The continuously infinite group ∞1 is omitted.
| Coordinates | Seitz symbol |
|---|---|
| a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
| a+1/2, -b, -c+1/2 | x, y, z | { 1 ‖ 2100 | 1/2 0 1/2 } |
| -a, b, -c+1/2 | x, y, z | { 1 ‖ 2010 | 0 0 1/2 } |
| -a+1/2, -b, c | x, y, z | { 1 ‖ 2001 | 1/2 0 0 } |
| -a, -b, -c | x, y, z | { 1 ‖ -1 | 0 } |
| -a+1/2, b, c+1/2 | x, y, z | { 1 ‖ m100 | 1/2 0 1/2 } |
| a, -b, c+1/2 | x, y, z | { 1 ‖ m010 | 0 0 1/2 } |
| a+1/2, b, -c | x, y, z | { 1 ‖ m001 | 1/2 0 0 } |
| a, b+1/2, c | -x, -y, -z | { -1 ‖ 1 | 0 1/2 0 } |
| a+1/2, -b+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ 2100 | 1/2 1/2 1/2 } |
| -a, b+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ 2010 | 0 1/2 1/2 } |
| -a+1/2, -b+1/2, c | -x, -y, -z | { -1 ‖ 2001 | 1/2 1/2 0 } |
| -a, -b+1/2, -c | -x, -y, -z | { -1 ‖ -1 | 0 1/2 0 } |
| -a+1/2, b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m100 | 1/2 1/2 1/2 } |
| a, -b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m010 | 0 1/2 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 } |
| a+1/2, -b, -c+1/2 | -x, y, z | { m ‖ 2100 | 1/2 0 1/2 } |
| -a, b, -c+1/2 | -x, y, z | { m ‖ 2010 | 0 0 1/2 } |
| -a+1/2, -b, c | -x, y, z | { m ‖ 2001 | 1/2 0 0 } |
| -a, -b, -c | -x, y, z | { m ‖ -1 | 0 } |
| -a+1/2, b, c+1/2 | -x, y, z | { m ‖ m100 | 1/2 0 1/2 } |
| a, -b, c+1/2 | -x, y, z | { m ‖ m010 | 0 0 1/2 } |
| a+1/2, b, -c | -x, y, z | { m ‖ m001 | 1/2 0 0 } |
| a, b+1/2, c | x, -y, -z | { 2 ‖ 1 | 0 1/2 0 } |
| a+1/2, -b+1/2, -c+1/2 | x, -y, -z | { 2 ‖ 2100 | 1/2 1/2 1/2 } |
| -a, b+1/2, -c+1/2 | x, -y, -z | { 2 ‖ 2010 | 0 1/2 1/2 } |
| -a+1/2, -b+1/2, c | x, -y, -z | { 2 ‖ 2001 | 1/2 1/2 0 } |
| -a, -b+1/2, -c | x, -y, -z | { 2 ‖ -1 | 0 1/2 0 } |
| -a+1/2, b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m100 | 1/2 1/2 1/2 } |
| a, -b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m010 | 0 1/2 1/2 } |
| a+1/2, b+1/2, -c | x, -y, -z | { 2 ‖ m001 | 1/2 1/2 0 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 8a | $\ce{^{1}{-1}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,z) |
| 8b | $\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $ | (0,1/4,0 | 0,0,0) |
| 8c | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (0,b,1/4 | 0,0,z) |
| 8d | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/4,0,c | 0,0,z) |
| 8e | $..\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/4,1/4,c | 0,0,0) |
| 16f | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
| Wavevector-k | Little co-group |
|---|---|
