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 ‖ 2001 | 0 } |
| -a+1/2, b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m100 | 1/2 1/2 1/2 } |
| a+1/2, -b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m010 | 1/2 1/2 1/2 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| -a, -b, c | -x, y, z | { m ‖ 2001 | 0 } |
| -a+1/2, b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m100 | 1/2 1/2 1/2 } |
| a+1/2, -b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m010 | 1/2 1/2 1/2 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 2a | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,z) |
| 2b | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,1/2,c | 0,0,z) |
| 4c | $\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}{2}}\ce{^{\infty m}{1}} $ |
| R:(1/2,1/2,1/2) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| S:(1/2,1/2,0) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| T:(0,1/2,1/2) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| U:(1/2,0,1/2) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| X:(1/2,0,0) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| Y:(0,1/2,0) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| Z:(0,0,1/2) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
| A:(u,0,1/2) | $ \ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| B:(0,v,1/2) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| C:(u,1/2,0) | $ \ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| D:(1/2,v,0) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| E:(u,1/2,1/2) | $ \ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| G:(1/2,0,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| H:(0,1/2,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| Λ:(0,0,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| P:(1/2,v,1/2) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| Q:(1/2,1/2,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $ \ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| K:(0,v,w) | $ \ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| L:(1/2,v,w) | $ \ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| M:(u,0,w) | $ \ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| N:(u,1/2,w) | $ \ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| V:(u,v,0) | $ \ce{^{m}{2}}\ce{^{\infty}{1}} $ |
| W:(u,v,1/2) | $ \ce{^{m}{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) | A:(1/2,0,1/2) | $(S)A_{1}^{S}(2) $ | |
| T:(0,1/2,-1/2) | D:(0,1/2,1/2) | $(T)D_{1}^{S}(2) $ | |
| U:(1/2,0,-1/2) | C:(1/2,1/2,0) | $(U)C_{1}^{S}(2) $ | |
| X:(1/2,0,0) | Y:(1/2,0,0) | $(X)Y_{1}^{S}(2) $ | |
| Y:(0,1/2,0) | B:(0,0,1/2) | $(Y)B_{1}^{S}(2) $ | |
| Z:(0,0,-1/2) | Z:(0,1/2,0) | $Z_{1}^{S}(2) $ | |
| A:(u,0,-1/2) | G:(u,1/2,0) | $(A)G_{1}^{S}(2) $ | |
| B:(0,v,-1/2) | G:(0,1/2,v) | $(B)G_{1}^{S}(2) $ | |
| C:(u,1/2,0) | F:(u,0,1/2) | $(C)F_{1}^{S}(2) $ | |
| D:(1/2,v,0) | F:(1/2,0,v) | $(D)F_{1}^{S}(2) $ | |
| Δ:(0,v,0) | F:(0,0,v) | $(Δ)F_{1}^{S}(2) $ | |
| E:(u,1/2,-1/2) | G:(u,1/2,1/2) | $(E)G_{1}^{S}(2) $ | |
| G:(1/2,0,w) | W:(1/2,-w,0) | $(G)W_{1}^{S}(2) $ | |
| H:(0,1/2,w) | V:(0,-w,1/2) | $(H)V_{1}^{S}(2) $ | |
| Λ:(0,0,w) | Λ:(0,-w,0) | $Λ_{1}^{S}(2) $ | |
| P:(1/2,v,-1/2) | G:(1/2,1/2,v) | $(P)G_{1}^{S}(2) $ | |
| Q:(1/2,1/2,w) | U:(1/2,-w,1/2) | $(Q)U_{1}^{S}(2) $ | |
| Σ:(u,0,0) | F:(u,0,0) | $(Σ)F_{1}^{S}(2) $ | |
| K:(0,v,w) | GP:(0,-w,v) | $(K)GP_{1}^{S}(2) $ | |
