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 ‖ 2010 | 1/2 0 1/2 } |
| -a, b, c | x, y, z | { 1 ‖ m100 | 0 } |
| a+1/2, b, -c+1/2 | x, y, z | { 1 ‖ m001 | 1/2 0 1/2 } |
| a, -b, -c | -x, -y, -z | { -1 ‖ 2100 | 0 } |
| -a+1/2, -b, c+1/2 | -x, -y, -z | { -1 ‖ 2001 | 1/2 0 1/2 } |
| -a, -b, -c | -x, -y, -z | { -1 ‖ -1 | 0 } |
| a+1/2, -b, c+1/2 | -x, -y, -z | { -1 ‖ m010 | 1/2 0 1/2 } |
| a+1/2, b+1/2, c | x, y, z | { 1 ‖ 1 | 1/2 1/2 0 } |
| -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 ‖ m100 | 1/2 1/2 0 } |
| a, b+1/2, -c+1/2 | x, y, z | { 1 ‖ m001 | 0 1/2 1/2 } |
| a+1/2, -b+1/2, -c | -x, -y, -z | { -1 ‖ 2100 | 1/2 1/2 0 } |
| -a, -b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ 2001 | 0 1/2 1/2 } |
| -a+1/2, -b+1/2, -c | -x, -y, -z | { -1 ‖ -1 | 1/2 1/2 0 } |
| a, -b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m010 | 0 1/2 1/2 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| -a+1/2, b, -c+1/2 | -x, y, z | { m ‖ 2010 | 1/2 0 1/2 } |
| -a, b, c | -x, y, z | { m ‖ m100 | 0 } |
| a+1/2, b, -c+1/2 | -x, y, z | { m ‖ m001 | 1/2 0 1/2 } |
| a, -b, -c | x, -y, -z | { 2 ‖ 2100 | 0 } |
| -a+1/2, -b, c+1/2 | x, -y, -z | { 2 ‖ 2001 | 1/2 0 1/2 } |
| -a, -b, -c | x, -y, -z | { 2 ‖ -1 | 0 } |
| a+1/2, -b, c+1/2 | x, -y, -z | { 2 ‖ m010 | 1/2 0 1/2 } |
| a+1/2, b+1/2, c | -x, y, z | { m ‖ 1 | 1/2 1/2 0 } |
| -a, b+1/2, -c+1/2 | -x, y, z | { m ‖ 2010 | 0 1/2 1/2 } |
| -a+1/2, b+1/2, c | -x, y, z | { m ‖ m100 | 1/2 1/2 0 } |
| a, b+1/2, -c+1/2 | -x, y, z | { m ‖ m001 | 0 1/2 1/2 } |
| a+1/2, -b+1/2, -c | x, -y, -z | { 2 ‖ 2100 | 1/2 1/2 0 } |
| -a, -b+1/2, c+1/2 | x, -y, -z | { 2 ‖ 2001 | 0 1/2 1/2 } |
| -a+1/2, -b+1/2, -c | x, -y, -z | { 2 ‖ -1 | 1/2 1/2 0 } |
| a, -b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m010 | 0 1/2 1/2 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 4a | $\ce{^{-1}{2}}/\ce{^{1}{m}}..\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
| 4b | $\ce{^{-1}{2}}/\ce{^{1}{m}}..\ce{^{\infty m}{1}} $ | (1/2,0,0 | 0,0,0) |
| 8c | $\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $ | (1/4,1/4,0 | 0,0,0) |
| 8d | $\ce{^{-1}{2}}..\ce{^{\infty m}{1}} $ | (a,0,0 | 0,0,0) |
