The continuously infinite group ∞1 is omitted.
| Coordinates | Seitz symbol |
|---|---|
| a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
| a-b, a, c | x, y, z | { 1 ‖ 6+001 | 0 } |
| -b, a-b, c | x, y, z | { 1 ‖ 3+001 | 0 } |
| -a, -b, c | x, y, z | { 1 ‖ 2001 | 0 } |
| -a+b, -a, c | x, y, z | { 1 ‖ 3-001 | 0 } |
| b, -a+b, c | x, y, z | { 1 ‖ 6-001 | 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, -a+b, c | x, y, z | { 1 ‖ m210 | 0 } |
| a-b, -b, c | x, y, z | { 1 ‖ m120 | 0 } |
| b, a, c | x, y, z | { 1 ‖ m1-10 | 0 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| a-b, a, c | -x, y, z | { m ‖ 6+001 | 0 } |
| -b, a-b, c | -x, y, z | { m ‖ 3+001 | 0 } |
| -a, -b, c | -x, y, z | { m ‖ 2001 | 0 } |
| -a+b, -a, c | -x, y, z | { m ‖ 3-001 | 0 } |
| b, -a+b, c | -x, y, z | { m ‖ 6-001 | 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, -a+b, c | -x, y, z | { m ‖ m210 | 0 } |
| a-b, -b, c | -x, y, z | { m ‖ m120 | 0 } |
| b, a, c | -x, y, z | { m ‖ m1-10 | 0 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 1a | $\ce{^{1}{6}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (0,0,c |0,0,z) |
| 2b | $\ce{^{1}{3}}\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (1/3,2/3,c |0,0,z) |
| 3c | $\ce{^{1}{2}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (1/2,0,c |0,0,z) |
| 6d | $..\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (a,0,c |0,0,z) |
| 6e | $.\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (a,-a,c |0,0,z) |
| 12f | $\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}{6}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| Γ:(0,0,0) | $\ce{^{1}{6}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| H:(1/3,1/3,1/2) | $\ce{^{m}{6}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| K:(1/3,1/3,0) | $\ce{^{m}{6}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| L:(1/2,0,1/2) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| M:(1/2,0,0) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| Δ:(0,0,w) | $\ce{^{1}{6}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| P:(1/3,1/3,w) | $\ce{^{1}{3}}\ce{^{1}{1}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Λ:(u,u,0) | $\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| Q:(u,u,1/2) | $\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| R:(u,0,1/2) | $\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| U:(1/2,0,w) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| B:(u,v,0) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| C:(u,u,w) | $\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| D:(u,0,w) | $\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| E:(u,v,1/2) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| GP:(u,v,w) | $\ce{^{1}{1}}\ce{^{\infty}{1}}$ |
Spin Brillouin Zone
| k-vector | A↑G(12) |
