The continuously infinite group ∞1 is omitted.
| Coordinates | Seitz symbol |
|---|---|
| a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
| a+1/2, -b+1/2, -c+1/2 | x, y, z | { 1 ‖ 2100 | 1/2 1/2 1/2 } |
| -a+1/2, b+1/2, -c+1/2 | x, y, z | { 1 ‖ 2010 | 1/2 1/2 1/2 } |
| -a, -b, c | x, y, z | { 1 ‖ 2001 | 0 } |
| b, -a, -c | x, y, z | { 1 ‖ -4+001 | 0 } |
| -b, a, -c | x, y, z | { 1 ‖ -4-001 | 0 } |
| -b+1/2, -a+1/2, c+1/2 | x, y, z | { 1 ‖ m110 | 1/2 1/2 1/2 } |
| b+1/2, a+1/2, c+1/2 | x, y, z | { 1 ‖ m1-10 | 1/2 1/2 1/2 } |
| -b, a, c | -x, -y, -z | { -1 ‖ 4+001 | 0 } |
| b, -a, c | -x, -y, -z | { -1 ‖ 4-001 | 0 } |
| b+1/2, a+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ 2110 | 1/2 1/2 1/2 } |
| -b+1/2, -a+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ 21-10 | 1/2 1/2 1/2 } |
| -a, -b, -c | -x, -y, -z | { -1 ‖ -1 | 0 } |
| -a+1/2, b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m100 | 1/2 1/2 1/2 } |
| a+1/2, -b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m010 | 1/2 1/2 1/2 } |
| a, b, -c | -x, -y, -z | { -1 ‖ m001 | 0 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| a+1/2, -b+1/2, -c+1/2 | -x, y, z | { m ‖ 2100 | 1/2 1/2 1/2 } |
| -a+1/2, b+1/2, -c+1/2 | -x, y, z | { m ‖ 2010 | 1/2 1/2 1/2 } |
| -a, -b, c | -x, y, z | { m ‖ 2001 | 0 } |
| b, -a, -c | -x, y, z | { m ‖ -4+001 | 0 } |
| -b, a, -c | -x, y, z | { m ‖ -4-001 | 0 } |
| -b+1/2, -a+1/2, c+1/2 | -x, y, z | { m ‖ m110 | 1/2 1/2 1/2 } |
| b+1/2, a+1/2, c+1/2 | -x, y, z | { m ‖ m1-10 | 1/2 1/2 1/2 } |
| -b, a, c | x, -y, -z | { 2 ‖ 4+001 | 0 } |
| b, -a, c | x, -y, -z | { 2 ‖ 4-001 | 0 } |
| b+1/2, a+1/2, -c+1/2 | x, -y, -z | { 2 ‖ 2110 | 1/2 1/2 1/2 } |
| -b+1/2, -a+1/2, -c+1/2 | x, -y, -z | { 2 ‖ 21-10 | 1/2 1/2 1/2 } |
| -a, -b, -c | x, -y, -z | { 2 ‖ -1 | 0 } |
| -a+1/2, b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m100 | 1/2 1/2 1/2 } |
| a+1/2, -b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m010 | 1/2 1/2 1/2 } |
| a, b, -c | x, -y, -z | { 2 ‖ m001 | 0 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 2a | $\ce{^{-1}{4}}/\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
| 2b | $\ce{^{-1}{4}}/\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,0) |
| 4c | $\ce{^{1}{2}}/\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (0,1/2,0 | 0,0,0) |
| 4d | $\ce{^{1}{2}}.\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (0,1/2,1/4 | 0,0,0) |
| 4e | $\ce{^{-1}{4}}..\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,0) |
| 8f | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (0,1/2,c | 0,0,z) |
| 8g | $..\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (a,a+1/2,1/4 | 0,0,0) |
| 8h | $\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (a,b,0 | 0,0,0) |
| 16i | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
| Wavevector-k | Little co-group |
|---|---|
| A:(1/2,1/2,1/2) | $\ce{^{-1}{4/}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| Γ:(0,0,0) | $\ce{^{-1}{4/}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| M:(1/2,1/2,0) | $\ce{^{-1}{4/}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| Z:(0,0,1/2) | $\ce{^{-1}{4/}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| R:(0,1/2,1/2) | $\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty m}{1}} $ |
| X:(0,1/2,0) | $\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty m}{1}} $ |
| Λ:(0,0,w) | $\ce{^{2}{4/}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| V:(1/2,1/2,w) | $\ce{^{2}{4/}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| S:(u,u,1/2) | $\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| Σ:(u,u,0) | $\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| T:(u,1/2,1/2) | $\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| U:(0,v,1/2) | $\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| W:(0,1/2,w) | $\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
