The continuously infinite group ∞1 is omitted.
| Coordinates | Seitz symbol |
|---|---|
| a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
| -a+1/2, -b+1/2, c | x, y, z | { 1 ‖ 2001 | 1/2 1/2 0 } |
| -a, -b, -c | x, y, z | { 1 ‖ -1 | 0 } |
| a+1/2, b+1/2, -c | x, y, z | { 1 ‖ m001 | 1/2 1/2 0 } |
| -b, a+1/2, c+1/2 | -x, -y, -z | { -1 ‖ 4+001 | 0 1/2 1/2 } |
| b+1/2, -a, c+1/2 | -x, -y, -z | { -1 ‖ 4-001 | 1/2 0 1/2 } |
| b, -a+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ -4+001 | 0 1/2 1/2 } |
| -b+1/2, a, -c+1/2 | -x, -y, -z | { -1 ‖ -4-001 | 1/2 0 1/2 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| -a+1/2, -b+1/2, c | -x, y, z | { m ‖ 2001 | 1/2 1/2 0 } |
| -a, -b, -c | -x, y, z | { m ‖ -1 | 0 } |
| a+1/2, b+1/2, -c | -x, y, z | { m ‖ m001 | 1/2 1/2 0 } |
| -b, a+1/2, c+1/2 | x, -y, -z | { 2 ‖ 4+001 | 0 1/2 1/2 } |
| b+1/2, -a, c+1/2 | x, -y, -z | { 2 ‖ 4-001 | 1/2 0 1/2 } |
| b, -a+1/2, -c+1/2 | x, -y, -z | { 2 ‖ -4+001 | 0 1/2 1/2 } |
| -b+1/2, a, -c+1/2 | x, -y, -z | { 2 ‖ -4-001 | 1/2 0 1/2 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 2a | $\ce{^{-1}{-4}}..\ce{^{\infty m}{1}} $ | (1/4,1/4,1/4 | 0,0,0) |
| 2b | $\ce{^{-1}{-4}}..\ce{^{\infty m}{1}} $ | (1/4,1/4,3/4 | 0,0,0) |
| 4c | $\ce{^{1}{-1}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,z) |
| 4d | $\ce{^{1}{-1}}\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,z) |
| 4e | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (3/4,1/4,c | 0,0,z) |
| 4f | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (1/4,1/4,c | 0,0,z) |
| 8g | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
| Wavevector-k | Little co-group |
|---|---|
| A:(1/2,1/2,1/2) | $\ce{^{-1}{4/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| Γ:(0,0,0) | $\ce{^{-1}{4/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| M:(1/2,1/2,0) | $\ce{^{-1}{4/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| Z:(0,0,1/2) | $\ce{^{-1}{4/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| R:(0,1/2,1/2) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| X:(0,1/2,0) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| Λ:(0,0,w) | $\ce{^{2}{4/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| V:(1/2,1/2,w) | $\ce{^{2}{4/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| D:(u,v,0) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| E:(u,v,1/2) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| S:(u,u,1/2) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Σ:(u,u,0) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| T:(u,1/2,1/2) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| U:(0,v,1/2) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| W:(0,1/2,w) | $\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| Y:(u,1/2,0) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| B:(0,v,w) | $\ce{^{m}{-1}}\ce{^{\infty}{1}} $ |
