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, -a, -c+1/2 | x, y, z | { 1 ‖ -6+001 | 0 0 1/2 } |
| a, b, -c+1/2 | x, y, z | { 1 ‖ m001 | 0 0 1/2 } |
| -b, a-b, -c+1/2 | x, y, z | { 1 ‖ -6-001 | 0 0 1/2 } |
| 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, -a+b, c+1/2 | -x, -y, -z | { -1 ‖ m210 | 0 0 1/2 } |
| a-b, -b, c+1/2 | -x, -y, -z | { -1 ‖ m120 | 0 0 1/2 } |
| b, a, c+1/2 | -x, -y, -z | { -1 ‖ m1-10 | 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, -a, -c+1/2 | -x, y, z | { m ‖ -6+001 | 0 0 1/2 } |
| a, b, -c+1/2 | -x, y, z | { m ‖ m001 | 0 0 1/2 } |
| -b, a-b, -c+1/2 | -x, y, z | { m ‖ -6-001 | 0 0 1/2 } |
| 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, -a+b, c+1/2 | x, -y, -z | { 2 ‖ m210 | 0 0 1/2 } |
| a-b, -b, c+1/2 | x, -y, -z | { 2 ‖ m120 | 0 0 1/2 } |
| b, a, c+1/2 | x, -y, -z | { 2 ‖ m1-10 | 0 0 1/2 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 2a | $\ce{^{1}{3}}\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
| 2b | $\ce{^{1}{-6}}..\ce{^{\infty m}{1}} $ | (0,0,1/4 | 0,0,z) |
| 2c | $\ce{^{1}{-6}}..\ce{^{\infty m}{1}} $ | (1/3,2/3,1/4 | 0,0,z) |
| 2d | $\ce{^{1}{-6}}..\ce{^{\infty m}{1}} $ | (2/3,1/3,1/4 | 0,0,z) |
| 4e | $\ce{^{1}{3}}..\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,z) |
| 4f | $\ce{^{1}{3}}..\ce{^{\infty m}{1}} $ | (1/3,2/3,c | 0,0,z) |
| 6g | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (a,0,0 | 0,0,0) |
| 6h | $\ce{^{1}{m}}..\ce{^{\infty m}{1}} $ | (a,b,1/4 | 0,0,z) |
| 12i | $\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}{2}}\ce{^{\infty m}{1}} $ |
| Γ:(0,0,0) | $\ce{^{1}{-6}}\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ |
| H:(1/3,1/3,1/2) | $\ce{^{1}{-6}}\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| K:(1/3,1/3,0) | $\ce{^{1}{-6}}\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| L:(1/2,0,1/2) | $\ce{^{2}{2}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| M:(1/2,0,0) | $\ce{^{2}{2}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| Δ:(0,0,w) | $\ce{^{m}{-6}}\ce{^{2}{m}}\ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| P:(1/3,1/3,w) | $\ce{^{1}{3}}\ce{^{1}{1}}\ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| Λ:(u,u,0) | $\ce{^{-1}{2}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $\ce{^{2}{2}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Q:(u,u,1/2) | $\ce{^{-1}{2}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| R:(u,0,1/2) | $\ce{^{2}{2}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| U:(1/2,0,w) | $\ce{^{-1}{2}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| B:(u,v,0) | $\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| C:(u,u,w) | $\ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| D:(u,0,w) | $\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| E:(u,v,1/2) | $\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| GP:(u,v,w) | $\ce{^{1}{1}}\ce{^{\infty}{1}}$ |