| A:(0,0,1/2) | $A_{1}^{S}(1)⊕A_{2}^{S}(1)⊕A_{3}^{S}(1)⊕A_{4}^{S}(1)⊕2A_{5}^{S}(2)⊕2A_{6}^{S}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}(1)⊕Γ_{3}^{S}(1)⊕Γ_{4}^{S}(1)⊕2Γ_{5}^{S}(2)⊕2Γ_{6}^{S}(2) $ |
| H:(1/3,1/3,1/2) | $2H_{1}^{S}(1)⊕2H_{2}^{S}(1)⊕4H_{3}^{S}(2) $ |
| K:(1/3,1/3,0) | $2K_{1}^{S}(1)⊕2K_{2}^{S}(1)⊕4K_{3}^{S}(2) $ |
| L:(1/2,0,1/2) | $3L_{1}^{S}(1)⊕3L_{2}^{S}(1)⊕3L_{3}^{S}(1)⊕3L_{4}^{S}(1) $ |
| M:(1/2,0,0) | $3M_{1}^{S}(1)⊕3M_{2}^{S}(1)⊕3M_{3}^{S}(1)⊕3M_{4}^{S}(1) $ |
| Δ:(0,0,w) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1)⊕Δ_{3}^{S}(1)⊕Δ_{4}^{S}(1)⊕2Δ_{5}^{S}(2)⊕2Δ_{6}^{S}(2) $ |
| P:(1/3,1/3,w) | $2P_{1}^{S}(1)⊕2P_{2}^{S}(1)⊕4P_{3}^{S}(2) $ |
| Λ:(u,u,0) | $6Λ_{1}^{S}(1)⊕6Λ_{2}^{S}(1) $ |
| Σ:(u,0,0) | $6Σ_{1}^{S}(1)⊕6Σ_{2}^{S}(1) $ |
| Q:(u,u,1/2) | $6Q_{1}^{S}(1)⊕6Q_{2}^{S}(1) $ |
| R:(u,0,1/2) | $6R_{1}^{S}(1)⊕6R_{2}^{S}(1) $ |
| U:(1/2,0,w) | $3U_{1}^{S}(1)⊕3U_{2}^{S}(1)⊕3U_{3}^{S}(1)⊕3U_{4}^{S}(1) $ |
| B:(u,v,0) | $12B_{1}^{S}(1) $ |
| C:(u,u,w) | $6C_{1}^{S}(1)⊕6C_{2}^{S}(1) $ |
| D:(u,0,w) | $6D_{1}^{S}(1)⊕6D_{2}^{S}(1) $ |
| E:(u,v,1/2) | $12E_{1}^{S}(1) $ |
| GP:(u,v,w) | $12GP_{1}^{S}(1) $ |
| k-vector | A1↑G(1) |
| A:(0,0,1/2) | $A_{1}^{S}(1) $ |
| Γ:(0,0,0) | $Γ_{1}^{S}(1) $ |
| H:(1/3,1/3,1/2) | $H_{1}^{S}(1) $ |
| K:(1/3,1/3,0) | $K_{1}^{S}(1) $ |
| L:(1/2,0,1/2) | $L_{1}^{S}(1) $ |
| M:(1/2,0,0) | $M_{1}^{S}(1) $ |
| Δ:(0,0,w) | $Δ_{1}^{S}(1) $ |
| P:(1/3,1/3,w) | $P_{1}^{S}(1) $ |
| Λ:(u,u,0) | $Λ_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1) $ |
| Q:(u,u,1/2) | $Q_{1}^{S}(1) $ |
| R:(u,0,1/2) | $R_{1}^{S}(1) $ |
| U:(1/2,0,w) | $U_{1}^{S}(1) $ |
| B:(u,v,0) | $B_{1}^{S}(1) $ |
| C:(u,u,w) | $C_{1}^{S}(1) $ |
| D:(u,0,w) | $D_{1}^{S}(1) $ |
| E:(u,v,1/2) | $E_{1}^{S}(1) $ |
| GP:(u,v,w) | $GP_{1}^{S}(1) $ |
| k-vector | A1↑G(2) |
| A:(0,0,1/2) | $A_{1}^{S}(1)⊕A_{4}^{S}(1) $ |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{4}^{S}(1) $ |
| H:(1/3,1/3,1/2) | $H_{3}^{S}(2) $ |
| K:(1/3,1/3,0) | $K_{3}^{S}(2) $ |
| L:(1/2,0,1/2) | $L_{1}^{S}(1)⊕L_{4}^{S}(1) $ |
| M:(1/2,0,0) | $M_{1}^{S}(1)⊕M_{4}^{S}(1) $ |
| Δ:(0,0,w) | $Δ_{1}^{S}(1)⊕Δ_{4}^{S}(1) $ |
| P:(1/3,1/3,w) | $P_{3}^{S}(2) $ |
| Λ:(u,u,0) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $ |
| Σ:(u,0,0) | $2Σ_{1}^{S}(1) $ |
| Q:(u,u,1/2) | $Q_{1}^{S}(1)⊕Q_{2}^{S}(1) $ |
| R:(u,0,1/2) | $2R_{1}^{S}(1) $ |
| U:(1/2,0,w) | $U_{1}^{S}(1)⊕U_{4}^{S}(1) $ |
| B:(u,v,0) | $2B_{1}^{S}(1) $ |
| C:(u,u,w) | $C_{1}^{S}(1)⊕C_{2}^{S}(1) $ |
| D:(u,0,w) | $2D_{1}^{S}(1) $ |
| E:(u,v,1/2) | $2E_{1}^{S}(1) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
| k-vector | A1↑G(3) |
| A:(0,0,1/2) | $A_{1}^{S}(1)⊕A_{5}^{S}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{5}^{S}(2) $ |
| H:(1/3,1/3,1/2) | $H_{1}^{S}(1)⊕H_{3}^{S}(2) $ |
| K:(1/3,1/3,0) | $K_{1}^{S}(1)⊕K_{3}^{S}(2) $ |
