The continuously infinite group ∞1 is omitted.
| Coordinates | Seitz symbol |
|---|---|
| a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
| -b, a, c | x, y, z | { 1 ‖ 4+001 | 0 } |
| b, -a, c | x, y, z | { 1 ‖ 4-001 | 0 } |
| -a, -b, c | x, y, z | { 1 ‖ 2001 | 0 } |
| -a, -b, -c | x, y, z | { 1 ‖ -1 | 0 } |
| b, -a, -c | x, y, z | { 1 ‖ -4+001 | 0 } |
| -b, a, -c | x, y, z | { 1 ‖ -4-001 | 0 } |
| a, b, -c | x, y, z | { 1 ‖ m001 | 0 } |
| a+1/2, b+1/2, c+1/2 | x, y, z | { 1 ‖ 1 | 1/2 1/2 1/2 } |
| -b+1/2, a+1/2, c+1/2 | x, y, z | { 1 ‖ 4+001 | 1/2 1/2 1/2 } |
| b+1/2, -a+1/2, c+1/2 | x, y, z | { 1 ‖ 4-001 | 1/2 1/2 1/2 } |
| -a+1/2, -b+1/2, c+1/2 | x, y, z | { 1 ‖ 2001 | 1/2 1/2 1/2 } |
| -a+1/2, -b+1/2, -c+1/2 | x, y, z | { 1 ‖ -1 | 1/2 1/2 1/2 } |
| b+1/2, -a+1/2, -c+1/2 | x, y, z | { 1 ‖ -4+001 | 1/2 1/2 1/2 } |
| -b+1/2, a+1/2, -c+1/2 | x, y, z | { 1 ‖ -4-001 | 1/2 1/2 1/2 } |
| a+1/2, b+1/2, -c+1/2 | x, y, z | { 1 ‖ m001 | 1/2 1/2 1/2 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| -b, a, c | -x, y, z | { m ‖ 4+001 | 0 } |
| b, -a, c | -x, y, z | { m ‖ 4-001 | 0 } |
| -a, -b, c | -x, y, z | { m ‖ 2001 | 0 } |
| -a, -b, -c | -x, y, z | { m ‖ -1 | 0 } |
| b, -a, -c | -x, y, z | { m ‖ -4+001 | 0 } |
| -b, a, -c | -x, y, z | { m ‖ -4-001 | 0 } |
| a, b, -c | -x, y, z | { m ‖ m001 | 0 } |
| a+1/2, b+1/2, c+1/2 | -x, y, z | { m ‖ 1 | 1/2 1/2 1/2 } |
| -b+1/2, a+1/2, c+1/2 | -x, y, z | { m ‖ 4+001 | 1/2 1/2 1/2 } |
| b+1/2, -a+1/2, c+1/2 | -x, y, z | { m ‖ 4-001 | 1/2 1/2 1/2 } |
| -a+1/2, -b+1/2, c+1/2 | -x, y, z | { m ‖ 2001 | 1/2 1/2 1/2 } |
| -a+1/2, -b+1/2, -c+1/2 | -x, y, z | { m ‖ -1 | 1/2 1/2 1/2 } |
| b+1/2, -a+1/2, -c+1/2 | -x, y, z | { m ‖ -4+001 | 1/2 1/2 1/2 } |
| -b+1/2, a+1/2, -c+1/2 | -x, y, z | { m ‖ -4-001 | 1/2 1/2 1/2 } |
| a+1/2, b+1/2, -c+1/2 | -x, y, z | { m ‖ m001 | 1/2 1/2 1/2 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 2a | $\ce{^{1}{4}}/\ce{^{1}{m}}..\ce{^{\infty m}{1}} $ | (0,0,0 |0,0,z) |
| 2b | $\ce{^{1}{4}}/\ce{^{1}{m}}..\ce{^{\infty m}{1}} $ | (0,0,1/2 |0,0,z) |
| 4c | $\ce{^{1}{2}}/\ce{^{1}{m}}..\ce{^{\infty m}{1}} $ | (0,1/2,0 |0,0,z) |
| 4d | $\ce{^{1}{-4}}..\ce{^{\infty m}{1}} $ | (0,1/2,1/4 |0,0,z) |
| 4e | $\ce{^{1}{4}}..\ce{^{\infty m}{1}} $ | (0,0,c |0,0,z) |
| 8f | $\ce{^{1}{-1}}\ce{^{\infty m}{1}} $ | (1/4,1/4,1/4 |0,0,z) |
| 8g | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (0,1/2,c |0,0,z) |
| 8h | $\ce{^{1}{m}}..\ce{^{\infty m}{1}} $ | (a,b,0 |0,0,z) |
| 16i | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c |0,0,z) |
| Wavevector-k | Little co-group |
