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, a-b, -c | x, y, z | { 1 ‖ 2210 | 0 } |
| -a+b, b, -c | x, y, z | { 1 ‖ 2120 | 0 } |
| -b, -a, -c | x, y, z | { 1 ‖ 21-10 | 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, -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, a, c | -x, -y, -z | { -1 ‖ 6+001 | 0 } |
| -a, -b, c | -x, -y, -z | { -1 ‖ 2001 | 0 } |
| b, -a+b, c | -x, -y, -z | { -1 ‖ 6-001 | 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, -a, -c | -x, -y, -z | { -1 ‖ -6+001 | 0 } |
| a, b, -c | -x, -y, -z | { -1 ‖ m001 | 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, 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, a-b, -c | -x, y, z | { m ‖ 2210 | 0 } |
| -a+b, b, -c | -x, y, z | { m ‖ 2120 | 0 } |
| -b, -a, -c | -x, y, z | { m ‖ 21-10 | 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, -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 } |
| a-b, a, c | x, -y, -z | { 2 ‖ 6+001 | 0 } |
| -a, -b, c | x, -y, -z | { 2 ‖ 2001 | 0 } |
| b, -a+b, c | x, -y, -z | { 2 ‖ 6-001 | 0 } |
| a-b, -b, -c | x, -y, -z | { 2 ‖ 2100 | 0 } |
| b, a, -c | x, -y, -z | { 2 ‖ 2110 | 0 } |
| -a, -a+b, -c | x, -y, -z | { 2 ‖ 2010 | 0 } |
| -a+b, -a, -c | x, -y, -z | { 2 ‖ -6+001 | 0 } |
| a, b, -c | x, -y, -z | { 2 ‖ m001 | 0 } |
| -b, a-b, -c | x, -y, -z | { 2 ‖ -6-001 | 0 } |
| -a+b, b, c | x, -y, -z | { 2 ‖ m100 | 0 } |
| -b, -a, c | x, -y, -z | { 2 ‖ m110 | 0 } |
| a, a-b, c | x, -y, -z | { 2 ‖ m010 | 0 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 1a | $\ce{^{-1}{6}}/\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
| 1b | $\ce{^{-1}{6}}/\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,0) |
| 2c | $\ce{^{-1}{-6}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/3,2/3,0 | 0,0,0) |
| 2d | $\ce{^{-1}{-6}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/3,2/3,1/2 | 0,0,0) |
| 2e | $\ce{^{-1}{6}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,0) |
| 3f | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (1/2,0,0 | 0,0,0) |
| 3g | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (1/2,0,1/2 | 0,0,0) |
| 4h | $\ce{^{1}{3}}\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (1/3,2/3,c | 0,0,0) |
| 6i | $\ce{^{-1}{2}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (1/2,0,c | 0,0,0) |
| 6j | $\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (a,0,0 | 0,0,0) |
| 6k | $\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (a,0,1/2 | 0,0,0) |
| 6l | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (a,2a,0 | 0,0,0) |
| 6m | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (a,2a,1/2 | 0,0,0) |
| 12n | $..\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (a,0,c | 0,0,z) |
| 12o | $.\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (a,2a,c | 0,0,0) |
| 12p | $\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (a,b,0 | 0,0,0) |
| 12q | $\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (a,b,1/2 | 0,0,0) |
| 24r | $\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{^{1}{m}}\ce{^{\infty m}{1}} $ |
| Γ:(0,0,0) | $\ce{^{-1}{6/}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| H:(1/3,1/3,1/2) | $\ce{^{-1}{6/}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| K:(1/3,1/3,0) | $\ce{^{-1}{6/}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| L:(1/2,0,1/2) | $\ce{^{1}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty m}{1}} $ |
| M:(1/2,0,0) | $\ce{^{1}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty m}{1}} $ |