| C:(u,u,w) | $\ce{^{m}{-1}}\ce{^{\infty}{1}} $ |
| F:(u,1/2,w) | $\ce{^{m}{-1}}\ce{^{\infty}{1}} $ |
| GP:(u,v,w) | $\ce{^{m}{-1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
| k-vector | k-vector-G↑ | Ag↑G(4) | |
| A:(1/2,-1/2,-1/2) | C:(1/2,1/2,0) | $(A)C_{1}^{S,+}(2)⊕(A)C_{2}^{S,+}(2) $ | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{2}^{S,+}(2) $ | |
| M:(1/2,-1/2,0) | Y:(1/2,0,0) | $(M)Y_{1}^{S,+}(2)⊕(M)Y_{2}^{S,+}(2) $ | |
| R:(0,1/2,-1/2) | D:(0,1/2,1/2) | $2(R)D_{1}^{S}(2)$ | Spin Splitting |
| X:(0,1/2,0) | B:(0,0,1/2) | $2(X)B_{1}^{S}(2)$ | Spin Splitting |
| Z:(0,0,-1/2) | Z:(0,1/2,0) | $Z_{1}^{S,+}(2)⊕Z_{2}^{S,+}(2) $ | |
| B:(0,v,w) | GP:(0,-w,v) | $4(B)GP_{1}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | GP:(u,-w,2*u) | $4(C)GP_{1}^{S}(1)$ | Spin Splitting |
| D:(u,v,0) | F:(u,0,u+v) | $2(D)F_{1}^{S}(1)⊕2(D)F_{2}^{S}(1)$ | Spin Splitting |
| Δ:(0,v,0) | F:(0,0,v) | $2(Δ)F_{1}^{S}(1)⊕2(Δ)F_{2}^{S}(1)$ | Spin Splitting |
| E:(u,v,-1/2) | G:(u,1/2,u+v) | $2(E)G_{1}^{S}(1)⊕2(E)G_{2}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | GP:(u,-w,1/2+u) | $4(F)GP_{1}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,-w,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
| S:(u,u,-1/2) | G:(u,1/2,2*u) | $2(S)G_{1}^{S}(1)⊕2(S)G_{2}^{S}(1)$ | Spin Splitting |
| Σ:(u,u,0) | F:(u,0,2*u) | $2(Σ)F_{1}^{S}(1)⊕2(Σ)F_{2}^{S}(1)$ | Spin Splitting |
| T:(u,1/2,-1/2) | G:(u,1/2,1/2+u) | $2(T)G_{1}^{S}(1)⊕2(T)G_{2}^{S}(1)$ | Spin Splitting |
| U:(0,v,-1/2) | G:(0,1/2,v) | $2(U)G_{1}^{S}(1)⊕2(U)G_{2}^{S}(1)$ | Spin Splitting |
| V:(1/2,-1/2,w) | W:(1/2,-w,0) | $(V)W_{1}^{S}(2)⊕(V)W_{2}^{S}(2) $ | |
| W:(0,1/2,w) | V:(0,-w,1/2) | $2(W)V_{1}^{S}V_{2}^{S}(2)$ | Spin Splitting |
| Y:(u,1/2,0) | F:(u,0,1/2+u) | $2(Y)F_{1}^{S}(1)⊕2(Y)F_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,-w,u+v) | $4GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | Ag↑G(4) | |
| A:(1/2,-1/2,-1/2) | C:(1/2,1/2,0) | $(A)C_{1}^{S,-}(2)⊕(A)C_{2}^{S,-}(2) $ | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{2}^{S,+}(2) $ | |
| M:(1/2,-1/2,0) | Y:(1/2,0,0) | $(M)Y_{1}^{S,+}(2)⊕(M)Y_{2}^{S,+}(2) $ | |
| R:(0,1/2,-1/2) | D:(0,1/2,1/2) | $2(R)D_{1}^{S}(2)$ | Spin Splitting |
| X:(0,1/2,0) | B:(0,0,1/2) | $2(X)B_{1}^{S}(2)$ | Spin Splitting |
| Z:(0,0,-1/2) | Z:(0,1/2,0) | $Z_{1}^{S,-}(2)⊕Z_{2}^{S,-}(2) $ | |
| B:(0,v,w) | GP:(0,-w,v) | $4(B)GP_{1}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | GP:(u,-w,2*u) | $4(C)GP_{1}^{S}(1)$ | Spin Splitting |
| D:(u,v,0) | F:(u,0,u+v) | $2(D)F_{1}^{S}(1)⊕2(D)F_{2}^{S}(1)$ | Spin Splitting |
| Δ:(0,v,0) | F:(0,0,v) | $2(Δ)F_{1}^{S}(1)⊕2(Δ)F_{2}^{S}(1)$ | Spin Splitting |
| E:(u,v,-1/2) | G:(u,1/2,u+v) | $2(E)G_{1}^{S}(1)⊕2(E)G_{2}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | GP:(u,-w,1/2+u) | $4(F)GP_{1}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,-w,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
