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, -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 | { -1 ‖ 2100 | 0 } |
| -a+1/2, b, -c | -x, -y, -z | { -1 ‖ 2010 | 1/2 0 0 } |
| -a, b, c | -x, -y, -z | { -1 ‖ m100 | 0 } |
| a+1/2, -b, c | -x, -y, -z | { -1 ‖ m010 | 1/2 0 0 } |
| a+1/2, b+1/2, c | x, y, z | { 1 ‖ 1 | 1/2 1/2 0 } |
| -a, -b+1/2, c | x, y, z | { 1 ‖ 2001 | 0 1/2 0 } |
| -a+1/2, -b+1/2, -c | x, y, z | { 1 ‖ -1 | 1/2 1/2 0 } |
| a, b+1/2, -c | x, y, z | { 1 ‖ m001 | 0 1/2 0 } |
| a+1/2, -b+1/2, -c | -x, -y, -z | { -1 ‖ 2100 | 1/2 1/2 0 } |
| -a, b+1/2, -c | -x, -y, -z | { -1 ‖ 2010 | 0 1/2 0 } |
| -a+1/2, b+1/2, c | -x, -y, -z | { -1 ‖ m100 | 1/2 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+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 | -x, y, z | { m ‖ m001 | 1/2 0 0 } |
| a, -b, -c | x, -y, -z | { 2 ‖ 2100 | 0 } |
| -a+1/2, b, -c | x, -y, -z | { 2 ‖ 2010 | 1/2 0 0 } |
| -a, b, c | x, -y, -z | { 2 ‖ m100 | 0 } |
| a+1/2, -b, c | x, -y, -z | { 2 ‖ m010 | 1/2 0 0 } |
| a+1/2, b+1/2, c | -x, y, z | { m ‖ 1 | 1/2 1/2 0 } |
| -a, -b+1/2, c | -x, y, z | { m ‖ 2001 | 0 1/2 0 } |
| -a+1/2, -b+1/2, -c | -x, y, z | { m ‖ -1 | 1/2 1/2 0 } |
| a, b+1/2, -c | -x, y, z | { m ‖ m001 | 0 1/2 0 } |
| a+1/2, -b+1/2, -c | x, -y, -z | { 2 ‖ 2100 | 1/2 1/2 0 } |
| -a, b+1/2, -c | x, -y, -z | { 2 ‖ 2010 | 0 1/2 0 } |
| -a+1/2, b+1/2, c | x, -y, -z | { 2 ‖ m100 | 1/2 1/2 0 } |
| a, -b+1/2, c | x, -y, -z | { 2 ‖ m010 | 0 1/2 0 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 4a | $\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/4,0,0 | 0,0,0) |
| 4b | $\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/4,0,1/2 | 0,0,0) |
| 4c | $\ce{^{-1}{2}}/\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
| 4d | $\ce{^{-1}{2}}/\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,0) |
| 4e | $.\ce{^{-1}{2}}/\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (1/4,1/4,0 | 0,0,0) |
| 4f | $.\ce{^{-1}{2}}/\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (1/4,1/4,1/2 | 0,0,0) |
| 4g | $\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,1/4,c | 0,0,0) |
| 8h | $\ce{^{-1}{2}}..\ce{^{\infty m}{1}} $ | (a,0,0 | 0,0,0) |
| 8i | $\ce{^{-1}{2}}..\ce{^{\infty m}{1}} $ | (a,0,1/2 | 0,0,0) |
| 8j | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (1/4,b,0 | 0,0,0) |
| 8k | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (1/4,b,1/2 | 0,0,0) |
| 8l | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/4,0,c | 0,0,z) |
| 8m | $\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (0,b,c | 0,0,0) |
| 8n | $.\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (a,1/4,c | 0,0,0) |