| L:(1/2,0,1/2) | $L_{1}^{S}(1)⊕L_{3}^{S}(1)⊕L_{4}^{S}(1) $ |
| M:(1/2,0,0) | $M_{1}^{S}(1)⊕M_{3}^{S}(1)⊕M_{4}^{S}(1) $ |
| Δ:(0,0,w) | $Δ_{1}^{S}(1)⊕Δ_{5}^{S}(2) $ |
| P:(1/3,1/3,w) | $P_{1}^{S}(1)⊕P_{3}^{S}(2) $ |
| Λ:(u,u,0) | $2Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $ |
| Σ:(u,0,0) | $2Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
| Q:(u,u,1/2) | $2Q_{1}^{S}(1)⊕Q_{2}^{S}(1) $ |
| R:(u,0,1/2) | $2R_{1}^{S}(1)⊕R_{2}^{S}(1) $ |
| U:(1/2,0,w) | $U_{1}^{S}(1)⊕U_{3}^{S}(1)⊕U_{4}^{S}(1) $ |
| B:(u,v,0) | $3B_{1}^{S}(1) $ |
| C:(u,u,w) | $2C_{1}^{S}(1)⊕C_{2}^{S}(1) $ |
| D:(u,0,w) | $2D_{1}^{S}(1)⊕D_{2}^{S}(1) $ |
| E:(u,v,1/2) | $3E_{1}^{S}(1) $ |
| GP:(u,v,w) | $3GP_{1}^{S}(1) $ |
| k-vector | A'↑G(6) |
| A:(0,0,1/2) | $A_{1}^{S}(1)⊕A_{3}^{S}(1)⊕A_{5}^{S}(2)⊕A_{6}^{S}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{3}^{S}(1)⊕Γ_{5}^{S}(2)⊕Γ_{6}^{S}(2) $ |
| H:(1/3,1/3,1/2) | $2H_{1}^{S}(1)⊕2H_{3}^{S}(2) $ |
| K:(1/3,1/3,0) | $2K_{1}^{S}(1)⊕2K_{3}^{S}(2) $ |
| L:(1/2,0,1/2) | $2L_{1}^{S}(1)⊕L_{2}^{S}(1)⊕2L_{3}^{S}(1)⊕L_{4}^{S}(1) $ |
| M:(1/2,0,0) | $2M_{1}^{S}(1)⊕M_{2}^{S}(1)⊕2M_{3}^{S}(1)⊕M_{4}^{S}(1) $ |
| Δ:(0,0,w) | $Δ_{1}^{S}(1)⊕Δ_{3}^{S}(1)⊕Δ_{5}^{S}(2)⊕Δ_{6}^{S}(2) $ |
| P:(1/3,1/3,w) | $2P_{1}^{S}(1)⊕2P_{3}^{S}(2) $ |
| Λ:(u,u,0) | $4Λ_{1}^{S}(1)⊕2Λ_{2}^{S}(1) $ |
| Σ:(u,0,0) | $3Σ_{1}^{S}(1)⊕3Σ_{2}^{S}(1) $ |
| Q:(u,u,1/2) | $4Q_{1}^{S}(1)⊕2Q_{2}^{S}(1) $ |
| R:(u,0,1/2) | $3R_{1}^{S}(1)⊕3R_{2}^{S}(1) $ |
| U:(1/2,0,w) | $2U_{1}^{S}(1)⊕U_{2}^{S}(1)⊕2U_{3}^{S}(1)⊕U_{4}^{S}(1) $ |
| B:(u,v,0) | $6B_{1}^{S}(1) $ |
| C:(u,u,w) | $4C_{1}^{S}(1)⊕2C_{2}^{S}(1) $ |
| D:(u,0,w) | $3D_{1}^{S}(1)⊕3D_{2}^{S}(1) $ |
| E:(u,v,1/2) | $6E_{1}^{S}(1) $ |
| GP:(u,v,w) | $6GP_{1}^{S}(1) $ |
| k-vector | A'↑G(6) |
| A:(0,0,1/2) | $A_{1}^{S}(1)⊕A_{4}^{S}(1)⊕A_{5}^{S}(2)⊕A_{6}^{S}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{4}^{S}(1)⊕Γ_{5}^{S}(2)⊕Γ_{6}^{S}(2) $ |
| H:(1/3,1/3,1/2) | $H_{1}^{S}(1)⊕H_{2}^{S}(1)⊕2H_{3}^{S}(2) $ |
| K:(1/3,1/3,0) | $K_{1}^{S}(1)⊕K_{2}^{S}(1)⊕2K_{3}^{S}(2) $ |
| L:(1/2,0,1/2) | $2L_{1}^{S}(1)⊕L_{2}^{S}(1)⊕L_{3}^{S}(1)⊕2L_{4}^{S}(1) $ |
| M:(1/2,0,0) | $2M_{1}^{S}(1)⊕M_{2}^{S}(1)⊕M_{3}^{S}(1)⊕2M_{4}^{S}(1) $ |
| Δ:(0,0,w) | $Δ_{1}^{S}(1)⊕Δ_{4}^{S}(1)⊕Δ_{5}^{S}(2)⊕Δ_{6}^{S}(2) $ |
| P:(1/3,1/3,w) | $P_{1}^{S}(1)⊕P_{2}^{S}(1)⊕2P_{3}^{S}(2) $ |
| Λ:(u,u,0) | $3Λ_{1}^{S}(1)⊕3Λ_{2}^{S}(1) $ |
| Σ:(u,0,0) | $4Σ_{1}^{S}(1)⊕2Σ_{2}^{S}(1) $ |
| Q:(u,u,1/2) | $3Q_{1}^{S}(1)⊕3Q_{2}^{S}(1) $ |
| R:(u,0,1/2) | $4R_{1}^{S}(1)⊕2R_{2}^{S}(1) $ |
| U:(1/2,0,w) | $2U_{1}^{S}(1)⊕U_{2}^{S}(1)⊕U_{3}^{S}(1)⊕2U_{4}^{S}(1) $ |
| B:(u,v,0) | $6B_{1}^{S}(1) $ |
| C:(u,u,w) | $3C_{1}^{S}(1)⊕3C_{2}^{S}(1) $ |
| D:(u,0,w) | $4D_{1}^{S}(1)⊕2D_{2}^{S}(1) $ |
| E:(u,v,1/2) | $6E_{1}^{S}(1) $ |
| GP:(u,v,w) | $6GP_{1}^{S}(1) $ |