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+1/2 | -x, -y, -z | { -1 ‖ 2010 | 0 0 1/2 } |
| -a, -b, c+1/2 | -x, -y, -z | { -1 ‖ 2001 | 0 0 1/2 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| a, -b, -c | -x, y, z | { m ‖ 2100 | 0 } |
| -a, b, -c+1/2 | x, -y, -z | { 2 ‖ 2010 | 0 0 1/2 } |
| -a, -b, c+1/2 | x, -y, -z | { 2 ‖ 2001 | 0 0 1/2 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 2a | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,0,0 | 0,0,z) |
| 2b | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,1/2,0 | 0,0,z) |
| 2c | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (0,b,1/4 | 0,0,0) |
| 2d | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (1/2,b,1/4 | 0,0,0) |
| 4e | $\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}} $ |
| R:(1/2,1/2,1/2) | $ \ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ |
| S:(1/2,1/2,0) | $ \ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ |
| T:(0,1/2,1/2) | $ \ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ |
| U:(1/2,0,1/2) | $ \ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ |
| X:(1/2,0,0) | $ \ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ |
| Y:(0,1/2,0) | $ \ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ |
| Z:(0,0,1/2) | $ \ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ |
| A:(u,0,1/2) | $ \ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| B:(0,v,1/2) | $ \ce{^{m}{2}}\ce{^{2}{2}}\ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| C:(u,1/2,0) | $ \ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| D:(1/2,v,0) | $ \ce{^{m}{2}}\ce{^{2}{2}}\ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $ \ce{^{m}{2}}\ce{^{2}{2}}\ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| E:(u,1/2,1/2) | $ \ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| G:(1/2,0,w) | $ \ce{^{m}{2}}\ce{^{-1}{2}}\ce{^{2}{2}}\ce{^{\infty}{1}} $ |
| H:(0,1/2,w) | $ \ce{^{m}{2}}\ce{^{-1}{2}}\ce{^{2}{2}}\ce{^{\infty}{1}} $ |
| Λ:(0,0,w) | $ \ce{^{m}{2}}\ce{^{-1}{2}}\ce{^{2}{2}}\ce{^{\infty}{1}} $ |
| P:(1/2,v,1/2) | $ \ce{^{m}{2}}\ce{^{2}{2}}\ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| Q:(1/2,1/2,w) | $ \ce{^{m}{2}}\ce{^{-1}{2}}\ce{^{2}{2}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $ \ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| K:(0,v,w) | $ \ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| L:(1/2,v,w) | $ \ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| M:(u,0,w) | $ \ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| N:(u,1/2,w) | $ \ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| V:(u,v,0) | $ \ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| W:(u,v,1/2) | $ \ce{^{-1}{2}}\ce{^{\infty}{1}} $ |