Spin Brillouin Zone
| k-vector | k-vector-G↑ | A'↑G(2) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2) $ | |
| A:(0,0,1/2) | A:(0,0,1/2) | $A_{1}^{S}(2) $ | |
| H:(1/3,1/3,1/2) | H:(1/3,1/3,1/2) | $H_{1}^{S}(2) $ | |
| K:(1/3,1/3,0) | K:(1/3,1/3,0) | $K_{1}^{S}(2) $ | |
| L:(1/2,0,1/2) | L:(1/2,0,1/2) | $L_{1}^{S}(2) $ | |
| M:(1/2,0,0) | M:(1/2,0,0) | $M_{1}^{S}(2) $ | |
| Δ:(0,0,w) | Δ:(0,0,w) | $Δ_{1}^{S}(2) $ | |
| Λ:(u,u,0) | Λ:(u,u,0) | $Λ_{1}^{S}(2) $ | |
| P:(1/3,1/3,w) | P:(1/3,1/3,w) | $P_{1}^{S}(2) $ | |
| Q:(u,u,1/2) | Q:(u,u,1/2) | $Q_{1}^{S}(2) $ | |
| R:(u,0,1/2) | R:(u,0,1/2) | $R_{1}^{S}(2) $ | |
| Σ:(u,0,0) | Σ:(u,0,0) | $Σ_{1}^{S}(2) $ | |
| U:(1/2,0,w) | U:(1/2,0,w) | $U_{1}^{S}(2) $ | |
| B:(u,v,0) | B:(u,v,0) | $2 B_{1}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | C:(u,u,w) | $2 C_{1}^{S}(1)$ | Spin Splitting |
| D:(u,0,w) | D:(u,0,w) | $D_{1}^{S}(2) $ | |
| E:(u,v,1/2) | E:(u,v,1/2) | $E_{1}^{S}(2) $ | |
| GP:(u,v,w) | GP:(u,v,w) | $2 GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A'↑G(2) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2) $ | |
| A:(0,0,1/2) | A:(0,0,1/2) | $A_{1}^{S}(2) $ | |
| H:(1/3,1/3,1/2) | H:(1/3,1/3,1/2) | $H_{3}^{S}(2) $ | |
| K:(1/3,1/3,0) | K:(1/3,1/3,0) | $K_{3}^{S}(2) $ | |
| L:(1/2,0,1/2) | L:(1/2,0,1/2) | $L_{1}^{S}(2) $ | |
| M:(1/2,0,0) | M:(1/2,0,0) | $M_{1}^{S}(2) $ | |
| Δ:(0,0,w) | Δ:(0,0,w) | $Δ_{1}^{S}(2) $ | |
| Λ:(u,u,0) | Λ:(u,u,0) | $Λ_{1}^{S}(2) $ | |
| P:(1/3,1/3,w) | P:(1/3,1/3,w) | $P_{2}^{S}(2) $ | |
| Q:(u,u,1/2) | Q:(u,u,1/2) | $Q_{1}^{S}(2) $ | |
| R:(u,0,1/2) | R:(u,0,1/2) | $R_{1}^{S}(2) $ | |
| Σ:(u,0,0) | Σ:(u,0,0) | $Σ_{1}^{S}(2) $ | |
| U:(1/2,0,w) | U:(1/2,0,w) | $U_{1}^{S}(2) $ | |
| B:(u,v,0) | B:(u,v,0) | $2 B_{1}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | C:(u,u,w) | $2 C_{1}^{S}(1)$ | Spin Splitting |
| D:(u,0,w) | D:(u,0,w) | $D_{1}^{S}(2) $ | |
| E:(u,v,1/2) | E:(u,v,1/2) | $E_{1}^{S}(2) $ | |
| GP:(u,v,w) | GP:(u,v,w) | $2 GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A'↑G(2) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2) $ | |
| A:(0,0,1/2) | A:(0,0,1/2) | $A_{2}^{S}(2) $ | |
| H:(1/3,1/3,1/2) | H:(1/3,1/3,1/2) | $H_{4}^{S}(2) $ | |
| K:(1/3,1/3,0) | K:(1/3,1/3,0) | $K_{3}^{S}(2) $ | |
| L:(1/2,0,1/2) | L:(1/2,0,1/2) | $L_{2}^{S}(2) $ | |
| M:(1/2,0,0) | M:(1/2,0,0) | $M_{1}^{S}(2) $ | |
| Δ:(0,0,w) | Δ:(0,0,w) | $Δ_{1}^{S}(2) $ | |
| Λ:(u,u,0) | Λ:(u,u,0) | $Λ_{1}^{S}(2) $ | |
