The continuously infinite group ∞1 is omitted.
| Coordinates | Seitz symbol |
|---|---|
| a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
| -b+1/2, a, c+1/2 | x, y, z | { 1 ‖ 4+001 | 1/2 0 1/2 } |
| b, -a+1/2, c+1/2 | x, y, z | { 1 ‖ 4-001 | 0 1/2 1/2 } |
| a, -b+1/2, -c | x, y, z | { 1 ‖ 2100 | 0 1/2 0 } |
| -a+1/2, b, -c | x, y, z | { 1 ‖ 2010 | 1/2 0 0 } |
| -a+1/2, -b+1/2, c | x, y, z | { 1 ‖ 2001 | 1/2 1/2 0 } |
| b, a, -c+1/2 | x, y, z | { 1 ‖ 2110 | 0 0 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 } |
| b+1/2, -a, -c+1/2 | x, y, z | { 1 ‖ -4+001 | 1/2 0 1/2 } |
| -b, a+1/2, -c+1/2 | x, y, z | { 1 ‖ -4-001 | 0 1/2 1/2 } |
| -a, b+1/2, c | x, y, z | { 1 ‖ m100 | 0 1/2 0 } |
| a+1/2, -b, c | x, y, z | { 1 ‖ m010 | 1/2 0 0 } |
| a+1/2, b+1/2, -c | x, y, z | { 1 ‖ m001 | 1/2 1/2 0 } |
| -b, -a, c+1/2 | x, y, z | { 1 ‖ m110 | 0 0 1/2 } |
| b+1/2, a+1/2, c+1/2 | x, y, z | { 1 ‖ m1-10 | 1/2 1/2 1/2 } |
| a+1/2, b+1/2, c | -x, -y, -z | { -1 ‖ 1 | 1/2 1/2 0 } |
| -b, a+1/2, c+1/2 | -x, -y, -z | { -1 ‖ 4+001 | 0 1/2 1/2 } |
| b+1/2, -a, c+1/2 | -x, -y, -z | { -1 ‖ 4-001 | 1/2 0 1/2 } |
| a+1/2, -b, -c | -x, -y, -z | { -1 ‖ 2100 | 1/2 0 0 } |
| -a, b+1/2, -c | -x, -y, -z | { -1 ‖ 2010 | 0 1/2 0 } |
| -a, -b, c | -x, -y, -z | { -1 ‖ 2001 | 0 } |
| b+1/2, a+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ 2110 | 1/2 1/2 1/2 } |
| -b, -a, -c+1/2 | -x, -y, -z | { -1 ‖ 21-10 | 0 0 1/2 } |
| -a+1/2, -b+1/2, -c | -x, -y, -z | { -1 ‖ -1 | 1/2 1/2 0 } |
| b, -a+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ -4+001 | 0 1/2 1/2 } |
| -b+1/2, a, -c+1/2 | -x, -y, -z | { -1 ‖ -4-001 | 1/2 0 1/2 } |
| -a+1/2, b, c | -x, -y, -z | { -1 ‖ m100 | 1/2 0 0 } |
| a, -b+1/2, c | -x, -y, -z | { -1 ‖ m010 | 0 1/2 0 } |
| a, b, -c | -x, -y, -z | { -1 ‖ m001 | 0 } |
| -b+1/2, -a+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m110 | 1/2 1/2 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+1/2, a, c+1/2 | -x, y, z | { m ‖ 4+001 | 1/2 0 1/2 } |
| b, -a+1/2, c+1/2 | -x, y, z | { m ‖ 4-001 | 0 1/2 1/2 } |
| a, -b+1/2, -c | -x, y, z | { m ‖ 2100 | 0 1/2 0 } |
| -a+1/2, b, -c | -x, y, z | { m ‖ 2010 | 1/2 0 0 } |
| -a+1/2, -b+1/2, c | -x, y, z | { m ‖ 2001 | 1/2 1/2 0 } |
| b, a, -c+1/2 | -x, y, z | { m ‖ 2110 | 0 0 1/2 } |
| -b+1/2, -a+1/2, -c+1/2 | -x, y, z | { m ‖ 21-10 | 1/2 1/2 1/2 } |