| GP:(u,v,w) | $ \ce{^{1}{1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
| k-vector | k-vector-G↑ | A↑G(2) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2) $ | |
| R:(1/2,-1/2,1/2) | E:(1/2,1/2,1/2) | $(R)E_{1}^{S}(2) $ | |
| S:(1/2,-1/2,0) | C:(1/2,1/2,0) | $(S)C_{1}^{S}(2) $ | |
| T:(0,-1/2,1/2) | A:(1/2,0,1/2) | $(T)A_{1}^{S}(2) $ | |
| U:(1/2,0,1/2) | D:(0,1/2,1/2) | $(U)D_{1}^{S}(2) $ | |
| X:(1/2,0,0) | Z:(0,1/2,0) | $(X)Z_{1}^{S}(2) $ | |
| Y:(0,-1/2,0) | Y:(1/2,0,0) | $Y_{1}^{S}(2) $ | |
| Z:(0,0,1/2) | B:(0,0,1/2) | $(Z)B_{1}^{S}(2) $ | |
| A:(u,0,1/2) | V:(0,u,1/2) | $(A)V_{1}^{S}(2) $ | |
| B:(0,v,1/2) | F:(-v,0,1/2) | $(B)F_{1}^{S}(2) $ | |
| C:(u,-1/2,0) | W:(1/2,u,0) | $(C)W_{1}^{S}(2) $ | |
| D:(1/2,v,0) | G:(-v,1/2,0) | $(D)G_{1}^{S}(2) $ | |
| Δ:(0,v,0) | F:(-v,0,0) | $(Δ)F_{1}^{S}(2) $ | |
| E:(u,-1/2,1/2) | U:(1/2,u,1/2) | $(E)U_{1}^{S}(2) $ | |
| G:(1/2,0,w) | G:(0,1/2,w) | $G_{1}^{S}(2) $ | |
| H:(0,1/2,w) | F:(-1/2,0,w) | $(H)F_{1}^{S}(2) $ | |
| Λ:(0,0,w) | F:(0,0,w) | $(Λ)F_{1}^{S}(2) $ | |
| P:(1/2,v,1/2) | G:(-v,1/2,1/2) | $(P)G_{1}^{S}(2) $ | |
| Q:(1/2,1/2,w) | G:(-1/2,1/2,w) | $(Q)G_{1}^{S}(2) $ | |
| Σ:(u,0,0) | Λ:(0,u,0) | $(Σ)Λ_{1}^{S}(2) $ | |
| K:(0,v,w) | F:(-v,0,w) | $2 (K)F_{1}^{S}(1)$ | Spin Splitting |
| L:(1/2,v,w) | G:(-v,1/2,w) | $2 (L)G_{1}^{S}(1)$ | Spin Splitting |
| M:(u,0,w) | GP:(0,u,w) | $(M)GP_{1}^{S}(2) $ | |
| N:(u,1/2,w) | GP:(-1/2,u,w) | $(N)GP_{1}^{S}(2) $ | |
| V:(u,v,0) | GP:(-v,u,0) | $(V)GP_{1}^{S}(2) $ | |
| W:(u,v,1/2) | GP:(-v,u,1/2) | $(W)GP_{1}^{S}(2) $ | |
| GP:(u,v,w) | GP:(-v,u,w) | $2GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A↑G(2) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2) $ | |
| R:(1/2,-1/2,1/2) | E:(1/2,1/2,1/2) | $(R)E_{2}^{S}(2) $ | |
| S:(1/2,-1/2,0) | C:(1/2,1/2,0) | $(S)C_{1}^{S}(1) $ | |
| T:(0,-1/2,1/2) | A:(1/2,0,1/2) | $(T)A_{2}^{S}(2) $ | |
| U:(1/2,0,1/2) | D:(0,1/2,1/2) | $(U)D_{2}^{S}(2) $ | |
| X:(1/2,0,0) | Z:(0,1/2,0) | $(X)Z_{1}^{S}(2) $ | |
| Y:(0,-1/2,0) | Y:(1/2,0,0) | $Y_{1}^{S}(2) $ | |
| Z:(0,0,1/2) | B:(0,0,1/2) | $(Z)B_{2}^{S}(2) $ | |
| A:(u,0,1/2) | V:(0,u,1/2) | $(A)V_{2}^{S}(2) $ | |
| B:(0,v,1/2) | F:(-v,0,1/2) | $(B)F_{1}^{S}(2) $ | |
| C:(u,-1/2,0) | W:(1/2,u,0) | $(C)W_{1}^{S}(2) $ | |
| D:(1/2,v,0) | G:(-v,1/2,0) | $(D)G_{1}^{S}(2) $ | |