| Γ:(0,0,0) | $ \ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| R:(1/2,1/2,1/2) | $ \ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| S:(1/2,1/2,0) | $ \ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| T:(0,1/2,1/2) | $ \ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| U:(1/2,0,1/2) | $ \ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| X:(1/2,0,0) | $ \ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| Y:(0,1/2,0) | $ \ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| Z:(0,0,1/2) | $ \ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
| A:(u,0,1/2) | $ \ce{^{m}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| B:(0,v,1/2) | $ \ce{^{1}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| C:(u,1/2,0) | $ \ce{^{m}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| D:(1/2,v,0) | $ \ce{^{1}{m}}\ce{^{m}{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}} $ |
| E:(u,1/2,1/2) | $ \ce{^{m}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| G:(1/2,0,w) | $ \ce{^{1}{m}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty 2}{1}} $ |
| H:(0,1/2,w) | $ \ce{^{1}{m}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty 2}{1}} $ |
| Λ:(0,0,w) | $ \ce{^{1}{m}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty 2}{1}} $ |
| P:(1/2,v,1/2) | $ \ce{^{1}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| Q:(1/2,1/2,w) | $ \ce{^{1}{m}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty 2}{1}} $ |
| Σ:(u,0,0) | $ \ce{^{m}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| K:(0,v,w) | $ \ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| L:(1/2,v,w) | $ \ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| M:(u,0,w) | $ \ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| N:(u,1/2,w) | $ \ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| V:(u,v,0) | $ \ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| W:(u,v,1/2) | $ \ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
| GP:(u,v,w) | $ \ce{^{m}{-1}}\ce{^{\infty 2}{1}} $ |
Spin Brillouin Zone
mmmP
| k-vector | Ag↑G(8) |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{2}^{S,+}(2)⊕Γ_{3}^{S,+}(2)⊕Γ_{4}^{S,+}(2) $ |
| R:(1/2,1/2,1/2) | $R_{1}^{S}R_{2}^{S}(8) $ |
| S:(1/2,1/2,0) | $S_{1}^{S}(4)⊕S_{2}^{S}(4) $ |
| T:(0,1/2,1/2) | $T_{1}^{S}(4)⊕T_{2}^{S}(4) $ |
| U:(1/2,0,1/2) | $U_{1}^{S}U_{2}^{S}(8) $ |
| X:(1/2,0,0) | $X_{1}^{S}(4)⊕X_{2}^{S}(4) $ |
| Y:(0,1/2,0) | $Y_{1}^{S,+}(2)⊕Y_{2}^{S,+}(2)⊕Y_{3}^{S,+}(2)⊕Y_{4}^{S,+}(2) $ |
| Z:(0,0,1/2) | $Z_{1}^{S}(4)⊕Z_{2}^{S}(4) $ |
| A:(u,0,1/2) | $2A_{1}^{S}(4) $ |
| B:(0,v,1/2) | $2B_{1}^{S}(4) $ |
| C:(u,1/2,0) | $C_{1}^{S}(2)⊕C_{2}^{S}(2)⊕C_{3}^{S}(2)⊕C_{4}^{S}(2) $ |
| D:(1/2,v,0) | $2D_{1}^{S}(4) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2)⊕Δ_{3}^{S}(2)⊕Δ_{4}^{S}(2) $ |
| E:(u,1/2,1/2) | $2E_{1}^{S}(4) $ |