|---|---|
| Γ:(0,0,0) | $\ce{^{1}{4/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| M:(1,1,1) | $\ce{^{1}{4/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| P:(1/2,1/2,1/2) | $\ce{^{m}{4/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| X:(1/2,1/2,0) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| N:(1/2,0,1/2) | $\ce{^{1}{-1}}\ce{^{\infty m}{1}} $ |
| Λ:(0,0,w) | $\ce{^{1}{4/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| W:(1/2,1/2,w) | $\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| Q:(1/2,v,1/2) | $\ce{^{m}{-1}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Y:(u,1-u,0) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Δ:(u,u,0) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| A:(u,u,w) | $\ce{^{m}{-1}}\ce{^{\infty}{1}} $ |
| B:(u,0,w) | $\ce{^{m}{-1}}\ce{^{\infty}{1}} $ |
| C:(u,v,0) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| GP:(u,v,w) | $\ce{^{m}{-1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
| k-vector | A↑G(8) |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(1)⊕Γ_{1}^{S,-}(1)⊕Γ_{2}^{S,+}(1)⊕Γ_{2}^{S,-}(1)⊕Γ_{3}^{S,+}Γ_{4}^{S,+}(2)⊕Γ_{3}^{S,-}Γ_{4}^{S,-}(2) $ |
| M:(1,1,1) | $M_{1}^{S,+}(1)⊕M_{1}^{S,-}(1)⊕M_{2}^{S,+}(1)⊕M_{2}^{S,-}(1)⊕M_{3}^{S,+}M_{4}^{S,+}(2)⊕M_{3}^{S,-}M_{4}^{S,-}(2) $ |
| P:(1/2,1/2,1/2) | $2P_{1}^{S}(1)⊕2P_{2}^{S}(1)⊕2P_{3}^{S}P_{4}^{S}(2) $ |
| X:(1/2,1/2,0) | $2X_{1}^{S,+}(1)⊕2X_{1}^{S,-}(1)⊕2X_{2}^{S,+}(1)⊕2X_{2}^{S,-}(1) $ |
| N:(1/2,0,1/2) | $4N_{1}^{S,+}(1)⊕4N_{1}^{S,-}(1) $ |
| Λ:(0,0,w) | $2Λ_{1}^{S}(1)⊕2Λ_{2}^{S}(1)⊕2Λ_{3}^{S}Λ_{4}^{S}(2) $ |
| W:(1/2,1/2,w) | $4W_{1}^{S}(1)⊕4W_{2}^{S}(1) $ |
| Q:(1/2,v,1/2) | $8Q_{1}^{S}(1) $ |
| Σ:(u,0,0) | $4Σ_{1}^{S}(1)⊕4Σ_{2}^{S}(1) $ |
| Y:(u,1-u,0) | $4Y_{1}^{S}(1)⊕4Y_{2}^{S}(1) $ |
| Δ:(u,u,0) | $4Δ_{1}^{S}(1)⊕4Δ_{2}^{S}(1) $ |
| A:(u,u,w) | $8A_{1}^{S}(1) $ |
| B:(u,0,w) | $8B_{1}^{S}(1) $ |
| C:(u,v,0) | $4C_{1}^{S}(1)⊕4C_{2}^{S}(1) $ |
| GP:(u,v,w) | $8GP_{1}^{S}(1) $ |
| k-vector | Ag↑G(1) |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(1) $ |
| M:(1,1,1) | $M_{1}^{S,+}(1) $ |
| P:(1/2,1/2,1/2) | $P_{1}^{S}(1) $ |
| X:(1/2,1/2,0) | $X_{1}^{S,+}(1) $ |
| N:(1/2,0,1/2) | $N_{1}^{S,+}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1) $ |
| W:(1/2,1/2,w) | $W_{1}^{S}(1) $ |
| Q:(1/2,v,1/2) | $Q_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1) $ |
| Y:(u,1-u,0) | $Y_{1}^{S}(1) $ |
| Δ:(u,u,0) | $Δ_{1}^{S}(1) $ |
| A:(u,u,w) | $A_{1}^{S}(1) $ |
| B:(u,0,w) | $B_{1}^{S}(1) $ |
| C:(u,v,0) | $C_{1}^{S}(1) $ |
| GP:(u,v,w) | $GP_{1}^{S}(1) $ |
