | { -1 ‖ -3-001 | 0 0 1/2 } |
| -a+b, b, c+1/2 | -x, -y, -z | { -1 ‖ m100 | 0 0 1/2 } |
| -b, -a, c+1/2 | -x, -y, -z | { -1 ‖ m110 | 0 0 1/2 } |
| a, a-b, c+1/2 | -x, -y, -z | { -1 ‖ m010 | 0 0 1/2 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| -b, a-b, c | -x, y, z | { m ‖ 3+001 | 0 } |
| -a+b, -a, c | -x, y, z | { m ‖ 3-001 | 0 } |
| a-b, -b, -c | -x, y, z | { m ‖ 2100 | 0 } |
| b, a, -c | -x, y, z | { m ‖ 2110 | 0 } |
| -a, -a+b, -c | -x, y, z | { m ‖ 2010 | 0 } |
| -a, -b, -c | -x, y, z | { m ‖ -1 | 0 } |
| b, -a+b, -c | -x, y, z | { m ‖ -3+001 | 0 } |
| a-b, a, -c | -x, y, z | { m ‖ -3-001 | 0 } |
| -a+b, b, c | -x, y, z | { m ‖ m100 | 0 } |
| -b, -a, c | -x, y, z | { m ‖ m110 | 0 } |
| a, a-b, c | -x, y, z | { m ‖ m010 | 0 } |
| a, b, c+1/2 | x, -y, -z | { 2 ‖ 1 | 0 0 1/2 } |
| -b, a-b, c+1/2 | x, -y, -z | { 2 ‖ 3+001 | 0 0 1/2 } |
| -a+b, -a, c+1/2 | x, -y, -z | { 2 ‖ 3-001 | 0 0 1/2 } |
| a-b, -b, -c+1/2 | x, -y, -z | { 2 ‖ 2100 | 0 0 1/2 } |
| b, a, -c+1/2 | x, -y, -z | { 2 ‖ 2110 | 0 0 1/2 } |
| -a, -a+b, -c+1/2 | x, -y, -z | { 2 ‖ 2010 | 0 0 1/2 } |
| -a, -b, -c+1/2 | x, -y, -z | { 2 ‖ -1 | 0 0 1/2 } |
| b, -a+b, -c+1/2 | x, -y, -z | { 2 ‖ -3+001 | 0 0 1/2 } |
| a-b, a, -c+1/2 | x, -y, -z | { 2 ‖ -3-001 | 0 0 1/2 } |
| -a+b, b, c+1/2 | x, -y, -z | { 2 ‖ m100 | 0 0 1/2 } |
| -b, -a, c+1/2 | x, -y, -z | { 2 ‖ m110 | 0 0 1/2 } |
| a, a-b, c+1/2 | x, -y, -z | { 2 ‖ m010 | 0 0 1/2 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 2a | $\ce{^{1}{-3}}\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,z) |
| 2b | $\ce{^{-1}{-3}}\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (0,0,1/4 | 0,0,0) |
| 4c | $\ce{^{1}{3}}\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,z) |
| 4d | $\ce{^{1}{3}}\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (1/3,2/3,c | 0,0,z) |
| 6e | $.\ce{^{1}{2}}/\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (1/2,0,0 | 0,0,z) |
| 6f | $.\ce{^{-1}{2}}/\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (1/2,0,1/4 | 0,0,0) |
| 12g | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (a,0,0 | 0,0,z) |
| 12h | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (a,0,1/4 | 0,0,0) |
| 12i | $.\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (a,-a,c | 0,0,z) |
| 24j | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
| Wavevector-k | Little co-group |
|---|---|
| A:(0,0,1/2) | $\ce{^{1}{-3}}\ce{^{1}{m}}\ce{^{1}{1}}\ce{^{\infty /mm}{1}} $ |
| Γ:(0,0,0) | $\ce{^{1}{-3}}\ce{^{1}{m}}\ce{^{1}{1}}\ce{^{\infty /mm}{1}} $ |
