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