The continuously infinite group ∞1 is omitted.
| Coordinates | Seitz symbol |
|---|---|
| a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
| -a, b, -c | x, y, z | { 1 ‖ 2010 | 0 } |
| -a, -b, -c | x, y, z | { 1 ‖ -1 | 0 } |
| a, -b, c | x, y, z | { 1 ‖ m010 | 0 } |
| a, b+1/2, c | -x, -y, -z | { -1 ‖ 1 | 0 1/2 0 } |
| -a, b+1/2, -c | -x, -y, -z | { -1 ‖ 2010 | 0 1/2 0 } |
| -a, -b+1/2, -c | -x, -y, -z | { -1 ‖ -1 | 0 1/2 0 } |
| a, -b+1/2, c | -x, -y, -z | { -1 ‖ m010 | 0 1/2 0 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| -a, b, -c | -x, y, z | { m ‖ 2010 | 0 } |
| -a, -b, -c | -x, y, z | { m ‖ -1 | 0 } |
| a, -b, c | -x, y, z | { m ‖ m010 | 0 } |
| a, b+1/2, c | x, -y, -z | { 2 ‖ 1 | 0 1/2 0 } |
| -a, b+1/2, -c | x, -y, -z | { 2 ‖ 2010 | 0 1/2 0 } |
| -a, -b+1/2, -c | x, -y, -z | { 2 ‖ -1 | 0 1/2 0 } |
| a, -b+1/2, c | x, -y, -z | { 2 ‖ m010 | 0 1/2 0 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 2a | $\ce{^{1}{2}}/\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,z) |
| 2b | $\ce{^{1}{2}}/\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (0,1/4,0 | 0,0,0) |
| 2c | $\ce{^{1}{2}}/\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,z) |
| 2d | $\ce{^{1}{2}}/\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (1/2,0,0 | 0,0,z) |
| 2e | $\ce{^{1}{2}}/\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (1/2,1/4,0 | 0,0,0) |
| 2f | $\ce{^{1}{2}}/\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (0,1/4,1/2 | 0,0,0) |
| 2g | $\ce{^{1}{2}}/\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (1/2,0,1/2 | 0,0,z) |
| 2h | $\ce{^{1}{2}}/\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (1/2,1/4,1/2 | 0,0,0) |
| 4i | $\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,b,0 | 0,0,z) |
| 4j | $\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/2,b,0 | 0,0,z) |
| 4k | $\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,b,1/2 | 0,0,z) |
| 4l | $\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/2,b,1/2 | 0,0,z) |
| 4m | $\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (a,0,c | 0,0,z) |
| 4n | $\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (a,1/4,c | 0,0,0) |
| 8o | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
| Wavevector-k | Little co-group |
|---|---|