| H:(1/3,1/3,1/2) | $\ce{^{m}{-3}}\ce{^{m}{m}}\ce{^{1}{1}}\ce{^{\infty 2}{1}} $ |
| K:(1/3,1/3,0) | $\ce{^{m}{-3}}\ce{^{m}{m}}\ce{^{1}{1}}\ce{^{\infty 2}{1}} $ |
| L:(1/2,0,1/2) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| M:(1/2,0,0) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| Δ:(0,0,w) | $\ce{^{m}{-3}}\ce{^{1}{m}}\ce{^{1}{1}}\ce{^{\infty 2}{1}} $ |
| P:(1/3,1/3,w) | $\ce{^{m}{-3}}\ce{^{\infty 2}{1}} $ |
| Λ:(u,u,0) | $\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty 2}{1}} $ |
| Σ:(u,0,0) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| Q:(u,u,1/2) | $\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty 2}{1}} $ |
| R:(u,0,1/2) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| U:(1/2,0,w) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| B:(u,v,0) | $\ce{^{m}{-1}}\ce{^{\infty 2}{1}} $ |
| C:(u,u,w) | $\ce{^{m}{-1}}\ce{^{\infty 2}{1}} $ |
| D:(u,0,w) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| E:(u,v,1/2) | $\ce{^{m}{-1}}\ce{^{\infty 2}{1}} $ |
| GP:(u,v,w) | $\ce{^{m}{-1}}\ce{^{\infty 2}{1}} $ |
Spin Brillouin Zone
| k-vector | A1g↑G(2) |
| A:(0,0,1/2) | $A_{1}^{S,+}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2) $ |
| H:(1/3,1/3,1/2) | $H_{1}^{S}(2) $ |
| K:(1/3,1/3,0) | $K_{1}^{S}(2) $ |
| L:(1/2,0,1/2) | $L_{1}^{S,+}(2) $ |
| M:(1/2,0,0) | $M_{1}^{S,+}(2) $ |
| Δ:(0,0,w) | $Δ_{1}^{S}(2) $ |
| P:(1/3,1/3,w) | $P_{1}^{S}(2) $ |
| Λ:(u,u,0) | $Λ_{1}^{S}(2) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(2) $ |
| Q:(u,u,1/2) | $Q_{1}^{S}(2) $ |
| R:(u,0,1/2) | $R_{1}^{S}(2) $ |
| U:(1/2,0,w) | $U_{1}^{S}(2) $ |
| B:(u,v,0) | $B_{1}^{S}(2) $ |
| C:(u,u,w) | $C_{1}^{S}(2) $ |
| D:(u,0,w) | $D_{1}^{S}(2) $ |
| E:(u,v,1/2) | $E_{1}^{S}(2) $ |
| GP:(u,v,w) | $GP_{1}^{S}(2) $ |
| k-vector | A1↑G(4) |
| A:(0,0,1/2) | $A_{1}^{S,+}(2)⊕A_{2}^{S,-}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{2}^{S,-}(2) $ |
| H:(1/3,1/3,1/2) | $H_{1}^{S}(2)⊕H_{2}^{S}(2) $ |
| K:(1/3,1/3,0) | $K_{1}^{S}(2)⊕K_{2}^{S}(2) $ |
| L:(1/2,0,1/2) | $L_{1}^{S,+}(2)⊕L_{2}^{S,-}(2) $ |
| M:(1/2,0,0) | $M_{1}^{S,+}(2)⊕M_{2}^{S,-}(2) $ |
| Δ:(0,0,w) | $2Δ_{1}^{S}(2) $ |
| P:(1/3,1/3,w) | $2P_{1}^{S}(2) $ |
| Λ:(u,u,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ |
| Σ:(u,0,0) | $2Σ_{1}^{S}(2) $ |
| Q:(u,u,1/2) | $Q_{1}^{S}(2)⊕Q_{2}^{S}(2) $ |
| R:(u,0,1/2) | $2R_{1}^{S}(2) $ |
| U:(1/2,0,w) | $2U_{1}^{S}(2) $ |
| B:(u,v,0) | $2B_{1}^{S}(2) $ |
| C:(u,u,w) | $2C_{1}^{S}(2) $ |
| D:(u,0,w) | $2D_{1}^{S}(2) $ |