| S:(u,u,-1/2) | G:(u,1/2,2*u) | $2(S)G_{1}^{S}(1)⊕2(S)G_{2}^{S}(1)$ | Spin Splitting |
| Σ:(u,u,0) | F:(u,0,2*u) | $2(Σ)F_{1}^{S}(1)⊕2(Σ)F_{2}^{S}(1)$ | Spin Splitting |
| T:(u,1/2,-1/2) | G:(u,1/2,1/2+u) | $2(T)G_{1}^{S}(1)⊕2(T)G_{2}^{S}(1)$ | Spin Splitting |
| U:(0,v,-1/2) | G:(0,1/2,v) | $2(U)G_{1}^{S}(1)⊕2(U)G_{2}^{S}(1)$ | Spin Splitting |
| V:(1/2,-1/2,w) | W:(1/2,-w,0) | $(V)W_{1}^{S}(2)⊕(V)W_{2}^{S}(2) $ | |
| W:(0,1/2,w) | V:(0,-w,1/2) | $2(W)V_{1}^{S}V_{2}^{S}(2)$ | Spin Splitting |
| Y:(u,1/2,0) | F:(u,0,1/2+u) | $2(Y)F_{1}^{S}(1)⊕2(Y)F_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,-w,u+v) | $4GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A↑G(4) | |
| A:(1/2,-1/2,-1/2) | C:(1/2,1/2,0) | $(A)C_{2}^{S,+}(2)⊕(A)C_{2}^{S,-}(2) $ | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2) $ | |
| M:(1/2,-1/2,0) | Y:(1/2,0,0) | $(M)Y_{2}^{S,+}(2)⊕(M)Y_{2}^{S,-}(2) $ | |
| R:(0,1/2,-1/2) | D:(0,1/2,1/2) | $2(R)D_{1}^{S}(2)$ | Spin Splitting |
| X:(0,1/2,0) | B:(0,0,1/2) | $2(X)B_{1}^{S}(2)$ | Spin Splitting |
| Z:(0,0,-1/2) | Z:(0,1/2,0) | $Z_{1}^{S,+}(2)⊕Z_{1}^{S,-}(2) $ | |
| B:(0,v,w) | GP:(0,-w,v) | $4(B)GP_{1}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | GP:(u,-w,2*u) | $4(C)GP_{1}^{S}(1)$ | Spin Splitting |
| D:(u,v,0) | F:(u,0,u+v) | $2(D)F_{1}^{S}(1)⊕2(D)F_{2}^{S}(1)$ | Spin Splitting |
| Δ:(0,v,0) | F:(0,0,v) | $2(Δ)F_{1}^{S}(1)⊕2(Δ)F_{2}^{S}(1)$ | Spin Splitting |
| E:(u,v,-1/2) | G:(u,1/2,u+v) | $2(E)G_{1}^{S}(1)⊕2(E)G_{2}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | GP:(u,-w,1/2+u) | $4(F)GP_{1}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,-w,0) | $2 Λ_{1}^{S}(2) $ | |
| S:(u,u,-1/2) | G:(u,1/2,2*u) | $2(S)G_{1}^{S}(1)⊕2(S)G_{2}^{S}(1)$ | Spin Splitting |
| Σ:(u,u,0) | F:(u,0,2*u) | $2(Σ)F_{1}^{S}(1)⊕2(Σ)F_{2}^{S}(1)$ | Spin Splitting |
| T:(u,1/2,-1/2) | G:(u,1/2,1/2+u) | $2(T)G_{1}^{S}(1)⊕2(T)G_{2}^{S}(1)$ | Spin Splitting |
| U:(0,v,-1/2) | G:(0,1/2,v) | $2(U)G_{1}^{S}(1)⊕2(U)G_{2}^{S}(1)$ | Spin Splitting |
| V:(1/2,-1/2,w) | W:(1/2,-w,0) | $2 (V)W_{2}^{S}(2) $ | |
| W:(0,1/2,w) | V:(0,-w,1/2) | $2(W)V_{1}^{S}V_{2}^{S}(2)$ | Spin Splitting |
| Y:(u,1/2,0) | F:(u,0,1/2+u) | $2(Y)F_{1}^{S}(1)⊕2(Y)F_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,-w,u+v) | $4GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A↑G(4) | |
| A:(1/2,-1/2,-1/2) | C:(1/2,1/2,0) | $(A)C_{1}^{S,+}(2)⊕(A)C_{1}^{S,-}(2) $ | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2) $ | |
| M:(1/2,-1/2,0) | Y:(1/2,0,0) | $(M)Y_{1}^{S,+}(2)⊕(M)Y_{1}^{S,-}(2) $ | |
| R:(0,1/2,-1/2) | D:(0,1/2,1/2) | $2(R)D_{1}^{S}(2)$ | Spin Splitting |
| X:(0,1/2,0) | B:(0,0,1/2) | $2(X)B_{1}^{S}(2)$ | Spin Splitting |
| Z:(0,0,-1/2) | Z:(0,1/2,0) | $Z_{1}^{S,+}(2)⊕Z_{1}^{S,-}(2) $ | |