| 8e | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (1/4,b,1/4 | 0,0,z) |
| 8f | $\ce{^{1}{m}}..\ce{^{\infty m}{1}} $ | (0,b,c | 0,0,z) |
| 16g | $\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}} $ |
| T:(1,0,1/2) | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| Y:(1,0,0) | $\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}} $ |
| R:(1/2,1/2,1/2) | $\ce{^{2}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| S:(1/2,1/2,0) | $\ce{^{2}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| A:(u,0,1/2) | $\ce{^{m}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| B:(0,v,1/2) | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| H:(1,0,w) | $\ce{^{1}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| Λ:(0,0,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $\ce{^{m}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| D:(1/2,1/2,w) | $\ce{^{2}{2/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| K:(0,v,w) | $\ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| M:(u,0,w) | $\ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| P:(u,v,0) | $\ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Q:(u,v,1/2) | $\ce{^{-1}{2/}}\ce{^{1}{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:(0,1/2,-1/2) | $S_{1}^{S}S_{2}^{S}(4) $ |
| T:(0,-1,1/2) | T:(1/2,0,-1) | $T_{1}^{S}(2)⊕T_{2}^{S}(2) $ |
| Y:(0,-1,0) | Y:(0,0,-1) | $Y_{1}^{S}(2)⊕Y_{2}^{S}(2) $ |
| Z:(0,0,1/2) | Z:(1/2,0,0) | $Z_{1}^{S}(2)⊕Z_{2}^{S}(2) $ |
| A:(u,0,1/2) | B:(1/2,u,0) | $(A)B_{1}^{S}(2)⊕(A)B_{2}^{S}(2) $ |
| B:(0,v,1/2) | A:(1/2,0,v) | $(B)A_{1}^{S}(2)⊕(B)A_{2}^{S}(2) $ |
| D:(1/2,-1/2,-w) | D:(-w,1/2,-1/2) | $D_{1}^{S}D_{1}^{S}(4) $ |
| Δ:(0,v,0) | Σ:(0,0,v) | $(Δ)Σ_{1}^{S}(2)⊕(Δ)Σ_{2}^{S}(2) $ |
| H:(0,-1,w) | H:(w,0,-1) | $H_{1}^{S}(2)⊕H_{2}^{S}(2) $ |
| Λ:(0,0,w) | Λ:(w,0,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ |
| Σ:(u,0,0) | Δ:(0,u,0) | $(Σ)Δ_{1}^{S}(2)⊕(Σ)Δ_{2}^{S}(2) $ |
| K:(0,v,w) | M:(w,0,v) | $(K)M_{1}^{S}(2)⊕(K)M_{2}^{S}(2) $ |
| M:(u,0,w) | K:(w,u,0) | $2(M)K_{1}^{S}(2) $ |
| P:(u,v,0) | P:(0,u,v) | $P_{1}^{S}(2)⊕P_{2}^{S}(2) $ |
| Q:(u,v,1/2) | Q:(1/2,u,v) | $Q_{1}^{S}(2)⊕Q_{2}^{S}(2) $ |