| Y:(u,1/2,0) | $\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| B:(0,v,w) | $\ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| C:(u,u,w) | $\ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| D:(u,v,0) | $\ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| E:(u,v,1/2) | $\ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| F:(u,1/2,w) | $\ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| GP:(u,v,w) | $\ce{^{-1}{-1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
| k-vector | k-vector-G↑ | A↑G(8) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2)⊕Γ_{3}^{S}(2)⊕Γ_{4}^{S}(2) $ | |
| A:(1/2,1/2,1/2) | A:(1/2,1/2,1/2) | $A_{5}^{S}A_{5}^{S}(8) $ | |
| M:(1/2,1/2,0) | M:(1/2,1/2,0) | $M_{1}^{S}M_{3}^{S}(4)⊕M_{2}^{S}M_{4}^{S}(4) $ | |
| R:(0,1/2,1/2) | R:(0,1/2,1/2) | $2R_{1}^{S}(4) $ | |
| X:(0,1/2,0) | X:(0,1/2,0) | $2X_{1}^{S}(4) $ | |
| Z:(0,0,1/2) | Z:(0,0,1/2) | $2Z_{5}^{S}(4) $ | |
| Δ:(0,v,0) | Δ:(0,v,0) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $ | |
| Λ:(0,0,w) | Λ:(0,0,w) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2) $ | |
| S:(u,u,1/2) | S:(u,u,1/2) | $2S_{1}^{S}S_{2}^{S}(4) $ | |
| Σ:(u,u,0) | Σ:(u,u,0) | $2Σ_{1}^{S}(2)⊕2Σ_{2}^{S}(2) $ | |
| T:(u,1/2,1/2) | T:(u,1/2,1/2) | $2T_{1}^{S}T_{2}^{S}(4) $ | |
| U:(0,v,1/2) | U:(0,v,1/2) | $2U_{1}^{S}(2)⊕2U_{2}^{S}(2) $ | |
| V:(1/2,1/2,w) | V:(1/2,1/2,w) | $V_{3}^{S}V_{3}^{S}(4)⊕V_{4}^{S}V_{4}^{S}(4) $ | |
| W:(0,1/2,w) | W:(0,1/2,w) | $2W_{1}^{S}W_{2}^{S}(4) $ | |
| Y:(u,1/2,0) | Y:(u,1/2,0) | $2Y_{1}^{S}Y_{2}^{S}(4) $ | |
| B:(0,v,w) | B:(0,v,w) | $4B_{1}^{S}(2) $ | |
| C:(u,u,w) | C:(u,u,w) | $2C_{1}^{S}(2)⊕2C_{2}^{S}(2) $ | |
| D:(u,v,0) | D:(u,v,0) | $4D_{1}^{S}(2) $ | |
| E:(u,v,1/2) | E:(u,v,1/2) | $4E_{1}^{S}(2) $ | |
| F:(u,1/2,w) | F:(u,1/2,w) | $2F_{1}^{S}F_{1}^{S}(4) $ | |
| GP:(u,v,w) | GP:(u,v,w) | $4GP_{1}^{S}(2) $ |
| k-vector | k-vector-G↑ | A↑G(16) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2)⊕Γ_{3}^{S}(2)⊕Γ_{4}^{S}(2)⊕2Γ_{5}^{S}(4) $ | |
| A:(1/2,1/2,1/2) | A:(1/2,1/2,1/2) | $A_{1}^{S}A_{4}^{S}(4)⊕A_{2}^{S}A_{3}^{S}(4)⊕A_{5}^{S}A_{5}^{S}(8) $ | |
| M:(1/2,1/2,0) | M:(1/2,1/2,0) | $M_{1}^{S}M_{3}^{S}(4)⊕M_{2}^{S}M_{4}^{S}(4)⊕2M_{5}^{S}(4) $ | |
| R:(0,1/2,1/2) | R:(0,1/2,1/2) | $4R_{1}^{S}(4) $ | |
| X:(0,1/2,0) | X:(0,1/2,0) | $4X_{1}^{S}(4) $ | |
| Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}Z_{2}^{S}(4)⊕Z_{3}^{S}Z_{4}^{S}(4)⊕2Z_{5}^{S}(4) $ | |
| Δ:(0,v,0) | Δ:(0,v,0) | $4Δ_{1}^{S}(2)⊕4Δ_{2}^{S}(2) $ | |
| Λ:(0,0,w) | Λ:(0,0,w) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2)⊕2Λ_{3}^{S}Λ_{4}^{S}(4) $ | |
| S:(u,u,1/2) | S:(u,u,1/2) | $4S_{1}^{S}S_{2}^{S}(4) $ | |
| Σ:(u,u,0) | Σ:(u,u,0) | $4Σ_{1}^{S}(2)⊕4Σ_{2}^{S}(2) $ | |
| T:(u,1/2,1/2) | T:(u,1/2,1/2) | $4T_{1}^{S}T_{2}^{S}(4) $ | |
| U:(0,v,1/2) | U:(0,v,1/2) | $4U_{1}^{S}(2)⊕4U_{2}^{S}(2) $ | |
| V:(1/2,1/2,w) | V:(1/2,1/2,w) | $2V_{1}^{S}V_{2}^{S}(4)⊕V_{3}^{S}V_{3}^{S}(4)⊕V_{4}^{S}V_{4}^{S}(4) $ | |
| W:(0,1/2,w) | W:(0,1/2,w) | $4W_{1}^{S}W_{2}^{S}(4) $ | |
| Y:(u,1/2,0) | Y:(u,1/2,0) | $4Y_{1}^{S}Y_{2}^{S}(4) $ | |
| B:(0,v,w) | B:(0,v,w) | $8B_{1}^{S}(2) $ | |
| C:(u,u,w) | C:(u,u,w) | $4C_{1}^{S}(2)⊕4C_{2}^{S}(2) $ | |
| D:(u,v,0) | D:(u,v,0) | $8D_{1}^{S}(2) $ | |
| E:(u,v,1/2) | E:(u,v,1/2) | $8E_{1}^{S}(2) $ | |
| F:(u,1/2,w) | F:(u,1/2,w) | $4F_{1}^{S}F_{1}^{S}(4) $ | |
| GP:(u,v,w) | GP:(u,v,w) | $8GP_{1}^{S}(2) $ |