| E:(u,v,1/2) | $2E_{1}^{S}(2) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(2) $ |
| k-vector | A1↑G(4) |
| A:(0,0,1/2) | $A_{1}^{S,+}(2)⊕A_{2}^{S,-}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{2}^{S,-}(2) $ |
| H:(1/3,1/3,1/2) | $H_{3}^{S}(4) $ |
| K:(1/3,1/3,0) | $K_{3}^{S}(4) $ |
| L:(1/2,0,1/2) | $L_{1}^{S,+}(2)⊕L_{2}^{S,-}(2) $ |
| M:(1/2,0,0) | $M_{1}^{S,+}(2)⊕M_{2}^{S,-}(2) $ |
| Δ:(0,0,w) | $2Δ_{1}^{S}(2) $ |
| P:(1/3,1/3,w) | $P_{2}^{S}P_{3}^{S}(4) $ |
| Λ:(u,u,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ |
| Σ:(u,0,0) | $2Σ_{1}^{S}(2) $ |
| Q:(u,u,1/2) | $Q_{1}^{S}(2)⊕Q_{2}^{S}(2) $ |
| R:(u,0,1/2) | $2R_{1}^{S}(2) $ |
| U:(1/2,0,w) | $2U_{1}^{S}(2) $ |
| B:(u,v,0) | $2B_{1}^{S}(2) $ |
| C:(u,u,w) | $2C_{1}^{S}(2) $ |
| D:(u,0,w) | $2D_{1}^{S}(2) $ |
| E:(u,v,1/2) | $2E_{1}^{S}(2) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(2) $ |
| k-vector | Ag↑G(6) |
| A:(0,0,1/2) | $A_{1}^{S,+}(2)⊕A_{3}^{S,+}(4) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{3}^{S,+}(4) $ |
| H:(1/3,1/3,1/2) | $H_{1}^{S}(2)⊕H_{3}^{S}(4) $ |
| K:(1/3,1/3,0) | $K_{1}^{S}(2)⊕K_{3}^{S}(4) $ |
| L:(1/2,0,1/2) | $L_{1}^{S,+}(2)⊕L_{1}^{S,-}(2)⊕L_{2}^{S,-}(2) $ |
| M:(1/2,0,0) | $M_{1}^{S,+}(2)⊕M_{1}^{S,-}(2)⊕M_{2}^{S,-}(2) $ |
| Δ:(0,0,w) | $Δ_{1}^{S}(2)⊕Δ_{3}^{S}(4) $ |
| P:(1/3,1/3,w) | $P_{1}^{S}(2)⊕P_{2}^{S}P_{3}^{S}(4) $ |
| Λ:(u,u,0) | $2Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ |
| Σ:(u,0,0) | $2Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2) $ |
| Q:(u,u,1/2) | $2Q_{1}^{S}(2)⊕Q_{2}^{S}(2) $ |
| R:(u,0,1/2) | $2R_{1}^{S}(2)⊕R_{2}^{S}(2) $ |
| U:(1/2,0,w) | $2U_{1}^{S}(2)⊕U_{2}^{S}(2) $ |
| B:(u,v,0) | $3B_{1}^{S}(2) $ |
| C:(u,u,w) | $3C_{1}^{S}(2) $ |
| D:(u,0,w) | $2D_{1}^{S}(2)⊕D_{2}^{S}(2) $ |
| E:(u,v,1/2) | $3E_{1}^{S}(2) $ |
| GP:(u,v,w) | $3GP_{1}^{S}(2) $ |
| k-vector | A↑G(12) |
| A:(0,0,1/2) | $A_{1}^{S,+}(2)⊕A_{1}^{S,-}(2)⊕A_{3}^{S,+}(4)⊕A_{3}^{S,-}(4) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2)⊕Γ_{3}^{S,+}(4)⊕Γ_{3}^{S,-}(4) $ |
| H:(1/3,1/3,1/2) | $2H_{1}^{S}(2)⊕2H_{3}^{S}(4) $ |
| K:(1/3,1/3,0) | $2K_{1}^{S}(2)⊕2K_{3}^{S}(4) $ |
| L:(1/2,0,1/2) | $2L_{1}^{S,+}(2)⊕2L_{1}^{S,-}(2)⊕L_{2}^{S,+}(2)⊕L_{2}^{S,-}(2) $ |
| M:(1/2,0,0) | $2M_{1}^{S,+}(2)⊕2M_{1}^{S,-}(2)⊕M_{2}^{S,+}(2)⊕M_{2}^{S,-}(2) $ |
| Δ:(0,0,w) | $Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2)⊕2Δ_{3}^{S}(4) $ |
| P:(1/3,1/3,w) | $2P_{1}^{S}(2)⊕2P_{2}^{S}P_{3}^{S}(4) $ |
| Λ:(u,u,0) | $4Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2) $ |