| GP:(u,v,w) | GP:(w,u,v) | $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_{3}^{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:(0,1/2,-1/2) | $S_{1}^{S}S_{2}^{S}(4) $ |
| T:(0,-1,1/2) | T:(1/2,0,-1) | $T_{2}^{S}(2)⊕T_{4}^{S}(2) $ |
| Y:(0,-1,0) | Y:(0,0,-1) | $Y_{2}^{S}(2)⊕Y_{4}^{S}(2) $ |
| Z:(0,0,1/2) | Z:(1/2,0,0) | $Z_{1}^{S}(2)⊕Z_{3}^{S}(2) $ |
| A:(u,0,1/2) | B:(1/2,u,0) | $(A)B_{1}^{S}(2)⊕(A)B_{2}^{S}(2) $ |
| B:(0,v,1/2) | A:(1/2,0,v) | $(B)A_{1}^{S}(2)⊕(B)A_{3}^{S}(2) $ |
| D:(1/2,-1/2,-w) | D:(-w,1/2,-1/2) | $D_{1}^{S}D_{1}^{S}(4) $ |
| Δ:(0,v,0) | Σ:(0,0,v) | $(Δ)Σ_{1}^{S}(2)⊕(Δ)Σ_{3}^{S}(2) $ |
| H:(0,-1,w) | H:(w,0,-1) | $2H_{2}^{S}(2) $ |
| Λ:(0,0,w) | Λ:(w,0,0) | $2Λ_{1}^{S}(2) $ |
| Σ:(u,0,0) | Δ:(0,u,0) | $(Σ)Δ_{1}^{S}(2)⊕(Σ)Δ_{2}^{S}(2) $ |
| K:(0,v,w) | M:(w,0,v) | $2(K)M_{1}^{S}(2) $ |
| M:(u,0,w) | K:(w,u,0) | $2(M)K_{1}^{S}(2) $ |
| P:(u,v,0) | P:(0,u,v) | $P_{1}^{S}(2)⊕P_{2}^{S}(2) $ |
| Q:(u,v,1/2) | Q:(1/2,u,v) | $Q_{1}^{S}(2)⊕Q_{2}^{S}(2) $ |
| GP:(u,v,w) | GP:(w,u,v) | $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) | $2R_{1}^{S}R_{2}^{S}(4) $ |
| S:(1/2,-1/2,0) | S:(0,1/2,-1/2) | $2S_{1}^{S}S_{2}^{S}(4) $ |
| T:(0,-1,1/2) | T:(1/2,0,-1) | $T_{1}^{S}(2)⊕T_{2}^{S}(2)⊕T_{3}^{S}(2)⊕T_{4}^{S}(2) $ |
| Y:(0,-1,0) | Y:(0,0,-1) | $Y_{1}^{S}(2)⊕Y_{2}^{S}(2)⊕Y_{3}^{S}(2)⊕Y_{4}^{S}(2) $ |
| Z:(0,0,1/2) | Z:(1/2,0,0) | $Z_{1}^{S}(2)⊕Z_{2}^{S}(2)⊕Z_{3}^{S}(2)⊕Z_{4}^{S}(2) $ |
| A:(u,0,1/2) | B:(1/2,u,0) | $2(A)B_{1}^{S}(2)⊕2(A)B_{2}^{S}(2) $ |
| B:(0,v,1/2) | A:(1/2,0,v) | $(B)A_{1}^{S}(2)⊕(B)A_{2}^{S}(2)⊕(B)A_{3}^{S}(2)⊕(B)A_{4}^{S}(2) $ |
| D:(1/2,-1/2,-w) | D:(-w,1/2,-1/2) | $2D_{1}^{S}D_{1}^{S}(4) $ |
| Δ:(0,v,0) | Σ:(0,0,v) | $(Δ)Σ_{1}^{S}(2)⊕(Δ)Σ_{2}^{S}(2)⊕(Δ)Σ_{3}^{S}(2)⊕(Δ)Σ_{4}^{S}(2) $ |
| H:(0,-1,w) | H:(w,0,-1) | $2H_{1}^{S}(2)⊕2H_{2}^{S}(2) $ |
| Λ:(0,0,w) | Λ:(w,0,0) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2) $ |
| Σ:(u,0,0) | Δ:(0,u,0) | $2(Σ)Δ_{1}^{S}(2)⊕2(Σ)Δ_{2}^{S}(2) $ |
| K:(0,v,w) | M:(w,0,v) | $2(K)M_{1}^{S}(2)⊕2(K)M_{2}^{S}(2) $ |
| M:(u,0,w) | K:(w,u,0) | $4(M)K_{1}^{S}(2) $ |
| P:(u,v,0) | P:(0,u,v) | $2P_{1}^{S}(2)⊕2P_{2}^{S}(2) $ |
| Q:(u,v,1/2) | Q:(1/2,u,v) | $2Q_{1}^{S}(2)⊕2Q_{2}^{S}(2) $ |
| GP:(u,v,w) | GP:(w,u,v) | $4GP_{1}^{S}(2) $ |