| Δ:(0,v,0) | F:(-v,0,0) | $(Δ)F_{1}^{S}(2) $ | |
| E:(u,-1/2,1/2) | U:(1/2,u,1/2) | $(E)U_{2}^{S}(2) $ | |
| G:(1/2,0,w) | G:(0,1/2,w) | $G_{1}^{S}(2) $ | |
| H:(0,1/2,w) | F:(-1/2,0,w) | $(H)F_{1}^{S}(2) $ | |
| Λ:(0,0,w) | F:(0,0,w) | $(Λ)F_{1}^{S}(2) $ | |
| P:(1/2,v,1/2) | G:(-v,1/2,1/2) | $(P)G_{1}^{S}(2) $ | |
| Q:(1/2,1/2,w) | G:(-1/2,1/2,w) | $(Q)G_{1}^{S}(2) $ | |
| Σ:(u,0,0) | Λ:(0,u,0) | $(Σ)Λ_{1}^{S}(2) $ | |
| K:(0,v,w) | F:(-v,0,w) | $2 (K)F_{1}^{S}(1)$ | Spin Splitting |
| L:(1/2,v,w) | G:(-v,1/2,w) | $2 (L)G_{1}^{S}(1)$ | Spin Splitting |
| M:(u,0,w) | GP:(0,u,w) | $(M)GP_{1}^{S}(2) $ | |
| N:(u,1/2,w) | GP:(-1/2,u,w) | $(N)GP_{1}^{S}(2) $ | |
| V:(u,v,0) | GP:(-v,u,0) | $(V)GP_{1}^{S}(2) $ | |
| W:(u,v,1/2) | GP:(-v,u,1/2) | $(W)GP_{1}^{S}(2) $ | |
| GP:(u,v,w) | GP:(-v,u,w) | $2GP_{1}^{S}(1)$ | Spin Splitting |
| 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) | E:(1/2,1/2,1/2) | $(R)E_{1}^{S}(2)⊕(R)E_{2}^{S}(2) $ | |
| S:(1/2,-1/2,0) | C:(1/2,1/2,0) | $(S)C_{1}^{S}(2)⊕(S)C_{2}^{S}(2) $ | |
| T:(0,-1/2,1/2) | A:(1/2,0,1/2) | $(T)A_{1}^{S}(2)⊕(T)A_{2}^{S}(2) $ | |
| U:(1/2,0,1/2) | D:(0,1/2,1/2) | $(U)D_{1}^{S}(2)⊕(U)D_{2}^{S}(2) $ | |
| X:(1/2,0,0) | Z:(0,1/2,0) | $(X)Z_{1}^{S}(2)⊕(X)Z_{2}^{S}(2) $ | |
| Y:(0,-1/2,0) | Y:(1/2,0,0) | $Y_{1}^{S}(2)⊕Y_{2}^{S}(2) $ | |
| Z:(0,0,1/2) | B:(0,0,1/2) | $(Z)B_{1}^{S}(2)⊕(Z)B_{2}^{S}(2) $ | |
| A:(u,0,1/2) | V:(0,u,1/2) | $(A)V_{1}^{S}(2)⊕(A)V_{2}^{S}(2) $ | |
| B:(0,v,1/2) | F:(-v,0,1/2) | $2 (B)F_{1}^{S}(2) $ | |
| C:(u,-1/2,0) | W:(1/2,u,0) | $(C)W_{1}^{S}(2)⊕(C)W_{2}^{S}(2) $ | |
| D:(1/2,v,0) | G:(-v,1/2,0) | $2 (D)G_{1}^{S}(2) $ | |
| Δ:(0,v,0) | F:(-v,0,0) | $2 (Δ)F_{1}^{S}(2) $ | |
| E:(u,-1/2,1/2) | U:(1/2,u,1/2) | $(E)U_{1}^{S}(2)⊕(E)U_{2}^{S}(2) $ | |
| G:(1/2,0,w) | G:(0,1/2,w) | $2 G_{1}^{S}(2) $ | |
| H:(0,1/2,w) | F:(-1/2,0,w) | $2 (H)F_{1}^{S}(2) $ | |
| Λ:(0,0,w) | F:(0,0,w) | $2 (Λ)F_{1}^{S}(2) $ | |
| P:(1/2,v,1/2) | G:(-v,1/2,1/2) | $2 (P)G_{1}^{S}(2) $ | |
| Q:(1/2,1/2,w) | G:(-1/2,1/2,w) | $2 (Q)G_{1}^{S}(2) $ | |
| Σ:(u,0,0) | Λ:(0,u,0) | $(Σ)Λ_{1}^{S}(2)⊕2(Σ)Λ_{2}^{S}(2) $ | |
| K:(0,v,w) | F:(-v,0,w) | $4 (K)F_{1}^{S}(1)$ | Spin Splitting |
| L:(1/2,v,w) | G:(-v,1/2,w) | $4 (L)G_{1}^{S}(1)$ | Spin Splitting |
| M:(u,0,w) | GP:(0,u,w) | $2 (M)GP_{1}^{S}(2) $ | |
| N:(u,1/2,w) | GP:(-1/2,u,w) | $2 (N)GP_{1}^{S}(2) $ | |
| V:(u,v,0) | GP:(-v,u,0) | $2(V)GP_{1}^{S}(2) $ | |
| W:(u,v,1/2) | GP:(-v,u,1/2) | $2(W)GP_{1}^{S}(2) $ | |
| GP:(u,v,w) | GP:(-v,u,w) | $4GP_{1}^{S}(1)$ | Spin Splitting |