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 ‖ 2100 | 0 } |
| -a, b, -c | x, y, z | { 1 ‖ 2010 | 0 } |
| -a, -b, c | x, y, z | { 1 ‖ 2001 | 0 } |
| a, b+1/2, c+1/2 | x, y, z | { 1 ‖ 1 | 0 1/2 1/2 } |
| a, -b+1/2, -c+1/2 | x, y, z | { 1 ‖ 2100 | 0 1/2 1/2 } |
| -a, b+1/2, -c+1/2 | x, y, z | { 1 ‖ 2010 | 0 1/2 1/2 } |
| -a, -b+1/2, c+1/2 | x, y, z | { 1 ‖ 2001 | 0 1/2 1/2 } |
| a+1/2, b, c+1/2 | x, y, z | { 1 ‖ 1 | 1/2 0 1/2 } |
| a+1/2, -b, -c+1/2 | x, y, z | { 1 ‖ 2100 | 1/2 0 1/2 } |
| -a+1/2, b, -c+1/2 | x, y, z | { 1 ‖ 2010 | 1/2 0 1/2 } |
| -a+1/2, -b, c+1/2 | x, y, z | { 1 ‖ 2001 | 1/2 0 1/2 } |
| a+1/2, b+1/2, c | x, y, z | { 1 ‖ 1 | 1/2 1/2 0 } |
| a+1/2, -b+1/2, -c | x, y, z | { 1 ‖ 2100 | 1/2 1/2 0 } |
| -a+1/2, b+1/2, -c | x, y, z | { 1 ‖ 2010 | 1/2 1/2 0 } |
| -a+1/2, -b+1/2, c | x, y, z | { 1 ‖ 2001 | 1/2 1/2 0 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| a, -b, -c | -x, y, z | { m ‖ 2100 | 0 } |
| -a, b, -c | -x, y, z | { m ‖ 2010 | 0 } |
| -a, -b, c | -x, y, z | { m ‖ 2001 | 0 } |
| a, b+1/2, c+1/2 | -x, y, z | { m ‖ 1 | 0 1/2 1/2 } |
| a, -b+1/2, -c+1/2 | -x, y, z | { m ‖ 2100 | 0 1/2 1/2 } |
| -a, b+1/2, -c+1/2 | -x, y, z | { m ‖ 2010 | 0 1/2 1/2 } |
| -a, -b+1/2, c+1/2 | -x, y, z | { m ‖ 2001 | 0 1/2 1/2 } |
| a+1/2, b, c+1/2 | -x, y, z | { m ‖ 1 | 1/2 0 1/2 } |
| a+1/2, -b, -c+1/2 | -x, y, z | { m ‖ 2100 | 1/2 0 1/2 } |
| -a+1/2, b, -c+1/2 | -x, y, z | { m ‖ 2010 | 1/2 0 1/2 } |
| -a+1/2, -b, c+1/2 | -x, y, z | { m ‖ 2001 | 1/2 0 1/2 } |
| a+1/2, b+1/2, c | -x, y, z | { m ‖ 1 | 1/2 1/2 0 } |
| a+1/2, -b+1/2, -c | -x, y, z | { m ‖ 2100 | 1/2 1/2 0 } |
| -a+1/2, b+1/2, -c | -x, y, z | { m ‖ 2010 | 1/2 1/2 0 } |
| -a+1/2, -b+1/2, c | -x, y, z | { m ‖ 2001 | 1/2 1/2 0 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 4a | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,0 |0,0,z) |
| 4b | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,1/2 |0,0,z) |
| 4c | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/4,1/4,1/4 |0,0,z) |
| 4d | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/4,1/4,3/4 |0,0,z) |
| 8e | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,0,0 |0,0,z) |
| 8f | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (0,b,0 |0,0,z) |
| 8g | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,c |0,0,z) |
| 8h | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/4,1/4,c |0,0,z) |
| 8i | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (1/4,b,1/4 |0,0,z) |
| 8j | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,1/4,1/4 |0,0,z) |
| 16k | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c |0,0,z) |