| Δ:(0,0,w) | $\ce{^{2}{6/}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| P:(1/3,1/3,w) | $\ce{^{m}{-3}}\ce{^{1}{1}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Λ:(u,u,0) | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $\ce{^{m}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| Q:(u,u,1/2) | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| R:(u,0,1/2) | $\ce{^{m}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| U:(1/2,0,w) | $\ce{^{1}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
| B:(u,v,0) | $\ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| C:(u,u,w) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| D:(u,0,w) | $\ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| E:(u,v,1/2) | $\ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| GP:(u,v,w) | $\ce{^{m}{-1}}\ce{^{\infty}{1}}$ |
Spin Brillouin Zone
| k-vector | k-vector-G↑ | A'↑G(12) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{2}^{S,-}(2)⊕Γ_{3}^{S,+}(4)⊕Γ_{3}^{S,-}(4) $ | |
| A:(0,0,1/2) | A:(0,0,1/2) | $A_{1}^{S,+}(2)⊕A_{2}^{S,-}(2)⊕A_{3}^{S,+}(4)⊕A_{3}^{S,-}(4) $ | |
| H:(1/3,1/3,1/2) | H:(1/3,1/3,1/2) | $2H_{1}^{S}(2)⊕2H_{3}^{S}(4) $ | |
| K:(1/3,1/3,0) | K:(1/3,1/3,0) | $2K_{1}^{S}(2)⊕2K_{3}^{S}(4) $ | |
| L:(1/2,0,1/2) | 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) | 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) | Δ:(0,0,w) | $2Δ_{1}^{S}(2)⊕2Δ_{3}^{S}(4) $ | |
| Λ:(u,u,0) | Λ:(u,u,0) | $4Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2) $ | |
| P:(1/3,1/3,w) | P:(1/3,1/3,w) | $4P_{1}^{S}(1)⊕4P_{3}^{S}(2)$ | Spin Splitting |
| Q:(u,u,1/2) | Q:(u,u,1/2) | $4Q_{1}^{S}(2)⊕2Q_{2}^{S}(2) $ | |
| R:(u,0,1/2) | R:(u,0,1/2) | $3R_{1}^{S}(2)⊕3R_{2}^{S}(2) $ | |
| Σ:(u,0,0) | Σ:(u,0,0) | $3Σ_{1}^{S}(2)⊕3Σ_{2}^{S}(2) $ | |
| U:(1/2,0,w) | U:(1/2,0,w) | $4U_{1}^{S}(2)⊕2U_{2}^{S}(2) $ | |
| B:(u,v,0) | B:(u,v,0) | $6B_{1}^{S}(2) $ | |
| C:(u,u,w) | C:(u,u,w) | $8C_{1}^{S}(1)⊕4C_{2}^{S}(1)$ | Spin Splitting |
| D:(u,0,w) | D:(u,0,w) | $6D_{1}^{S}(2) $ | |
| E:(u,v,1/2) | E:(u,v,1/2) | $6E_{1}^{S}(2) $ | |
| GP:(u,v,w) | GP:(u,v,w) | $12GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A↑G(24) | |
| Γ:(0,0,0) | 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) $ | |
| A:(0,0,1/2) | 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) $ | |
| H:(1/3,1/3,1/2) | 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) | K:(1/3,1/3,0) | $2K_{1}^{S}(2)⊕2K_{2}^{S}(2)⊕4K_{3}^{S}(4) $ | |
| L:(1/2,0,1/2) | 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) | 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) | Δ:(0,0,w) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2)⊕4Δ_{3}^{S}(4) $ | |
| Λ:(u,u,0) | Λ:(u,u,0) | $6Λ_{1}^{S}(2)⊕6Λ_{2}^{S}(2) $ | |
| P:(1/3,1/3,w) | P:(1/3,1/3,w) | $4P_{1}^{S}(1)⊕4P_{2}^{S}(1)⊕8P_{3}^{S}(2)$ | Spin Splitting |
| Q:(u,u,1/2) | Q:(u,u,1/2) | $6Q_{1}^{S}(2)⊕6Q_{2}^{S}(2) $ | |
| R:(u,0,1/2) | R:(u,0,1/2) | $6R_{1}^{S}(2)⊕6R_{2}^{S}(2) $ | |
| Σ:(u,0,0) | Σ:(u,0,0) | $6Σ_{1}^{S}(2)⊕6Σ_{2}^{S}(2) $ | |
| U:(1/2,0,w) | U:(1/2,0,w) | $6U_{1}^{S}(2)⊕6U_{2}^{S}(2) $ | |
| B:(u,v,0) | B:(u,v,0) | $12B_{1}^{S}(2) $ | |
| C:(u,u,w) | C:(u,u,w) | $12C_{1}^{S}(1)⊕12C_{2}^{S}(1)$ | Spin Splitting |
| D:(u,0,w) | D:(u,0,w) | $12D_{1}^{S}(2) $ | |
| E:(u,v,1/2) | E:(u,v,1/2) | $12E_{1}^{S}(2) $ | |
| GP:(u,v,w) | GP:(u,v,w) | $24GP_{1}^{S}(1)$ | Spin Splitting |