| -a, -b, -c | -x, y, z | { m ‖ -1 | 0 } |
| b+1/2, -a, -c+1/2 | -x, y, z | { m ‖ -4+001 | 1/2 0 1/2 } |
| -b, a+1/2, -c+1/2 | -x, y, z | { m ‖ -4-001 | 0 1/2 1/2 } |
| -a, b+1/2, c | -x, y, z | { m ‖ m100 | 0 1/2 0 } |
| a+1/2, -b, c | -x, y, z | { m ‖ m010 | 1/2 0 0 } |
| a+1/2, b+1/2, -c | -x, y, z | { m ‖ m001 | 1/2 1/2 0 } |
| -b, -a, c+1/2 | -x, y, z | { m ‖ m110 | 0 0 1/2 } |
| b+1/2, a+1/2, c+1/2 | -x, y, z | { m ‖ m1-10 | 1/2 1/2 1/2 } |
| a+1/2, b+1/2, c | x, -y, -z | { 2 ‖ 1 | 1/2 1/2 0 } |
| -b, a+1/2, c+1/2 | x, -y, -z | { 2 ‖ 4+001 | 0 1/2 1/2 } |
| b+1/2, -a, c+1/2 | x, -y, -z | { 2 ‖ 4-001 | 1/2 0 1/2 } |
| a+1/2, -b, -c | x, -y, -z | { 2 ‖ 2100 | 1/2 0 0 } |
| -a, b+1/2, -c | x, -y, -z | { 2 ‖ 2010 | 0 1/2 0 } |
| -a, -b, c | x, -y, -z | { 2 ‖ 2001 | 0 } |
| b+1/2, a+1/2, -c+1/2 | x, -y, -z | { 2 ‖ 2110 | 1/2 1/2 1/2 } |
| -b, -a, -c+1/2 | x, -y, -z | { 2 ‖ 21-10 | 0 0 1/2 } |
| -a+1/2, -b+1/2, -c | x, -y, -z | { 2 ‖ -1 | 1/2 1/2 0 } |
| b, -a+1/2, -c+1/2 | x, -y, -z | { 2 ‖ -4+001 | 0 1/2 1/2 } |
| -b+1/2, a, -c+1/2 | x, -y, -z | { 2 ‖ -4-001 | 1/2 0 1/2 } |
| -a+1/2, b, c | x, -y, -z | { 2 ‖ m100 | 1/2 0 0 } |
| a, -b+1/2, c | x, -y, -z | { 2 ‖ m010 | 0 1/2 0 } |
| a, b, -c | x, -y, -z | { 2 ‖ m001 | 0 } |
| -b+1/2, -a+1/2, c+1/2 | x, -y, -z | { 2 ‖ m110 | 1/2 1/2 1/2 } |
| b, a, c+1/2 | x, -y, -z | { 2 ‖ m1-10 | 0 0 1/2 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 4a | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (3/4,1/4,1/2 | 0,0,0) |
| 4b | $\ce{^{1}{-4}}\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (3/4,1/4,3/4 | 0,0,0) |
| 4c | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (3/4,3/4,1/2 | 0,0,0) |
| 4d | $\ce{^{-1}{-4}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (3/4,3/4,3/4 | 0,0,0) |
| 8e | $\ce{^{-1}{2}}.\ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/2,1/2,3/4 | 0,0,0) |
| 8f | $\ce{^{-1}{2}}/\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (1/2,1/2,1/2 | 0,0,0) |
| 8g | $\ce{^{1}{2}}\ce{^{-1}{m}}\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (3/4,1/4,c | 0,0,0) |
| 8h | $\ce{^{1}{2}}\ce{^{-1}{m}}\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (3/4,3/4,c | 0,0,0) |
| 8i | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (3/4,b,1/2 | 0,0,0) |
| 8j | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (3/4,b,0 | 0,0,0) |