| P:(1/3,1/3,w) | P:(1/3,1/3,w) | $P_{2}^{S}(2) $ | |
| Q:(u,u,1/2) | Q:(u,u,1/2) | $Q_{2}^{S}(2) $ | |
| R:(u,0,1/2) | R:(u,0,1/2) | $R_{2}^{S}(2) $ | |
| Σ:(u,0,0) | Σ:(u,0,0) | $Σ_{1}^{S}(2) $ | |
| U:(1/2,0,w) | U:(1/2,0,w) | $U_{1}^{S}(2) $ | |
| B:(u,v,0) | B:(u,v,0) | $2 B_{1}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | C:(u,u,w) | $2 C_{1}^{S}(1)$ | Spin Splitting |
| D:(u,0,w) | D:(u,0,w) | $D_{1}^{S}(2) $ | |
| E:(u,v,1/2) | E:(u,v,1/2) | $E_{2}^{S}(2) $ | |
| GP:(u,v,w) | GP:(u,v,w) | $2 GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A1↑G(4) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2) $ | |
| A:(0,0,1/2) | A:(0,0,1/2) | $A_{1}^{S}(2)⊕A_{2}^{S}(2) $ | |
| H:(1/3,1/3,1/2) | H:(1/3,1/3,1/2) | $H_{1}^{S}(2)⊕H_{2}^{S}(2) $ | |
| K:(1/3,1/3,0) | K:(1/3,1/3,0) | $K_{1}^{S}(2)⊕K_{2}^{S}(2) $ | |
| L:(1/2,0,1/2) | L:(1/2,0,1/2) | $L_{1}^{S}(2)⊕L_{2}^{S}(2) $ | |
| M:(1/2,0,0) | M:(1/2,0,0) | $M_{1}^{S}(2)⊕M_{2}^{S}(2) $ | |
| Δ:(0,0,w) | Δ:(0,0,w) | $2Δ_{1}^{S}(2) $ | |
| Λ:(u,u,0) | Λ:(u,u,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
| P:(1/3,1/3,w) | P:(1/3,1/3,w) | $2P_{1}^{S}(2) $ | |
| Q:(u,u,1/2) | Q:(u,u,1/2) | $Q_{1}^{S}(2)⊕Q_{2}^{S}(2) $ | |
| R:(u,0,1/2) | R:(u,0,1/2) | $R_{1}^{S}(2)⊕R_{2}^{S}(2) $ | |
| Σ:(u,0,0) | Σ:(u,0,0) | $Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2) $ | |
| U:(1/2,0,w) | U:(1/2,0,w) | $2U_{1}^{S}(2) $ | |
| B:(u,v,0) | B:(u,v,0) | $2 B_{1}^{S}(1)⊕2 B_{2}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | C:(u,u,w) | $2C_{1}^{S}(2) $ | |
| D:(u,0,w) | D:(u,0,w) | $2D_{1}^{S}(2) $ | |
| E:(u,v,1/2) | E:(u,v,1/2) | $2 E_{1}^{S}(1)⊕2 E_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,v,w) | $4GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A1↑G(4) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2) $ | |
| A:(0,0,1/2) | A:(0,0,1/2) | $A_{1}^{S}(2)⊕A_{2}^{S}(2) $ | |
| H:(1/3,1/3,1/2) | H:(1/3,1/3,1/2) | $H_{3}^{S}(2)⊕H_{4}^{S}(2) $ | |
| K:(1/3,1/3,0) | K:(1/3,1/3,0) | $K_{3}^{S}(2)⊕K_{4}^{S}(2) $ | |
| L:(1/2,0,1/2) | L:(1/2,0,1/2) | $L_{1}^{S}(2)⊕L_{2}^{S}(2) $ | |
| M:(1/2,0,0) | M:(1/2,0,0) | $M_{1}^{S}(2)⊕M_{2}^{S}(2) $ | |
| Δ:(0,0,w) | Δ:(0,0,w) | $2Δ_{1}^{S}(2) $ | |
| Λ:(u,u,0) | Λ:(u,u,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
| P:(1/3,1/3,w) | P:(1/3,1/3,w) | $2P_{2}^{S}(2) $ | |
| Q:(u,u,1/2) | Q:(u,u,1/2) | $Q_{1}^{S}(2)⊕Q_{2}^{S}(2) $ | |
| R:(u,0,1/2) | R:(u,0,1/2) | $R_{1}^{S}(2)⊕R_{2}^{S}(2) $ | |
| Σ:(u,0,0) | Σ:(u,0,0) | $Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2) $ | |
| U:(1/2,0,w) | U:(1/2,0,w) | $2U_{1}^{S}(2) $ | |