| B:(0,v,w) | GP:(0,-w,v) | $4(B)GP_{1}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | GP:(u,-w,2*u) | $4(C)GP_{1}^{S}(1)$ | Spin Splitting |
| D:(u,v,0) | F:(u,0,u+v) | $2(D)F_{1}^{S}(1)⊕2(D)F_{2}^{S}(1)$ | Spin Splitting |
| Δ:(0,v,0) | F:(0,0,v) | $2(Δ)F_{1}^{S}(1)⊕2(Δ)F_{2}^{S}(1)$ | Spin Splitting |
| E:(u,v,-1/2) | G:(u,1/2,u+v) | $2(E)G_{1}^{S}(1)⊕2(E)G_{2}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | GP:(u,-w,1/2+u) | $4(F)GP_{1}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,-w,0) | $2 Λ_{1}^{S}(2) $ | |
| S:(u,u,-1/2) | G:(u,1/2,2*u) | $2(S)G_{1}^{S}(1)⊕2(S)G_{2}^{S}(1)$ | Spin Splitting |
| Σ:(u,u,0) | F:(u,0,2*u) | $2(Σ)F_{1}^{S}(1)⊕2(Σ)F_{2}^{S}(1)$ | Spin Splitting |
| T:(u,1/2,-1/2) | G:(u,1/2,1/2+u) | $2(T)G_{1}^{S}(1)⊕2(T)G_{2}^{S}(1)$ | Spin Splitting |
| U:(0,v,-1/2) | G:(0,1/2,v) | $2(U)G_{1}^{S}(1)⊕2(U)G_{2}^{S}(1)$ | Spin Splitting |
| V:(1/2,-1/2,w) | W:(1/2,-w,0) | $2 (V)W_{1}^{S}(2) $ | |
| W:(0,1/2,w) | V:(0,-w,1/2) | $2(W)V_{1}^{S}V_{2}^{S}(2)$ | Spin Splitting |
| Y:(u,1/2,0) | F:(u,0,1/2+u) | $2(Y)F_{1}^{S}(1)⊕2(Y)F_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,-w,u+v) | $4GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A↑G(8) | |
| A:(1/2,-1/2,-1/2) | C:(1/2,1/2,0) | $(A)C_{1}^{S,+}(2)⊕(A)C_{1}^{S,-}(2)⊕(A)C_{2}^{S,+}(2)⊕(A)C_{2}^{S,-}(2) $ | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2)⊕Γ_{2}^{S,+}(2)⊕Γ_{2}^{S,-}(2) $ | |
| M:(1/2,-1/2,0) | Y:(1/2,0,0) | $(M)Y_{1}^{S,+}(2)⊕(M)Y_{1}^{S,-}(2)⊕(M)Y_{2}^{S,+}(2)⊕(M)Y_{2}^{S,-}(2) $ | |
| R:(0,1/2,-1/2) | D:(0,1/2,1/2) | $4(R)D_{1}^{S}(2)$ | Spin Splitting |
| X:(0,1/2,0) | B:(0,0,1/2) | $4(X)B_{1}^{S}(2)$ | Spin Splitting |
| 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) $ | |
| B:(0,v,w) | GP:(0,-w,v) | $8(B)GP_{1}^{S}(1)$ | Spin Splitting |
| C:(u,u,w) | GP:(u,-w,2*u) | $8(C)GP_{1}^{S}(1)$ | Spin Splitting |
| D:(u,v,0) | F:(u,0,u+v) | $4(D)F_{1}^{S}(1)⊕4(D)F_{2}^{S}(1)$ | Spin Splitting |
| Δ:(0,v,0) | F:(0,0,v) | $4(Δ)F_{1}^{S}(1)⊕4(Δ)F_{2}^{S}(1)$ | Spin Splitting |
| E:(u,v,-1/2) | G:(u,1/2,u+v) | $4(E)G_{1}^{S}(1)⊕4(E)G_{2}^{S}(1)$ | Spin Splitting |
| F:(u,1/2,w) | GP:(u,-w,1/2+u) | $8(F)GP_{1}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,-w,0) | $2 Λ_{1}^{S}(2)⊕2 Λ_{2}^{S}(2) $ | |
| S:(u,u,-1/2) | G:(u,1/2,2*u) | $4(S)G_{1}^{S}(1)⊕4(S)G_{2}^{S}(1)$ | Spin Splitting |
| Σ:(u,u,0) | F:(u,0,2*u) | $4(Σ)F_{1}^{S}(1)⊕4(Σ)F_{2}^{S}(1)$ | Spin Splitting |
| T:(u,1/2,-1/2) | G:(u,1/2,1/2+u) | $4(T)G_{1}^{S}(1)⊕4(T)G_{2}^{S}(1)$ | Spin Splitting |
| U:(0,v,-1/2) | G:(0,1/2,v) | $4(U)G_{1}^{S}(1)⊕4(U)G_{2}^{S}(1)$ | Spin Splitting |
| V:(1/2,-1/2,w) | W:(1/2,-w,0) | $2 (V)W_{1}^{S}(2)⊕2 (V)W_{2}^{S}(2) $ | |
| W:(0,1/2,w) | V:(0,-w,1/2) | $4(W)V_{1}^{S}V_{2}^{S}(2)$ | Spin Splitting |
| Y:(u,1/2,0) | F:(u,0,1/2+u) | $4(Y)F_{1}^{S}(1)⊕4(Y)F_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u,-w,u+v) | $8GP_{1}^{S}(1)$ | Spin Splitting |