| Wavevector-k | Little co-group |
|---|---|
| Γ:(0,0,0) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| T:(1,0,0) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| Y:(0,1,0) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| Z:(0,0,1) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| L:(1/2,1/2,1/2) | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ |
| A:(u,0,1) | $\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| B:(0,v,1) | $\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| H:(0,1,w) | $\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| Λ:(0,0,w) | $\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| E:(0,v,w) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| J:(u,0,w) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| M:(u,v,0) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| GP:(u,v,w) | $\ce{^{1}{1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
| k-vector | A↑G(4) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}(1)⊕Γ_{3}^{S}(1)⊕Γ_{4}^{S}(1) $ |
| T:(1,0,0) | $T_{1}^{S}(1)⊕T_{2}^{S}(1)⊕T_{3}^{S}(1)⊕T_{4}^{S}(1) $ |
| Y:(0,1,0) | $Y_{1}^{S}(1)⊕Y_{2}^{S}(1)⊕Y_{3}^{S}(1)⊕Y_{4}^{S}(1) $ |
| Z:(0,0,1) | $Z_{1}^{S}(1)⊕Z_{2}^{S}(1)⊕Z_{3}^{S}(1)⊕Z_{4}^{S}(1) $ |
| L:(1/2,1/2,1/2) | $4L_{1}^{S}(1) $ |
| A:(u,0,1) | $2A_{1}^{S}(1)⊕2A_{2}^{S}(1) $ |
| B:(0,v,1) | $2B_{1}^{S}(1)⊕2B_{2}^{S}(1) $ |
| Δ:(0,v,0) | $2Δ_{1}^{S}(1)⊕2Δ_{2}^{S}(1) $ |
| H:(0,1,w) | $2H_{1}^{S}(1)⊕2H_{2}^{S}(1) $ |
| Λ:(0,0,w) | $2Λ_{1}^{S}(1)⊕2Λ_{2}^{S}(1) $ |
| Σ:(u,0,0) | $2Σ_{1}^{S}(1)⊕2Σ_{2}^{S}(1) $ |
| E:(0,v,w) | $4E_{1}^{S}(1) $ |
| J:(u,0,w) | $4J_{1}^{S}(1) $ |
| M:(u,v,0) | $4M_{1}^{S}(1) $ |
| GP:(u,v,w) | $4GP_{1}^{S}(1) $ |
| k-vector | A↑G(1) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1) $ |
| T:(1,0,0) | $T_{1}^{S}(1) $ |
| Y:(0,1,0) | $Y_{1}^{S}(1) $ |
| Z:(0,0,1) | $Z_{1}^{S}(1) $ |
| L:(1/2,1/2,1/2) | $L_{1}^{S}(1) $ |
| A:(u,0,1) | $A_{1}^{S}(1) $ |
| B:(0,v,1) | $B_{1}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1) $ |
| H:(0,1,w) | $H_{1}^{S}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1) $ |
| E:(0,v,w) | $E_{1}^{S}(1) $ |
| J:(u,0,w) | $J_{1}^{S}(1) $ |
| M:(u,v,0) | $M_{1}^{S}(1) $ |
| GP:(u,v,w) | $GP_{1}^{S}(1) $ |
| k-vector | A↑G(1) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1) $ |
| T:(1,0,0) | $T_{1}^{S}(1) $ |
| Y:(0,1,0) | $Y_{1}^{S}(1) $ |
| Z:(0,0,1) | $Z_{1}^{S}(1) $ |
| L:(1/2,1/2,1/2) | $L_{1}^{S}(1) $ |
| A:(u,0,1) | $A_{1}^{S}(1) $ |
| B:(0,v,1) | $B_{1}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1) $ |