| 16k | $\ce{^{-1}{2}}..\ce{^{\infty m}{1}} $ | (1/2,1/2,c | 0,0,0) |
| 16l | $..\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (a,a+1/2,3/4 | 0,0,0) |
| 16m | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (a,a,3/4 | 0,0,z) |
| 16n | $\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (a,b,1/2 | 0,0,0) |
| 16o | $.\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (3/4,b,c | 0,0,0) |
| 32p | $\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 /mm}{1}} $ |
| Γ:(0,0,0) | $\ce{^{1}{4/}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| M:(1/2,1/2,0) | $\ce{^{1}{4/}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| Z:(0,0,1/2) | $\ce{^{1}{4/}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| R:(0,1/2,1/2) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| X:(0,1/2,0) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| Λ:(0,0,w) | $\ce{^{1}{4/}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| V:(1/2,1/2,w) | $\ce{^{1}{4/}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| Δ:(0,v,0) | $\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| S:(u,u,1/2) | $\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| Σ:(u,u,0) | $\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| T:(u,1/2,1/2) | $\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| U:(0,v,1/2) | $\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| W:(0,1/2,w) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty 2}{1}} $ |
| Y:(u,1/2,0) | $\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| B:(0,v,w) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| C:(u,u,w) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| D:(u,v,0) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| E:(u,v,1/2) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| F:(u,1/2,w) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| GP:(u,v,w) | $\ce{^{m}{-1}}\ce{^{\infty 2}{1}} $ |
Spin Brillouin Zone
| k-vector | A↑G(16) |
| A:(1/2,1/2,1/2) | $A_{1}^{S}(4)⊕A_{2}^{S}(4)⊕A_{3}^{S}A_{4}^{S}(8) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2)⊕Γ_{4}^{S,+}(2)⊕Γ_{4}^{S,-}(2)⊕Γ_{5}^{S,+}(4)⊕Γ_{5}^{S,-}(4) $ |
| M:(1/2,1/2,0) | $M_{1}^{S}(4)⊕M_{2}^{S}(4)⊕2M_{4}^{S}(4) $ |
| Z:(0,0,1/2) | $Z_{1}^{S}(4)⊕Z_{2}^{S}(4)⊕Z_{3}^{S}(4)⊕Z_{4}^{S}(4) $ |
| R:(0,1/2,1/2) | $2R_{1}^{S}(4)⊕2R_{2}^{S}(4) $ |