| k-vector | Ag↑G(1) |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(1) $ |
| M:(1,1,1) | $M_{1}^{S,+}(1) $ |
| P:(1/2,1/2,1/2) | $P_{2}^{S}(1) $ |
| X:(1/2,1/2,0) | $X_{1}^{S,+}(1) $ |
| N:(1/2,0,1/2) | $N_{1}^{S,-}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1) $ |
| W:(1/2,1/2,w) | $W_{1}^{S}(1) $ |
| Q:(1/2,v,1/2) | $Q_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1) $ |
| Y:(u,1-u,0) | $Y_{1}^{S}(1) $ |
| Δ:(u,u,0) | $Δ_{1}^{S}(1) $ |
| A:(u,u,w) | $A_{1}^{S}(1) $ |
| B:(u,0,w) | $B_{1}^{S}(1) $ |
| C:(u,v,0) | $C_{1}^{S}(1) $ |
| GP:(u,v,w) | $GP_{1}^{S}(1) $ |
| k-vector | Ag↑G(2) |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(1)⊕Γ_{2}^{S,+}(1) $ |
| M:(1,1,1) | $M_{1}^{S,+}(1)⊕M_{2}^{S,+}(1) $ |
| P:(1/2,1/2,1/2) | $P_{3}^{S}P_{4}^{S}(2) $ |
| X:(1/2,1/2,0) | $2X_{2}^{S,-}(1) $ |
| N:(1/2,0,1/2) | $N_{1}^{S,+}(1)⊕N_{1}^{S,-}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $ |
| W:(1/2,1/2,w) | $2W_{2}^{S}(1) $ |
| Q:(1/2,v,1/2) | $2Q_{1}^{S}(1) $ |
| Σ:(u,0,0) | $2Σ_{1}^{S}(1) $ |
| Y:(u,1-u,0) | $2Y_{1}^{S}(1) $ |
| Δ:(u,u,0) | $2Δ_{1}^{S}(1) $ |
| A:(u,u,w) | $2A_{1}^{S}(1) $ |
| B:(u,0,w) | $2B_{1}^{S}(1) $ |
| C:(u,v,0) | $2C_{1}^{S}(1) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
| k-vector | A↑G(2) |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(1)⊕Γ_{2}^{S,-}(1) $ |
| M:(1,1,1) | $M_{1}^{S,-}(1)⊕M_{2}^{S,+}(1) $ |
| P:(1/2,1/2,1/2) | $P_{3}^{S}P_{4}^{S}(2) $ |
| X:(1/2,1/2,0) | $X_{2}^{S,+}(1)⊕X_{2}^{S,-}(1) $ |
| N:(1/2,0,1/2) | $N_{1}^{S,+}(1)⊕N_{1}^{S,-}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $ |
| W:(1/2,1/2,w) | $2W_{2}^{S}(1) $ |
| Q:(1/2,v,1/2) | $2Q_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
| Y:(u,1-u,0) | $Y_{1}^{S}(1)⊕Y_{2}^{S}(1) $ |
| Δ:(u,u,0) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1) $ |
| A:(u,u,w) | $2A_{1}^{S}(1) $ |
| B:(u,0,w) | $2B_{1}^{S}(1) $ |
| C:(u,v,0) | $C_{1}^{S}(1)⊕C_{2}^{S}(1) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
| k-vector | A↑G(2) |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(1)⊕Γ_{1}^{S,-}(1) $ |
| M:(1,1,1) | $M_{1}^{S,+}(1)⊕M_{1}^{S,-}(1) $ |
| P:(1/2,1/2,1/2) | $P_{1}^{S}(1)⊕P_{2}^{S}(1) $ |
| X:(1/2,1/2,0) | $X_{1}^{S,+}(1)⊕X_{1}^{S,-}(1) $ |
| N:(1/2,0,1/2) | $N_{1}^{S,+}(1)⊕N_{1}^{S,-}(1) $ |
| Λ:(0,0,w) | $2Λ_{1}^{S}(1) $ |
| W:(1/2,1/2,w) | $2W_{1}^{S}(1) $ |
| Q:(1/2,v,1/2) | $2Q_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
| Y:(u,1-u,0) | $Y_{1}^{S}(1)⊕Y_{2}^{S}(1) $ |
| Δ:(u,u,0) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1) $ |