| H:(0,1,w) | $H_{1}^{S}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1) $ |
| E:(0,v,w) | $E_{1}^{S}(1) $ |
| J:(u,0,w) | $J_{1}^{S}(1) $ |
| M:(u,v,0) | $M_{1}^{S}(1) $ |
| GP:(u,v,w) | $GP_{1}^{S}(1) $ |
| k-vector | A↑G(1) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1) $ |
| T:(1,0,0) | $T_{3}^{S}(1) $ |
| Y:(0,1,0) | $Y_{4}^{S}(1) $ |
| Z:(0,0,1) | $Z_{2}^{S}(1) $ |
| L:(1/2,1/2,1/2) | $L_{1}^{S}(1) $ |
| A:(u,0,1) | $A_{2}^{S}(1) $ |
| B:(0,v,1) | $B_{2}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1) $ |
| H:(0,1,w) | $H_{2}^{S}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1) $ |
| E:(0,v,w) | $E_{1}^{S}(1) $ |
| J:(u,0,w) | $J_{1}^{S}(1) $ |
| M:(u,v,0) | $M_{1}^{S}(1) $ |
| GP:(u,v,w) | $GP_{1}^{S}(1) $ |
| k-vector | A↑G(1) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1) $ |
| T:(1,0,0) | $T_{3}^{S}(1) $ |
| Y:(0,1,0) | $Y_{4}^{S}(1) $ |
| Z:(0,0,1) | $Z_{2}^{S}(1) $ |
| L:(1/2,1/2,1/2) | $L_{1}^{S}(1) $ |
| A:(u,0,1) | $A_{2}^{S}(1) $ |
| B:(0,v,1) | $B_{2}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1) $ |
| H:(0,1,w) | $H_{2}^{S}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1) $ |
| E:(0,v,w) | $E_{1}^{S}(1) $ |
| J:(u,0,w) | $J_{1}^{S}(1) $ |
| M:(u,v,0) | $M_{1}^{S}(1) $ |
| GP:(u,v,w) | $GP_{1}^{S}(1) $ |
| k-vector | A↑G(2) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{3}^{S}(1) $ |
| T:(1,0,0) | $T_{1}^{S}(1)⊕T_{3}^{S}(1) $ |
| Y:(0,1,0) | $Y_{1}^{S}(1)⊕Y_{3}^{S}(1) $ |
| Z:(0,0,1) | $Z_{1}^{S}(1)⊕Z_{3}^{S}(1) $ |
| L:(1/2,1/2,1/2) | $2L_{1}^{S}(1) $ |
| A:(u,0,1) | $2A_{1}^{S}(1) $ |
| B:(0,v,1) | $B_{1}^{S}(1)⊕B_{2}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1) $ |
| H:(0,1,w) | $H_{1}^{S}(1)⊕H_{2}^{S}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $ |
| Σ:(u,0,0) | $2Σ_{1}^{S}(1) $ |
| E:(0,v,w) | $2E_{1}^{S}(1) $ |
| J:(u,0,w) | $2J_{1}^{S}(1) $ |
| M:(u,v,0) | $2M_{1}^{S}(1) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
| k-vector | A↑G(2) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{4}^{S}(1) $ |
| T:(1,0,0) | $T_{1}^{S}(1)⊕T_{4}^{S}(1) $ |
| Y:(0,1,0) | $Y_{1}^{S}(1)⊕Y_{4}^{S}(1) $ |
| Z:(0,0,1) | $Z_{1}^{S}(1)⊕Z_{4}^{S}(1) $ |
| L:(1/2,1/2,1/2) | $2L_{1}^{S}(1) $ |
| A:(u,0,1) | $A_{1}^{S}(1)⊕A_{2}^{S}(1) $ |
| B:(0,v,1) | $2B_{1}^{S}(1) $ |
| Δ:(0,v,0) | $2Δ_{1}^{S}(1) $ |
| H:(0,1,w) | $H_{1}^{S}(1)⊕H_{2}^{S}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
| E:(0,v,w) | $2E_{1}^{S}(1) $ |
| J:(u,0,w) | $2J_{1}^{S}(1) $ |
| M:(u,v,0) | $2M_{1}^{S}(1) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
| k-vector | A↑G(2) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}(1) $ |