| G:(1/2,0,w) | $G_{1}^{S}G_{4}^{S}(4)⊕G_{2}^{S}G_{3}^{S}(4) $ |
| H:(0,1/2,w) | $H_{1}^{S}(2)⊕H_{2}^{S}(2)⊕H_{3}^{S}(2)⊕H_{4}^{S}(2) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2)⊕Λ_{3}^{S}(2)⊕Λ_{4}^{S}(2) $ |
| P:(1/2,v,1/2) | $P_{1}^{S}P_{4}^{S}(4)⊕P_{2}^{S}P_{3}^{S}(4) $ |
| Q:(1/2,1/2,w) | $Q_{1}^{S}Q_{4}^{S}(4)⊕Q_{2}^{S}Q_{3}^{S}(4) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2)⊕Σ_{3}^{S}(2)⊕Σ_{4}^{S}(2) $ |
| K:(0,v,w) | $2K_{1}^{S}(2)⊕2K_{2}^{S}(2) $ |
| L:(1/2,v,w) | $2L_{1}^{S}L_{2}^{S}(4) $ |
| M:(u,0,w) | $2M_{1}^{S}(2)⊕2M_{2}^{S}(2) $ |
| N:(u,1/2,w) | $2N_{1}^{S}(2)⊕2N_{2}^{S}(2) $ |
| V:(u,v,0) | $2V_{1}^{S}(2)⊕2V_{2}^{S}(2) $ |
| W:(u,v,1/2) | $2W_{1}^{S}(2)⊕2W_{2}^{S}(2) $ |
| GP:(u,v,w) | $4GP_{1}^{S}(2) $ |
| k-vector | A↑G(8) |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2)⊕Γ_{4}^{S,+}(2)⊕Γ_{4}^{S,-}(2) $ |
| R:(1/2,1/2,1/2) | $R_{1}^{S}R_{2}^{S}(8) $ |
| S:(1/2,1/2,0) | $S_{1}^{S}(4)⊕S_{2}^{S}(4) $ |
| T:(0,1/2,1/2) | $T_{1}^{S}(4)⊕T_{2}^{S}(4) $ |
| U:(1/2,0,1/2) | $U_{1}^{S}U_{2}^{S}(8) $ |
| X:(1/2,0,0) | $X_{1}^{S}(4)⊕X_{2}^{S}(4) $ |
| Y:(0,1/2,0) | $Y_{1}^{S,+}(2)⊕Y_{1}^{S,-}(2)⊕Y_{4}^{S,+}(2)⊕Y_{4}^{S,-}(2) $ |
| Z:(0,0,1/2) | $Z_{1}^{S}(4)⊕Z_{2}^{S}(4) $ |
| A:(u,0,1/2) | $2A_{1}^{S}(4) $ |
| B:(0,v,1/2) | $2B_{1}^{S}(4) $ |
| C:(u,1/2,0) | $C_{1}^{S}(2)⊕C_{2}^{S}(2)⊕C_{3}^{S}(2)⊕C_{4}^{S}(2) $ |
| D:(1/2,v,0) | $2D_{1}^{S}(4) $ |
| Δ:(0,v,0) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $ |
| E:(u,1/2,1/2) | $2E_{1}^{S}(4) $ |
| G:(1/2,0,w) | $G_{1}^{S}G_{4}^{S}(4)⊕G_{2}^{S}G_{3}^{S}(4) $ |
| H:(0,1/2,w) | $H_{1}^{S}(2)⊕H_{2}^{S}(2)⊕H_{3}^{S}(2)⊕H_{4}^{S}(2) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2)⊕Λ_{3}^{S}(2)⊕Λ_{4}^{S}(2) $ |
| P:(1/2,v,1/2) | $P_{1}^{S}P_{4}^{S}(4)⊕P_{2}^{S}P_{3}^{S}(4) $ |
| Q:(1/2,1/2,w) | $Q_{1}^{S}Q_{4}^{S}(4)⊕Q_{2}^{S}Q_{3}^{S}(4) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2)⊕Σ_{3}^{S}(2)⊕Σ_{4}^{S}(2) $ |
| K:(0,v,w) | $2K_{1}^{S}(2)⊕2K_{2}^{S}(2) $ |
| L:(1/2,v,w) | $2L_{1}^{S}L_{2}^{S}(4) $ |
| M:(u,0,w) | $2M_{1}^{S}(2)⊕2M_{2}^{S}(2) $ |
| N:(u,1/2,w) | $2N_{1}^{S}(2)⊕2N_{2}^{S}(2) $ |
| V:(u,v,0) | $2V_{1}^{S}(2)⊕2V_{2}^{S}(2) $ |
| W:(u,v,1/2) | $2W_{1}^{S}(2)⊕2W_{2}^{S}(2) $ |
| GP:(u,v,w) | $4GP_{1}^{S}(2) $ |
| k-vector | A↑G(8) |
| Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2)⊕Γ_{2}^{S,+}(2)⊕Γ_{2}^{S,-}(2) $ |
| R:(1/2,1/2,1/2) | $R_{1}^{S}R_{2}^{S}(8) $ |
| S:(1/2,1/2,0) | $S_{1}^{S}(4)⊕S_{2}^{S}(4) $ |
| T:(0,1/2,1/2) | $2T_{1}^{S}(4) $ |
| U:(1/2,0,1/2) | $U_{1}^{S}U_{2}^{S}(8) $ |
| X:(1/2,0,0) | $X_{1}^{S}(4)⊕X_{2}^{S}(4) $ |
| Y:(0,1/2,0) | $Y_{1}^{S,+}(2)⊕Y_{1}^{S,-}(2)⊕Y_{2}^{S,+}(2)⊕Y_{2}^{S,-}(2) $ |