| X:(0,1/2,0) | $2X_{1}^{S}(4)⊕2X_{2}^{S}(4) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2)⊕Λ_{3}^{S}(2)⊕Λ_{4}^{S}(2)⊕2Λ_{5}^{S}(4) $ |
| V:(1/2,1/2,w) | $V_{1}^{S}(2)⊕V_{2}^{S}(2)⊕V_{3}^{S}(2)⊕V_{4}^{S}(2)⊕2V_{5}^{S}(4) $ |
| Δ:(0,v,0) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2)⊕2Δ_{3}^{S}(2)⊕2Δ_{4}^{S}(2) $ |
| S:(u,u,1/2) | $4S_{1}^{S}(4) $ |
| Σ:(u,u,0) | $3Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2)⊕Σ_{3}^{S}(2)⊕3Σ_{4}^{S}(2) $ |
| T:(u,1/2,1/2) | $4T_{1}^{S}(4) $ |
| U:(0,v,1/2) | $2U_{1}^{S}(2)⊕2U_{2}^{S}(2)⊕2U_{3}^{S}(2)⊕2U_{4}^{S}(2) $ |
| W:(0,1/2,w) | $4W_{1}^{S}(4) $ |
| Y:(u,1/2,0) | $4Y_{1}^{S}(4) $ |
| B:(0,v,w) | $4B_{1}^{S}(2)⊕4B_{2}^{S}(2) $ |
| C:(u,u,w) | $4C_{1}^{S}(2)⊕4C_{2}^{S}(2) $ |
| D:(u,v,0) | $4D_{1}^{S}(2)⊕4D_{2}^{S}(2) $ |
| E:(u,v,1/2) | $4E_{1}^{S}(2)⊕4E_{2}^{S}(2) $ |
| F:(u,1/2,w) | $4F_{1}^{S}(2)⊕4F_{2}^{S}(2) $ |
| GP:(u,v,w) | $8GP_{1}^{S}(2) $ |
| k-vector | A↑G(32) |
| A:(1/2,1/2,1/2) | $2A_{1}^{S}(4)⊕2A_{2}^{S}(4)⊕2A_{3}^{S}A_{4}^{S}(8) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2)⊕Γ_{2}^{S,+}(2)⊕Γ_{2}^{S,-}(2)⊕Γ_{3}^{S,+}(2)⊕Γ_{3}^{S,-}(2)⊕Γ_{4}^{S,+}(2)⊕Γ_{4}^{S,-}(2)⊕2Γ_{5}^{S,+}(4)⊕2Γ_{5}^{S,-}(4) $ |
| M:(1/2,1/2,0) | $2M_{1}^{S}(4)⊕2M_{2}^{S}(4)⊕2M_{3}^{S}(4)⊕2M_{4}^{S}(4) $ |
| Z:(0,0,1/2) | $2Z_{1}^{S}(4)⊕2Z_{2}^{S}(4)⊕2Z_{3}^{S}(4)⊕2Z_{4}^{S}(4) $ |
| R:(0,1/2,1/2) | $4R_{1}^{S}(4)⊕4R_{2}^{S}(4) $ |
| X:(0,1/2,0) | $4X_{1}^{S}(4)⊕4X_{2}^{S}(4) $ |
| Λ:(0,0,w) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2)⊕2Λ_{3}^{S}(2)⊕2Λ_{4}^{S}(2)⊕4Λ_{5}^{S}(4) $ |
| V:(1/2,1/2,w) | $2V_{1}^{S}(2)⊕2V_{2}^{S}(2)⊕2V_{3}^{S}(2)⊕2V_{4}^{S}(2)⊕4V_{5}^{S}(4) $ |
| Δ:(0,v,0) | $4Δ_{1}^{S}(2)⊕4Δ_{2}^{S}(2)⊕4Δ_{3}^{S}(2)⊕4Δ_{4}^{S}(2) $ |
| S:(u,u,1/2) | $8S_{1}^{S}(4) $ |
| Σ:(u,u,0) | $4Σ_{1}^{S}(2)⊕4Σ_{2}^{S}(2)⊕4Σ_{3}^{S}(2)⊕4Σ_{4}^{S}(2) $ |
| T:(u,1/2,1/2) | $8T_{1}^{S}(4) $ |
| U:(0,v,1/2) | $4U_{1}^{S}(2)⊕4U_{2}^{S}(2)⊕4U_{3}^{S}(2)⊕4U_{4}^{S}(2) $ |
| W:(0,1/2,w) | $8W_{1}^{S}(4) $ |
| Y:(u,1/2,0) | $8Y_{1}^{S}(4) $ |
| B:(0,v,w) | $8B_{1}^{S}(2)⊕8B_{2}^{S}(2) $ |
| C:(u,u,w) | $8C_{1}^{S}(2)⊕8C_{2}^{S}(2) $ |
| D:(u,v,0) | $8D_{1}^{S}(2)⊕8D_{2}^{S}(2) $ |
| E:(u,v,1/2) | $8E_{1}^{S}(2)⊕8E_{2}^{S}(2) $ |
| F:(u,1/2,w) | $8F_{1}^{S}(2)⊕8F_{2}^{S}(2) $ |
| GP:(u,v,w) | $16GP_{1}^{S}(2) $ |