| Σ:(u,0,0) | $3Σ_{1}^{S}(2)⊕3Σ_{2}^{S}(2) $ |
| Q:(u,u,1/2) | $4Q_{1}^{S}(2)⊕2Q_{2}^{S}(2) $ |
| R:(u,0,1/2) | $3R_{1}^{S}(2)⊕3R_{2}^{S}(2) $ |
| U:(1/2,0,w) | $3U_{1}^{S}(2)⊕3U_{2}^{S}(2) $ |
| B:(u,v,0) | $6B_{1}^{S}(2) $ |
| C:(u,u,w) | $6C_{1}^{S}(2) $ |
| D:(u,0,w) | $3D_{1}^{S}(2)⊕3D_{2}^{S}(2) $ |
| E:(u,v,1/2) | $6E_{1}^{S}(2) $ |
| GP:(u,v,w) | $6GP_{1}^{S}(2) $ |
| k-vector | A'↑G(12) |
| A:(0,0,1/2) | $A_{1}^{S,+}(2)⊕A_{2}^{S,-}(2)⊕A_{3}^{S,+}(4)⊕A_{3}^{S,-}(4) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{2}^{S,-}(2)⊕Γ_{3}^{S,+}(4)⊕Γ_{3}^{S,-}(4) $ |
| H:(1/3,1/3,1/2) | $H_{1}^{S}(2)⊕H_{2}^{S}(2)⊕2H_{3}^{S}(4) $ |
| K:(1/3,1/3,0) | $K_{1}^{S}(2)⊕K_{2}^{S}(2)⊕2K_{3}^{S}(4) $ |
| L:(1/2,0,1/2) | $2L_{1}^{S,+}(2)⊕L_{1}^{S,-}(2)⊕L_{2}^{S,+}(2)⊕2L_{2}^{S,-}(2) $ |
| M:(1/2,0,0) | $2M_{1}^{S,+}(2)⊕M_{1}^{S,-}(2)⊕M_{2}^{S,+}(2)⊕2M_{2}^{S,-}(2) $ |
| Δ:(0,0,w) | $2Δ_{1}^{S}(2)⊕2Δ_{3}^{S}(4) $ |
| P:(1/3,1/3,w) | $2P_{1}^{S}(2)⊕2P_{2}^{S}P_{3}^{S}(4) $ |
| Λ:(u,u,0) | $3Λ_{1}^{S}(2)⊕3Λ_{2}^{S}(2) $ |
| Σ:(u,0,0) | $4Σ_{1}^{S}(2)⊕2Σ_{2}^{S}(2) $ |
| Q:(u,u,1/2) | $3Q_{1}^{S}(2)⊕3Q_{2}^{S}(2) $ |
| R:(u,0,1/2) | $4R_{1}^{S}(2)⊕2R_{2}^{S}(2) $ |
| U:(1/2,0,w) | $4U_{1}^{S}(2)⊕2U_{2}^{S}(2) $ |
| B:(u,v,0) | $6B_{1}^{S}(2) $ |
| C:(u,u,w) | $6C_{1}^{S}(2) $ |
| D:(u,0,w) | $4D_{1}^{S}(2)⊕2D_{2}^{S}(2) $ |
| E:(u,v,1/2) | $6E_{1}^{S}(2) $ |
| GP:(u,v,w) | $6GP_{1}^{S}(2) $ |
| k-vector | |
| $A↑G(24) $ | |
| $ $ | |
| A:(0,0,1/2) | $A_{1}^{S,+}(2)⊕A_{1}^{S,-}(2)⊕A_{2}^{S,+}(2)⊕A_{2}^{S,-}(2)⊕2A_{3}^{S,+}(4)⊕2A_{3}^{S,-}(4) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2)⊕Γ_{2}^{S,+}(2)⊕Γ_{2}^{S,-}(2)⊕2Γ_{3}^{S,+}(4)⊕2Γ_{3}^{S,-}(4) $ |
| H:(1/3,1/3,1/2) | $2H_{1}^{S}(2)⊕2H_{2}^{S}(2)⊕4H_{3}^{S}(4) $ |
| K:(1/3,1/3,0) | $2K_{1}^{S}(2)⊕2K_{2}^{S}(2)⊕4K_{3}^{S}(4) $ |
| L:(1/2,0,1/2) | $3L_{1}^{S,+}(2)⊕3L_{1}^{S,-}(2)⊕3L_{2}^{S,+}(2)⊕3L_{2}^{S,-}(2) $ |
| M:(1/2,0,0) | $3M_{1}^{S,+}(2)⊕3M_{1}^{S,-}(2)⊕3M_{2}^{S,+}(2)⊕3M_{2}^{S,-}(2) $ |
| Δ:(0,0,w) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2)⊕4Δ_{3}^{S}(4) $ |
| P:(1/3,1/3,w) | $4P_{1}^{S}(2)⊕4P_{2}^{S}P_{3}^{S}(4) $ |
| Λ:(u,u,0) | $6Λ_{1}^{S}(2)⊕6Λ_{2}^{S}(2) $ |
| Σ:(u,0,0) | $6Σ_{1}^{S}(2)⊕6Σ_{2}^{S}(2) $ |
| Q:(u,u,1/2) | $6Q_{1}^{S}(2)⊕6Q_{2}^{S}(2) $ |
| R:(u,0,1/2) | $6R_{1}^{S}(2)⊕6R_{2}^{S}(2) $ |
| U:(1/2,0,w) | $6U_{1}^{S}(2)⊕6U_{2}^{S}(2) $ |
| B:(u,v,0) | $12B_{1}^{S}(2) $ |
| C:(u,u,w) | $12C_{1}^{S}(2) $ |
| D:(u,0,w) | $6D_{1}^{S}(2)⊕6D_{2}^{S}(2) $ |
| E:(u,v,1/2) | $12E_{1}^{S}(2) $ |