| Z:(0,0,1/2) | $2Z_{1}^{S}(4) $ |
| A:(u,0,1/2) | $2A_{1}^{S}(4) $ |
| B:(0,v,1/2) | $2B_{1}^{S}(4) $ |
| C:(u,1/2,0) | $C_{1}^{S}(2)⊕C_{2}^{S}(2)⊕C_{3}^{S}(2)⊕C_{4}^{S}(2) $ |
| D:(1/2,v,0) | $2D_{1}^{S}(4) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2)⊕Δ_{3}^{S}(2)⊕Δ_{4}^{S}(2) $ |
| E:(u,1/2,1/2) | $2E_{1}^{S}(4) $ |
| G:(1/2,0,w) | $G_{1}^{S}G_{4}^{S}(4)⊕G_{2}^{S}G_{3}^{S}(4) $ |
| H:(0,1/2,w) | $2H_{1}^{S}(2)⊕2H_{2}^{S}(2) $ |
| Λ:(0,0,w) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2) $ |
| P:(1/2,v,1/2) | $P_{1}^{S}P_{4}^{S}(4)⊕P_{2}^{S}P_{3}^{S}(4) $ |
| Q:(1/2,1/2,w) | $Q_{1}^{S}Q_{4}^{S}(4)⊕Q_{2}^{S}Q_{3}^{S}(4) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2)⊕Σ_{3}^{S}(2)⊕Σ_{4}^{S}(2) $ |
| K:(0,v,w) | $2K_{1}^{S}(2)⊕2K_{2}^{S}(2) $ |
| L:(1/2,v,w) | $2L_{1}^{S}L_{2}^{S}(4) $ |
| M:(u,0,w) | $2M_{1}^{S}(2)⊕2M_{2}^{S}(2) $ |
| N:(u,1/2,w) | $2N_{1}^{S}(2)⊕2N_{2}^{S}(2) $ |
| V:(u,v,0) | $2V_{1}^{S}(2)⊕2V_{2}^{S}(2) $ |
| W:(u,v,1/2) | $2W_{1}^{S}(2)⊕2W_{2}^{S}(2) $ |
| GP:(u,v,w) | $4GP_{1}^{S}(2) $ |
| k-vector | A↑G(16) |
| 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) $ |
| R:(1/2,1/2,1/2) | $2R_{1}^{S}R_{2}^{S}(8) $ |
| S:(1/2,1/2,0) | $2S_{1}^{S}(4)⊕2S_{2}^{S}(4) $ |
| T:(0,1/2,1/2) | $2T_{1}^{S}(4)⊕2T_{2}^{S}(4) $ |
| U:(1/2,0,1/2) | $2U_{1}^{S}U_{2}^{S}(8) $ |
| X:(1/2,0,0) | $2X_{1}^{S}(4)⊕2X_{2}^{S}(4) $ |
| Y:(0,1/2,0) | $Y_{1}^{S,+}(2)⊕Y_{1}^{S,-}(2)⊕Y_{2}^{S,+}(2)⊕Y_{2}^{S,-}(2)⊕Y_{3}^{S,+}(2)⊕Y_{3}^{S,-}(2)⊕Y_{4}^{S,+}(2)⊕Y_{4}^{S,-}(2) $ |
| Z:(0,0,1/2) | $2Z_{1}^{S}(4)⊕2Z_{2}^{S}(4) $ |
| A:(u,0,1/2) | $4A_{1}^{S}(4) $ |
| B:(0,v,1/2) | $4B_{1}^{S}(4) $ |
| C:(u,1/2,0) | $2C_{1}^{S}(2)⊕2C_{2}^{S}(2)⊕2C_{3}^{S}(2)⊕2C_{4}^{S}(2) $ |
| D:(1/2,v,0) | $4D_{1}^{S}(4) $ |
| Δ:(0,v,0) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2)⊕2Δ_{3}^{S}(2)⊕2Δ_{4}^{S}(2) $ |
| E:(u,1/2,1/2) | $4E_{1}^{S}(4) $ |
| G:(1/2,0,w) | $2G_{1}^{S}G_{4}^{S}(4)⊕2G_{2}^{S}G_{3}^{S}(4) $ |
| H:(0,1/2,w) | $2H_{1}^{S}(2)⊕2H_{2}^{S}(2)⊕2H_{3}^{S}(2)⊕2H_{4}^{S}(2) $ |
| Λ:(0,0,w) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2)⊕2Λ_{3}^{S}(2)⊕2Λ_{4}^{S}(2) $ |
| P:(1/2,v,1/2) | $2P_{1}^{S}P_{4}^{S}(4)⊕2P_{2}^{S}P_{3}^{S}(4) $ |
| Q:(1/2,1/2,w) | $2Q_{1}^{S}Q_{4}^{S}(4)⊕2Q_{2}^{S}Q_{3}^{S}(4) $ |
| Σ:(u,0,0) | $2Σ_{1}^{S}(2)⊕2Σ_{2}^{S}(2)⊕2Σ_{3}^{S}(2)⊕2Σ_{4}^{S}(2) $ |
| K:(0,v,w) | $4K_{1}^{S}(2)⊕4K_{2}^{S}(2) $ |
| L:(1/2,v,w) | $4L_{1}^{S}L_{2}^{S}(4) $ |
| M:(u,0,w) | $4M_{1}^{S}(2)⊕4M_{2}^{S}(2) $ |
| N:(u,1/2,w) | $4N_{1}^{S}(2)⊕4N_{2}^{S}(2) $ |
| V:(u,v,0) | $4V_{1}^{S}(2)⊕4V_{2}^{S}(2) $ |
| W:(u,v,1/2) | $4W_{1}^{S}(2)⊕4W_{2}^{S}(2) $ |
| GP:(u,v,w) | $8GP_{1}^{S}(2) $ |