| A:(1/2,0,1/2) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| B:(0,0,1/2) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| C:(1/2,1/2,0) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| D:(0,1/2,1/2) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| E:(1/2,1/2,1/2) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| Γ:(0,0,0) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| Y:(1/2,0,0) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| Z:(0,1/2,0) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| F:(u,0,w) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| G:(u,1/2,w) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| Λ:(0,v,0) | $\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty 2}{1}} $ |
| U:(1/2,v,1/2) | $\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty 2}{1}} $ |
| V:(0,v,1/2) | $\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty 2}{1}} $ |
| W:(1/2,v,0) | $\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty 2}{1}} $ |
| GP:(u,v,w) | $\ce{^{m}{-1}}\ce{^{\infty 2}{1}} $ |
Spin Brillouin Zone
| k-vector | Ag↑G(2) |
| A:(1/2,0,1/2) | $A_{1}^{S,+}(2) $ |
| B:(0,0,1/2) | $B_{1}^{S,+}(2) $ |
| C:(1/2,1/2,0) | $C_{1}^{S,+}(2) $ |
| D:(0,1/2,1/2) | $D_{1}^{S,+}(2) $ |
| E:(1/2,1/2,1/2) | $E_{1}^{S,+}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2) $ |
| Y:(1/2,0,0) | $Y_{1}^{S,+}(2) $ |
| Z:(0,1/2,0) | $Z_{1}^{S,+}(2) $ |
| F:(u,0,w) | $F_{1}^{S}(2) $ |
| G:(u,1/2,w) | $G_{1}^{S}(2) $ |
| Λ:(0,v,0) | $Λ_{1}^{S}(2) $ |
| U:(1/2,v,1/2) | $U_{1}^{S}(2) $ |
| V:(0,v,1/2) | $V_{1}^{S}(2) $ |
| W:(1/2,v,0) | $W_{1}^{S}(2) $ |
| GP:(u,v,w) | $GP_{1}^{S}(2) $ |
| k-vector | Ag↑G(2) |
| A:(1/2,0,1/2) | $A_{2}^{S,-}(2) $ |
| B:(0,0,1/2) | $B_{2}^{S,-}(2) $ |
| C:(1/2,1/2,0) | $C_{1}^{S,+}(2) $ |
| D:(0,1/2,1/2) | $D_{2}^{S,-}(2) $ |
| E:(1/2,1/2,1/2) | $E_{2}^{S,-}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2) $ |
| Y:(1/2,0,0) | $Y_{1}^{S,+}(2) $ |
| Z:(0,1/2,0) | $Z_{1}^{S,+}(2) $ |
| F:(u,0,w) | $F_{1}^{S}(2) $ |
| G:(u,1/2,w) | $G_{1}^{S}(2) $ |
| Λ:(0,v,0) | $Λ_{1}^{S}(2) $ |
| U:(1/2,v,1/2) | $U_{2}^{S}(2) $ |
| V:(0,v,1/2) | $V_{2}^{S}(2) $ |
| W:(1/2,v,0) | $W_{1}^{S}(2) $ |
| GP:(u,v,w) | $GP_{1}^{S}(2) $ |
| k-vector | Ag↑G(2) |
| A:(1/2,0,1/2) | $A_{2}^{S,-}(2) $ |
| B:(0,0,1/2) | $B_{1}^{S,+}(2) $ |
| C:(1/2,1/2,0) | $C_{2}^{S,-}(2) $ |
| D:(0,1/2,1/2) | $D_{1}^{S,+}(2) $ |
| E:(1/2,1/2,1/2) | $E_{2}^{S,-}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2) $ |
| Y:(1/2,0,0) | $Y_{2}^{S,-}(2) $ |
| Z:(0,1/2,0) | $Z_{1}^{S,+}(2) $ |
| F:(u,0,w) | $F_{1}^{S}(2) $ |
| G:(u,1/2,w) | $G_{1}^{S}(2) $ |
| Λ:(0,v,0) | $Λ_{1}^{S}(2) $ |
| U:(1/2,v,1/2) | $U_{2}^{S}(2) $ |
| V:(0,v,1/2) | $V_{1}^{S}(2) $ |
| W:(1/2,v,0) | $W_{2}^{S}(2) $ |
| GP:(u,v,w) | $GP_{1}^{S}(2) $ |
| k-vector | Ag↑G(2) |
| A:(1/2,0,1/2) | $A_{1}^{S,+}(2) $ |
| B:(0,0,1/2) | $B_{2}^{S,-}(2) $ |
| C:(1/2,1/2,0) | $C_{2}^{S,-}(2) $ |