| L:(1/2,v,w) | GP:(1/2,-w,v) | $(L)GP_{1}^{S}(2) $ | |
| M:(u,0,w) | GP:(u,-w,0) | $(M)GP_{1}^{S}(2) $ | |
| N:(u,1/2,w) | GP:(u,-w,1/2) | $(N)GP_{1}^{S}(2) $ | |
| V:(u,v,0) | F:(u,0,v) | $2(V)F_{1}^{S}(1)$ | Spin Splitting |
| W:(u,v,-1/2) | G:(u,1/2,v) | $2(W)G_{1}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,-w,v) | $2GP_{1}^{S}(1)$ | 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) | A:(1/2,0,1/2) | $(S)A_{2}^{S}(2) $ | |
| T:(0,1/2,-1/2) | D:(0,1/2,1/2) | $(T)D_{1}^{S}(2) $ | |
| U:(1/2,0,-1/2) | C:(1/2,1/2,0) | $(U)C_{2}^{S}(2) $ | |
| X:(1/2,0,0) | Y:(1/2,0,0) | $(X)Y_{2}^{S}(2) $ | |
| Y:(0,1/2,0) | B:(0,0,1/2) | $(Y)B_{1}^{S}(2) $ | |
| Z:(0,0,-1/2) | Z:(0,1/2,0) | $Z_{1}^{S}(2) $ | |
| A:(u,0,-1/2) | G:(u,1/2,0) | $(A)G_{1}^{S}(2) $ | |
| B:(0,v,-1/2) | G:(0,1/2,v) | $(B)G_{1}^{S}(2) $ | |
| C:(u,1/2,0) | F:(u,0,1/2) | $(C)F_{1}^{S}(2) $ | |
| D:(1/2,v,0) | F:(1/2,0,v) | $(D)F_{1}^{S}(2) $ | |
| Δ:(0,v,0) | F:(0,0,v) | $(Δ)F_{1}^{S}(2) $ | |
| E:(u,1/2,-1/2) | G:(u,1/2,1/2) | $(E)G_{1}^{S}(2) $ | |
| G:(1/2,0,w) | W:(1/2,-w,0) | $(G)W_{2}^{S}(2) $ | |
| H:(0,1/2,w) | V:(0,-w,1/2) | $(H)V_{1}^{S}(2) $ | |
| Λ:(0,0,w) | Λ:(0,-w,0) | $Λ_{1}^{S}(2) $ | |
| P:(1/2,v,-1/2) | G:(1/2,1/2,v) | $(P)G_{1}^{S}(2) $ | |
| Q:(1/2,1/2,w) | U:(1/2,-w,1/2) | $(Q)U_{2}^{S}(2) $ | |
| Σ:(u,0,0) | F:(u,0,0) | $(Σ)F_{1}^{S}(2) $ | |
| K:(0,v,w) | GP:(0,-w,v) | $(K)GP_{1}^{S}(2) $ | |
| L:(1/2,v,w) | GP:(1/2,-w,v) | $(L)GP_{1}^{S}(2) $ | |
| M:(u,0,w) | GP:(u,-w,0) | $(M)GP_{1}^{S}(2) $ | |
| N:(u,1/2,w) | GP:(u,-w,1/2) | $(N)GP_{1}^{S}(2) $ | |
| V:(u,v,0) | F:(u,0,v) | $2(V)F_{1}^{S}(1)$ | Spin Splitting |
| W:(u,v,-1/2) | G:(u,1/2,v) | $2(W)G_{1}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,-w,v) | $2GP_{1}^{S}(1)$ | 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) | A:(1/2,0,1/2) | $(S)A_{1}^{S}(2)⊕(S)A_{2}^{S}(2) $ | |
| T:(0,1/2,-1/2) | D:(0,1/2,1/2) | $(T)D_{1}^{S}(2)⊕(T)D_{2}^{S}(2) $ | |
| U:(1/2,0,-1/2) | C:(1/2,1/2,0) | $(U)C_{1}^{S}(2)⊕(U)C_{2}^{S}(2) $ | |
| X:(1/2,0,0) | Y:(1/2,0,0) | $(X)Y_{1}^{S}(2)⊕(X)Y_{2}^{S}(2) $ | |
| Y:(0,1/2,0) | B:(0,0,1/2) | $(Y)B_{1}^{S}(2)⊕(Y)B_{2}^{S}(2) $ | |
| Z:(0,0,-1/2) | Z:(0,1/2,0) | $Z_{1}^{S}(2)⊕Z_{2}^{S}(2) $ | |
| A:(u,0,-1/2) | G:(u,1/2,0) | $2(A)G_{1}^{S}(2) $ | |
| B:(0,v,-1/2) | G:(0,1/2,v) | $2(B)G_{1}^{S}(2) $ | |
| C:(u,1/2,0) | F:(u,0,1/2) | $2(C)F_{1}^{S}(2) $ | |
| D:(1/2,v,0) | F:(1/2,0,v) | $2(D)F_{1}^{S}(2) $ | |
| Δ:(0,v,0) | F:(0,0,v) | $2(Δ)F_{1}^{S}(2) $ | |
| E:(u,1/2,-1/2) | G:(u,1/2,1/2) | $2(E)G_{1}^{S}(2) $ | |
| G:(1/2,0,w) | W:(1/2,-w,0) | $(G)W_{1}^{S}(2)⊕(G)W_{2}^{S}(2) $ | |
| H:(0,1/2,w) | V:(0,-w,1/2) | $(H)V_{1}^{S}(2)⊕(H)V_{2}^{S}(2) $ | |
| Λ:(0,0,w) | Λ:(0,-w,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
| P:(1/2,v,-1/2) | G:(1/2,1/2,v) | $2(P)G_{1}^{S}(2) $ | |
| Q:(1/2,1/2,w) | U:(1/2,-w,1/2) | $(Q)U_{1}^{S}(2)⊕(Q)U_{2}^{S}(2) $ | |
| Σ:(u,0,0) | F:(u,0,0) | $2(Σ)F_{1}^{S}(2) $ | |
| K:(0,v,w) | GP:(0,-w,v) | $2(K)GP_{1}^{S}(2) $ | |
| L:(1/2,v,w) | GP:(1/2,-w,v) | $2(L)GP_{1}^{S}(2) $ | |
| M:(u,0,w) | GP:(u,-w,0) | $2(M)GP_{1}^{S}(2) $ | |
| N:(u,1/2,w) | GP:(u,-w,1/2) | $2(N)GP_{1}^{S}(2) $ | |
| V:(u,v,0) | F:(u,0,v) | $4(V)F_{1}^{S}(1)$ | Spin Splitting |
| W:(u,v,-1/2) | G:(u,1/2,v) | $4(W)G_{1}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,-w,v) | $4GP_{1}^{S}(1)$ | Spin Splitting |