| B:(u,v,0) | B:(u,v,0) | $2 B_{1}^{S}(1)⊕2 B_{2}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | C:(u,u,w) | $2C_{1}^{S}(2) $ | |
| D:(u,0,w) | D:(u,0,w) | $2D_{1}^{S}(2) $ | |
| E:(u,v,1/2) | E:(u,v,1/2) | $2 E_{1}^{S}(1)⊕2 E_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,v,w) | $4GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A'↑G(6) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{3}^{S}Γ_{5}^{S}(4) $ | |
| A:(0,0,1/2) | A:(0,0,1/2) | $A_{1}^{S}(2)⊕A_{3}^{S}A_{5}^{S}(4) $ | |
| H:(1/3,1/3,1/2) | H:(1/3,1/3,1/2) | $H_{1}^{S}(2)⊕H_{3}^{S}(2)⊕H_{5}^{S}(2) $ | |
| K:(1/3,1/3,0) | K:(1/3,1/3,0) | $K_{1}^{S}(2)⊕K_{3}^{S}(2)⊕K_{5}^{S}(2) $ | |
| L:(1/2,0,1/2) | L:(1/2,0,1/2) | $3L_{1}^{S}(2) $ | |
| M:(1/2,0,0) | M:(1/2,0,0) | $3M_{1}^{S}(2) $ | |
| Δ:(0,0,w) | Δ:(0,0,w) | $Δ_{1}^{S}(2)⊕Δ_{2}^{S}Δ_{3}^{S}(4) $ | |
| Λ:(u,u,0) | Λ:(u,u,0) | $3Λ_{1}^{S}(2) $ | |
| P:(1/3,1/3,w) | P:(1/3,1/3,w) | $P_{1}^{S}(2)⊕P_{2}^{S}(2)⊕P_{3}^{S}(2) $ | |
| Q:(u,u,1/2) | Q:(u,u,1/2) | $3Q_{1}^{S}(2) $ | |
| R:(u,0,1/2) | R:(u,0,1/2) | $3R_{1}^{S}(2) $ | |
| Σ:(u,0,0) | Σ:(u,0,0) | $3Σ_{1}^{S}(2) $ | |
| U:(1/2,0,w) | U:(1/2,0,w) | $3U_{1}^{S}(2) $ | |
| B:(u,v,0) | B:(u,v,0) | $6B_{1}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | C:(u,u,w) | $3C_{1}^{S}(2) $ | |
| D:(u,0,w) | D:(u,0,w) | $3D_{1}^{S}(2) $ | |
| E:(u,v,1/2) | E:(u,v,1/2) | $6E_{1}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,v,w) | $6GP_{1}^{S}(1)$ | Spin Splitting |
| 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}Γ_{5}^{S}(4)⊕Γ_{4}^{S}Γ_{6}^{S}(4) $ | |
| A:(0,0,1/2) | A:(0,0,1/2) | $A_{1}^{S}(2)⊕A_{2}^{S}(2)⊕A_{3}^{S}A_{5}^{S}(4)⊕A_{4}^{S}A_{6}^{S}(4) $ | |
| H:(1/3,1/3,1/2) | H:(1/3,1/3,1/2) | $H_{1}^{S}(2)⊕H_{2}^{S}(2)⊕H_{3}^{S}(2)⊕H_{4}^{S}(2)⊕H_{5}^{S}(2)⊕H_{6}^{S}(2) $ | |
| K:(1/3,1/3,0) | K:(1/3,1/3,0) | $K_{1}^{S}(2)⊕K_{2}^{S}(2)⊕K_{3}^{S}(2)⊕K_{4}^{S}(2)⊕K_{5}^{S}(2)⊕K_{6}^{S}(2) $ | |
| L:(1/2,0,1/2) | L:(1/2,0,1/2) | $3L_{1}^{S}(2)⊕3L_{2}^{S}(2) $ | |
| M:(1/2,0,0) | M:(1/2,0,0) | $3M_{1}^{S}(2)⊕3M_{2}^{S}(2) $ | |
| Δ:(0,0,w) | Δ:(0,0,w) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}Δ_{3}^{S}(4) $ | |
| Λ:(u,u,0) | Λ:(u,u,0) | $3Λ_{1}^{S}(2)⊕3Λ_{2}^{S}(2) $ | |
| P:(1/3,1/3,w) | P:(1/3,1/3,w) | $2P_{1}^{S}(2)⊕2P_{2}^{S}(2)⊕2P_{3}^{S}(2) $ | |
| Q:(u,u,1/2) | Q:(u,u,1/2) | $3Q_{1}^{S}(2)⊕3Q_{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) | $6U_{1}^{S}(2) $ | |
| B:(u,v,0) | B:(u,v,0) | $6B_{1}^{S}(1)⊕6B_{2}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | C:(u,u,w) | $6C_{1}^{S}(2) $ | |
| D:(u,0,w) | D:(u,0,w) | $6D_{1}^{S}(2) $ | |
| E:(u,v,1/2) | E:(u,v,1/2) | $6E_{1}^{S}(1)⊕6E_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,v,w) | $12GP_{1}^{S}(1)$ | Spin Splitting |