| A:(u,u,w) | $2A_{1}^{S}(1) $ |
| B:(u,0,w) | $2B_{1}^{S}(1) $ |
| C:(u,v,0) | $C_{1}^{S}(1)⊕C_{2}^{S}(1) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
| k-vector | Ag↑G(4) |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(1)⊕Γ_{2}^{S,+}(1)⊕Γ_{3}^{S,+}Γ_{4}^{S,+}(2) $ |
| M:(1,1,1) | $M_{1}^{S,-}(1)⊕M_{2}^{S,-}(1)⊕M_{3}^{S,-}M_{4}^{S,-}(2) $ |
| P:(1/2,1/2,1/2) | $P_{1}^{S}(1)⊕P_{2}^{S}(1)⊕P_{3}^{S}P_{4}^{S}(2) $ |
| X:(1/2,1/2,0) | $X_{1}^{S,+}(1)⊕X_{1}^{S,-}(1)⊕X_{2}^{S,+}(1)⊕X_{2}^{S,-}(1) $ |
| N:(1/2,0,1/2) | $2N_{1}^{S,+}(1)⊕2N_{1}^{S,-}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1)⊕Λ_{3}^{S}Λ_{4}^{S}(2) $ |
| W:(1/2,1/2,w) | $2W_{1}^{S}(1)⊕2W_{2}^{S}(1) $ |
| Q:(1/2,v,1/2) | $4Q_{1}^{S}(1) $ |
| Σ:(u,0,0) | $2Σ_{1}^{S}(1)⊕2Σ_{2}^{S}(1) $ |
| Y:(u,1-u,0) | $2Y_{1}^{S}(1)⊕2Y_{2}^{S}(1) $ |
| Δ:(u,u,0) | $2Δ_{1}^{S}(1)⊕2Δ_{2}^{S}(1) $ |
| A:(u,u,w) | $4A_{1}^{S}(1) $ |
| B:(u,0,w) | $4B_{1}^{S}(1) $ |
| C:(u,v,0) | $2C_{1}^{S}(1)⊕2C_{2}^{S}(1) $ |
| GP:(u,v,w) | $4GP_{1}^{S}(1) $ |
| k-vector | A↑G(4) |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(1)⊕Γ_{1}^{S,-}(1)⊕Γ_{2}^{S,+}(1)⊕Γ_{2}^{S,-}(1) $ |
| M:(1,1,1) | $M_{1}^{S,+}(1)⊕M_{1}^{S,-}(1)⊕M_{2}^{S,+}(1)⊕M_{2}^{S,-}(1) $ |
| P:(1/2,1/2,1/2) | $2P_{3}^{S}P_{4}^{S}(2) $ |
| X:(1/2,1/2,0) | $2X_{2}^{S,+}(1)⊕2X_{2}^{S,-}(1) $ |
| N:(1/2,0,1/2) | $2N_{1}^{S,+}(1)⊕2N_{1}^{S,-}(1) $ |
| Λ:(0,0,w) | $2Λ_{1}^{S}(1)⊕2Λ_{2}^{S}(1) $ |
| W:(1/2,1/2,w) | $4W_{2}^{S}(1) $ |
| Q:(1/2,v,1/2) | $4Q_{1}^{S}(1) $ |
| Σ:(u,0,0) | $2Σ_{1}^{S}(1)⊕2Σ_{2}^{S}(1) $ |
| Y:(u,1-u,0) | $2Y_{1}^{S}(1)⊕2Y_{2}^{S}(1) $ |
| Δ:(u,u,0) | $2Δ_{1}^{S}(1)⊕2Δ_{2}^{S}(1) $ |
| A:(u,u,w) | $4A_{1}^{S}(1) $ |
| B:(u,0,w) | $4B_{1}^{S}(1) $ |
| C:(u,v,0) | $2C_{1}^{S}(1)⊕2C_{2}^{S}(1) $ |
| GP:(u,v,w) | $4GP_{1}^{S}(1) $ |
| k-vector | A'↑G(4) |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(1)⊕Γ_{2}^{S,+}(1)⊕Γ_{3}^{S,-}Γ_{4}^{S,-}(2) $ |
| M:(1,1,1) | $M_{1}^{S,+}(1)⊕M_{2}^{S,+}(1)⊕M_{3}^{S,-}M_{4}^{S,-}(2) $ |
| P:(1/2,1/2,1/2) | $P_{1}^{S}(1)⊕P_{2}^{S}(1)⊕P_{3}^{S}P_{4}^{S}(2) $ |
| X:(1/2,1/2,0) | $2X_{1}^{S,+}(1)⊕2X_{2}^{S,-}(1) $ |
| N:(1/2,0,1/2) | $2N_{1}^{S,+}(1)⊕2N_{1}^{S,-}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1)⊕Λ_{3}^{S}Λ_{4}^{S}(2) $ |
| W:(1/2,1/2,w) | $2W_{1}^{S}(1)⊕2W_{2}^{S}(1) $ |
| Q:(1/2,v,1/2) | $4Q_{1}^{S}(1) $ |
| Σ:(u,0,0) | $4Σ_{1}^{S}(1) $ |
| Y:(u,1-u,0) | $4Y_{1}^{S}(1) $ |
| Δ:(u,u,0) | $4Δ_{1}^{S}(1) $ |
| A:(u,u,w) | $4A_{1}^{S}(1) $ |
| B:(u,0,w) | $4B_{1}^{S}(1) $ |
| C:(u,v,0) | $4C_{1}^{S}(1) $ |
| GP:(u,v,w) | $4GP_{1}^{S}(1) $ |