| T:(1,0,0) | $T_{1}^{S}(1)⊕T_{2}^{S}(1) $ |
| Y:(0,1,0) | $Y_{1}^{S}(1)⊕Y_{2}^{S}(1) $ |
| Z:(0,0,1) | $Z_{1}^{S}(1)⊕Z_{2}^{S}(1) $ |
| L:(1/2,1/2,1/2) | $2L_{1}^{S}(1) $ |
| A:(u,0,1) | $A_{1}^{S}(1)⊕A_{2}^{S}(1) $ |
| B:(0,v,1) | $B_{1}^{S}(1)⊕B_{2}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1) $ |
| H:(0,1,w) | $2H_{1}^{S}(1) $ |
| Λ:(0,0,w) | $2Λ_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
| E:(0,v,w) | $2E_{1}^{S}(1) $ |
| J:(u,0,w) | $2J_{1}^{S}(1) $ |
| M:(u,v,0) | $2M_{1}^{S}(1) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
| k-vector | A↑G(2) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}(1) $ |
| T:(1,0,0) | $T_{3}^{S}(1)⊕T_{4}^{S}(1) $ |
| Y:(0,1,0) | $Y_{3}^{S}(1)⊕Y_{4}^{S}(1) $ |
| Z:(0,0,1) | $Z_{1}^{S}(1)⊕Z_{2}^{S}(1) $ |
| L:(1/2,1/2,1/2) | $2L_{1}^{S}(1) $ |
| A:(u,0,1) | $A_{1}^{S}(1)⊕A_{2}^{S}(1) $ |
| B:(0,v,1) | $B_{1}^{S}(1)⊕B_{2}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1) $ |
| H:(0,1,w) | $2H_{2}^{S}(1) $ |
| Λ:(0,0,w) | $2Λ_{1}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
| E:(0,v,w) | $2E_{1}^{S}(1) $ |
| J:(u,0,w) | $2J_{1}^{S}(1) $ |
| M:(u,v,0) | $2M_{1}^{S}(1) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
| k-vector | A↑G(2) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{4}^{S}(1) $ |
| T:(1,0,0) | $T_{2}^{S}(1)⊕T_{3}^{S}(1) $ |
| Y:(0,1,0) | $Y_{1}^{S}(1)⊕Y_{4}^{S}(1) $ |
| Z:(0,0,1) | $Z_{2}^{S}(1)⊕Z_{3}^{S}(1) $ |
| L:(1/2,1/2,1/2) | $2L_{1}^{S}(1) $ |
| A:(u,0,1) | $A_{1}^{S}(1)⊕A_{2}^{S}(1) $ |
| B:(0,v,1) | $2B_{2}^{S}(1) $ |
| Δ:(0,v,0) | $2Δ_{1}^{S}(1) $ |
| H:(0,1,w) | $H_{1}^{S}(1)⊕H_{2}^{S}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $ |
| Σ:(u,0,0) | $Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
| E:(0,v,w) | $2E_{1}^{S}(1) $ |
| J:(u,0,w) | $2J_{1}^{S}(1) $ |
| M:(u,v,0) | $2M_{1}^{S}(1) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
| k-vector | A↑G(2) |
| Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{3}^{S}(1) $ |
| T:(1,0,0) | $T_{1}^{S}(1)⊕T_{3}^{S}(1) $ |
| Y:(0,1,0) | $Y_{2}^{S}(1)⊕Y_{4}^{S}(1) $ |
| Z:(0,0,1) | $Z_{2}^{S}(1)⊕Z_{4}^{S}(1) $ |
| L:(1/2,1/2,1/2) | $2L_{1}^{S}(1) $ |
| A:(u,0,1) | $2A_{2}^{S}(1) $ |
| B:(0,v,1) | $B_{1}^{S}(1)⊕B_{2}^{S}(1) $ |
| Δ:(0,v,0) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1) $ |
| H:(0,1,w) | $H_{1}^{S}(1)⊕H_{2}^{S}(1) $ |
| Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $ |
| Σ:(u,0,0) | $2Σ_{1}^{S}(1) $ |
| E:(0,v,w) | $2E_{1}^{S}(1) $ |
| J:(u,0,w) | $2J_{1}^{S}(1) $ |
| M:(u,v,0) | $2M_{1}^{S}(1) $ |
| GP:(u,v,w) | $2GP_{1}^{S}(1) $ |