| 16o | $\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{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| S:(1/2,1/2,0) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| A:(u,0,1/2) | $\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| B:(0,v,1/2) | $\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| H:(1,0,w) | $\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| Λ:(0,0,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| D:(1/2,1/2,w) | $\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| K:(0,v,w) | $\ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| M:(u,0,w) | $\ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| P:(u,v,0) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Q:(u,v,1/2) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| GP:(u,v,w) | $\ce{^{m}{-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_{1}^{S,-}(2) $ | |
| R:(-1/2,-1/2,1/2) | D:(0,1/2,1/2) | $2 (R)D_{1}^{S}(2)$ | Spin Splitting |
| S:(-1/2,-1/2,0) | B:(0,0,1/2) | $2 (S)B_{1}^{S}(2)$ | Spin Splitting |
| T:(1,0,1/2) | C:(1/2,1/2,0) | $(T)C_{1}^{S,+}(2)⊕(T)C_{1}^{S,-}(2) $ | |
| Y:(1,0,0) | Y:(1/2,0,0) | $Y_{1}^{S,+}(2)⊕Y_{1}^{S,-}(2) $ | |
| Z:(0,0,1/2) | Z:(0,1/2,0) | $Z_{1}^{S,+}(2)⊕Z_{1}^{S,-}(2) $ | |
| A:(u,0,1/2) | G:(u/2,1/2,0) | $(A)G_{1}^{S}(2)⊕(A)G_{2}^{S}(2) $ | |
| B:(0,v,1/2) | G:(-v/2,1/2,-v) | $(B)G_{1}^{S}(2)⊕(B)G_{2}^{S}(2) $ | |
| D:(-1/2,-1/2,w) | V:(0,w,1/2) | $2(D)V_{1}^{S}V_{2}^{S}(2)$ | Spin Splitting |
| Δ:(0,v,0) | F:(-v/2,0,-v) | $(Δ)F_{1}^{S}(2)⊕(Δ)F_{2}^{S}(2) $ | |
| H:(1,0,w) | W:(1/2,w,0) | $2(H)W_{1}^{S}(2) $ | |
| Λ:(0,0,w) | Λ:(0,w,0) | $2Λ_{1}^{S}(2) $ | |
| Σ:(u,0,0) | F:(u/2,0,0) | $(Σ)F_{1}^{S}(2)⊕(Σ)F_{2}^{S}(2) $ | |
| K:(0,v,w) | GP:(-v/2,w,-v) | $2(K)GP_{1}^{S}(2) $ | |
| M:(u,0,w) | GP:(u/2,w,0) | $2(M)GP_{1}^{S}(2) $ | |
| P:(u,v,0) | F:(u/2-v/2,0,-v) | $2(P)F_{1}^{S}(1)⊕2(P)F_{2}^{S}(1)$ | Spin Splitting |
| Q:(u,v,1/2) | G:(u/2-v/2,1/2,-v) | $2(Q)G_{1}^{S}(1)⊕2(Q)G_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u/2-v/2,w,-v) | $4GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A↑G(8) | |
| Γ:(0,0,0) | 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) | D:(0,1/2,1/2) | $4(R)D_{1}^{S}(2)$ | Spin Splitting |
| S:(-1/2,-1/2,0) | B:(0,0,1/2) | $4(S)B_{1}^{S}(2)$ | Spin Splitting |
| T:(1,0,1/2) | C:(1/2,1/2,0) | $(T)C_{1}^{S,+}(2)⊕(T)C_{1}^{S,-}(2)⊕(T)C_{2}^{S,+}(2)⊕(T)C_{2}^{S,-}(2) $ | |
| Y:(1,0,0) | Y:(1/2,0,0) | $Y_{1}^{S,+}(2)⊕Y_{1}^{S,-}(2)⊕Y_{2}^{S,+}(2)⊕Y_{2}^{S,-}(2) $ | |
| Z:(0,0,1/2) | Z:(0,1/2,0) | $Z_{1}^{S,+}(2)⊕Z_{1}^{S,-}(2)⊕Z_{2}^{S,+}(2)⊕Z_{2}^{S,-}(2) $ | |
| A:(u,0,1/2) | G:(u/2,1/2,0) | $2(A)G_{1}^{S}(2)⊕2(A)G_{2}^{S}(2) $ | |
| B:(0,v,1/2) | G:(-v/2,1/2,-v) | $2(B)G_{1}^{S}(2)⊕2(B)G_{2}^{S}(2) $ | |
| D:(-1/2,-1/2,w) | V:(0,w,1/2) | $4(D)V_{1}^{S}V_{2}^{S}(2)$ | Spin Splitting |
| Δ:(0,v,0) | F:(-v/2,0,-v) | $2(Δ)F_{1}^{S}(2)⊕2(Δ)F_{2}^{S}(2) $ | |
| H:(1,0,w) | W:(1/2,w,0) | $2(H)W_{1}^{S}(2)⊕2(H)W_{2}^{S}(2) $ | |
| Λ:(0,0,w) | Λ:(0,w,0) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2) $ | |
| Σ:(u,0,0) | F:(u/2,0,0) | $2(Σ)F_{1}^{S}(2)⊕2(Σ)F_{2}^{S}(2) $ | |
| K:(0,v,w) | GP:(-v/2,w,-v) | $4(K)GP_{1}^{S}(2) $ | |
| M:(u,0,w) | GP:(u/2,w,0) | $4(M)GP_{1}^{S}(2) $ | |
| P:(u,v,0) | F:(u/2-v/2,0,-v) | $4(P)F_{1}^{S}(1)⊕4(P)F_{2}^{S}(1)$ | Spin Splitting |
| Q:(u,v,1/2) | G:(u/2-v/2,1/2,-v) | $4(Q)G_{1}^{S}(1)⊕4(Q)G_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u/2-v/2,w,-v) | $8GP_{1}^{S}(1)$ | Spin Splitting |