| D:(0,1/2,1/2) | $D_{2}^{S,-}(2) $ |
| E:(1/2,1/2,1/2) | $E_{1}^{S,+}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2) $ |
| Y:(1/2,0,0) | $Y_{2}^{S,-}(2) $ |
| Z:(0,1/2,0) | $Z_{1}^{S,+}(2) $ |
| F:(u,0,w) | $F_{1}^{S}(2) $ |
| G:(u,1/2,w) | $G_{1}^{S}(2) $ |
| Λ:(0,v,0) | $Λ_{1}^{S}(2) $ |
| U:(1/2,v,1/2) | $U_{1}^{S}(2) $ |
| V:(0,v,1/2) | $V_{2}^{S}(2) $ |
| W:(1/2,v,0) | $W_{2}^{S}(2) $ |
| GP:(u,v,w) | $GP_{1}^{S}(2) $ |
| k-vector | A↑G(4) |
| A:(1/2,0,1/2) | $A_{1}^{S,+}(2)⊕A_{1}^{S,-}(2) $ |
| B:(0,0,1/2) | $B_{1}^{S,+}(2)⊕B_{1}^{S,-}(2) $ |
| C:(1/2,1/2,0) | $C_{1}^{S,+}(2)⊕C_{1}^{S,-}(2) $ |
| D:(0,1/2,1/2) | $D_{1}^{S,+}(2)⊕D_{1}^{S,-}(2) $ |
| E:(1/2,1/2,1/2) | $E_{1}^{S,+}(2)⊕E_{1}^{S,-}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2) $ |
| Y:(1/2,0,0) | $Y_{1}^{S,+}(2)⊕Y_{1}^{S,-}(2) $ |
| Z:(0,1/2,0) | $Z_{1}^{S,+}(2)⊕Z_{1}^{S,-}(2) $ |
| F:(u,0,w) | $F_{1}^{S}(2)⊕F_{2}^{S}(2) $ |
| G:(u,1/2,w) | $G_{1}^{S}(2)⊕G_{2}^{S}(2) $ |
| Λ:(0,v,0) | $2Λ_{1}^{S}(2) $ |
| U:(1/2,v,1/2) | $2U_{1}^{S}(2) $ |
| V:(0,v,1/2) | $2V_{1}^{S}(2) $ |
| W:(1/2,v,0) | $2W_{1}^{S}(2) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(2) $ |
| k-vector | A↑G(4) |
| A:(1/2,0,1/2) | $A_{2}^{S,+}(2)⊕A_{2}^{S,-}(2) $ |
| B:(0,0,1/2) | $B_{1}^{S,+}(2)⊕B_{1}^{S,-}(2) $ |
| C:(1/2,1/2,0) | $C_{2}^{S,+}(2)⊕C_{2}^{S,-}(2) $ |
| D:(0,1/2,1/2) | $D_{1}^{S,+}(2)⊕D_{1}^{S,-}(2) $ |
| E:(1/2,1/2,1/2) | $E_{2}^{S,+}(2)⊕E_{2}^{S,-}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2) $ |
| Y:(1/2,0,0) | $Y_{2}^{S,+}(2)⊕Y_{2}^{S,-}(2) $ |
| Z:(0,1/2,0) | $Z_{1}^{S,+}(2)⊕Z_{1}^{S,-}(2) $ |
| F:(u,0,w) | $F_{1}^{S}(2)⊕F_{2}^{S}(2) $ |
| G:(u,1/2,w) | $G_{1}^{S}(2)⊕G_{2}^{S}(2) $ |
| Λ:(0,v,0) | $2Λ_{1}^{S}(2) $ |
| U:(1/2,v,1/2) | $2U_{2}^{S}(2) $ |
| V:(0,v,1/2) | $2V_{1}^{S}(2) $ |
| W:(1/2,v,0) | $2W_{2}^{S}(2) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(2) $ |
| k-vector | A↑G(4) |
| A:(1/2,0,1/2) | $A_{2}^{S,+}(2)⊕A_{2}^{S,-}(2) $ |
| B:(0,0,1/2) | $B_{2}^{S,+}(2)⊕B_{2}^{S,-}(2) $ |
| C:(1/2,1/2,0) | $C_{1}^{S,+}(2)⊕C_{1}^{S,-}(2) $ |
| D:(0,1/2,1/2) | $D_{2}^{S,+}(2)⊕D_{2}^{S,-}(2) $ |
| E:(1/2,1/2,1/2) | $E_{2}^{S,+}(2)⊕E_{2}^{S,-}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2) $ |
| Y:(1/2,0,0) | $Y_{1}^{S,+}(2)⊕Y_{1}^{S,-}(2) $ |
| Z:(0,1/2,0) | $Z_{1}^{S,+}(2)⊕Z_{1}^{S,-}(2) $ |
| F:(u,0,w) | $F_{1}^{S}(2)⊕F_{2}^{S}(2) $ |
| G:(u,1/2,w) | $G_{1}^{S}(2)⊕G_{2}^{S}(2) $ |
| Λ:(0,v,0) | $2Λ_{1}^{S}(2) $ |
| U:(1/2,v,1/2) | $2U_{2}^{S}(2) $ |
| V:(0,v,1/2) | $2V_{2}^{S}(2) $ |
| W:(1/2,v,0) | $2W_{1}^{S}(2) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(2) $ |
