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