| k-vector | A↑G(4) |
| A:(1/2,0,1/2) | $A_{1}^{S,+}(2)⊕A_{1}^{S,-}(2) $ |
| B:(0,0,1/2) | $B_{2}^{S,+}(2)⊕B_{2}^{S,-}(2) $ |
| C:(1/2,1/2,0) | $C_{2}^{S,+}(2)⊕C_{2}^{S,-}(2) $ |
| D:(0,1/2,1/2) | $D_{2}^{S,+}(2)⊕D_{2}^{S,-}(2) $ |
| E:(1/2,1/2,1/2) | $E_{1}^{S,+}(2)⊕E_{1}^{S,-}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2) $ |
| Y:(1/2,0,0) | $Y_{2}^{S,+}(2)⊕Y_{2}^{S,-}(2) $ |
| Z:(0,1/2,0) | $Z_{1}^{S,+}(2)⊕Z_{1}^{S,-}(2) $ |
| F:(u,0,w) | $F_{1}^{S}(2)⊕F_{2}^{S}(2) $ |
| G:(u,1/2,w) | $G_{1}^{S}(2)⊕G_{2}^{S}(2) $ |
| Λ:(0,v,0) | $2Λ_{1}^{S}(2) $ |
| U:(1/2,v,1/2) | $2U_{1}^{S}(2) $ |
| V:(0,v,1/2) | $2V_{2}^{S}(2) $ |
| W:(1/2,v,0) | $2W_{2}^{S}(2) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(2) $ |
| k-vector | A'↑G(4) |
| A:(1/2,0,1/2) | $A_{1}^{S,+}(2)⊕A_{2}^{S,-}(2) $ |
| B:(0,0,1/2) | $B_{1}^{S,+}(2)⊕B_{2}^{S,-}(2) $ |
| C:(1/2,1/2,0) | $C_{1}^{S,+}(2)⊕C_{2}^{S,-}(2) $ |
| D:(0,1/2,1/2) | $D_{1}^{S,+}(2)⊕D_{2}^{S,-}(2) $ |
| E:(1/2,1/2,1/2) | $E_{1}^{S,+}(2)⊕E_{2}^{S,-}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{2}^{S,-}(2) $ |
| Y:(1/2,0,0) | $Y_{1}^{S,+}(2)⊕Y_{2}^{S,-}(2) $ |
| Z:(0,1/2,0) | $Z_{1}^{S,+}(2)⊕Z_{2}^{S,-}(2) $ |
| F:(u,0,w) | $2F_{1}^{S}(2) $ |
| G:(u,1/2,w) | $2G_{1}^{S}(2) $ |
| Λ:(0,v,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ |
| U:(1/2,v,1/2) | $U_{1}^{S}(2)⊕U_{2}^{S}(2) $ |
| V:(0,v,1/2) | $V_{1}^{S}(2)⊕V_{2}^{S}(2) $ |
| W:(1/2,v,0) | $W_{1}^{S}(2)⊕W_{2}^{S}(2) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(2) $ |
| k-vector | A↑G(8) |
| A:(1/2,0,1/2) | $A_{1}^{S,+}(2)⊕A_{1}^{S,-}(2)⊕A_{2}^{S,+}(2)⊕A_{2}^{S,-}(2) $ |
| B:(0,0,1/2) | $B_{1}^{S,+}(2)⊕B_{1}^{S,-}(2)⊕B_{2}^{S,+}(2)⊕B_{2}^{S,-}(2) $ |
| C:(1/2,1/2,0) | $C_{1}^{S,+}(2)⊕C_{1}^{S,-}(2)⊕C_{2}^{S,+}(2)⊕C_{2}^{S,-}(2) $ |
| D:(0,1/2,1/2) | $D_{1}^{S,+}(2)⊕D_{1}^{S,-}(2)⊕D_{2}^{S,+}(2)⊕D_{2}^{S,-}(2) $ |
| E:(1/2,1/2,1/2) | $E_{1}^{S,+}(2)⊕E_{1}^{S,-}(2)⊕E_{2}^{S,+}(2)⊕E_{2}^{S,-}(2) $ |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2)⊕Γ_{2}^{S,+}(2)⊕Γ_{2}^{S,-}(2) $ |
| Y:(1/2,0,0) | $Y_{1}^{S,+}(2)⊕Y_{1}^{S,-}(2)⊕Y_{2}^{S,+}(2)⊕Y_{2}^{S,-}(2) $ |
| Z:(0,1/2,0) | $Z_{1}^{S,+}(2)⊕Z_{1}^{S,-}(2)⊕Z_{2}^{S,+}(2)⊕Z_{2}^{S,-}(2) $ |
| F:(u,0,w) | $2F_{1}^{S}(2)⊕2F_{2}^{S}(2) $ |
| G:(u,1/2,w) | $2G_{1}^{S}(2)⊕2G_{2}^{S}(2) $ |
| Λ:(0,v,0) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2) $ |
| U:(1/2,v,1/2) | $2U_{1}^{S}(2)⊕2U_{2}^{S}(2) $ |
| V:(0,v,1/2) | $2V_{1}^{S}(2)⊕2V_{2}^{S}(2) $ |
| W:(1/2,v,0) | $2W_{1}^{S}(2)⊕2W_{2}^{S}(2) $ |
| GP:(u,v,w) | $4GP_{1}^{S}(2) $ |