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 ‖ 2100 | 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 ‖ m100 | 1/2 1/2 0 } |
| -a, b, -c+1/2 | -x, -y, -z | { -1 ‖ 2010 | 0 0 1/2 } |
| -a+1/2, -b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ 2001 | 1/2 1/2 1/2 } |
| a, -b, c+1/2 | -x, -y, -z | { -1 ‖ m010 | 0 0 1/2 } |
| a+1/2, b+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ m001 | 1/2 1/2 1/2 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| a+1/2, -b+1/2, -c | -x, y, z | { m ‖ 2100 | 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 ‖ m100 | 1/2 1/2 0 } |
| -a, b, -c+1/2 | x, -y, -z | { 2 ‖ 2010 | 0 0 1/2 } |
| -a+1/2, -b+1/2, c+1/2 | x, -y, -z | { 2 ‖ 2001 | 1/2 1/2 1/2 } |
| a, -b, c+1/2 | x, -y, -z | { 2 ‖ m010 | 0 0 1/2 } |
| a+1/2, b+1/2, -c+1/2 | x, -y, -z | { 2 ‖ m001 | 1/2 1/2 1/2 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 4a | $\ce{^{1}{-1}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,z) |
| 4b | $\ce{^{1}{-1}}\ce{^{\infty m}{1}} $ | (0,1/2,0 | 0,0,z) |
| 4c | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (0,b,1/4 | 0,0,0) |
| 8d | $\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}} $ |
| R:(1/2,1/2,1/2) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| S:(1/2,1/2,0) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| T:(0,1/2,1/2) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| U:(1/2,0,1/2) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| X:(1/2,0,0) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| Y:(0,1/2,0) | $ \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}} $ |
| A:(u,0,1/2) | $ \ce{^{m}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| B:(0,v,1/2) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| C:(u,1/2,0) | $ \ce{^{m}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| D:(1/2,v,0) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| E:(u,1/2,1/2) | $ \ce{^{m}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| G:(1/2,0,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
| H:(0,1/2,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
| Λ:(0,0,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
| P:(1/2,v,1/2) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| Q:(1/2,1/2,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $ \ce{^{m}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| K:(0,v,w) | $ \ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| L:(1/2,v,w) | $ \ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| M:(u,0,w) | $ \ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| N:(u,1/2,w) | $ \ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| V:(u,v,0) | $ \ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| W:(u,v,1/2) | $ \ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| GP:(u,v,w) | $ \ce{^{m}{-1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
| k-vector | k-vector-G↑ | Ag↑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,+}E_{2}^{S,+}(4) $ | |
| S:(1/2,-1/2,0) | D:(0,1/2,1/2) | $(S)D_{1}^{S,+}D_{2}^{S,+}(4) $ | |
| T:(0,-1/2,-1/2) | A:(1/2,0,1/2) | $(T)A_{1}^{S}(4) $ | |
| U:(1/2,0,-1/2) | C:(1/2,1/2,0) | $(U)C_{1}^{S}(4) $ | |
| X:(1/2,0,0) | Z:(0,1/2,0) | $(X)Z_{1}^{S}(4) $ | |
| Y:(0,-1/2,0) | B:(0,0,1/2) | $(Y)B_{1}^{S}(4) $ | |
| Z:(0,0,-1/2) | Y:(1/2,0,0) | $(Z)Y_{1}^{S,+}(2)⊕(Z)Y_{2}^{S,+}(2) $ | |
| A:(u,0,-1/2) | W:(1/2,u,0) | $(A)W_{1}^{S}(2)⊕(A)W_{2}^{S}(2) $ | |
| B:(0,v,1/2) | F:(-1/2,0,-v) | $(B)F_{1}^{S}(2)⊕(B)F_{2}^{S}(2) $ | |
| C:(u,-1/2,0) | V:(0,u,1/2) | $(C)V_{1}^{S}V_{2}^{S}(4) $ | |
| D:(1/2,v,0) | G:(0,1/2,-v) | $(D)G_{1}^{S}G_{2}^{S}(4) $ | |
| Δ:(0,v,0) | F:(0,0,-v) | $(Δ)F_{1}^{S}(2)⊕(Δ)F_{2}^{S}(2) $ | |
| E:(u,-1/2,-1/2) | U:(1/2,u,1/2) | $(E)U_{1}^{S}U_{2}^{S}(4) $ | |
| G:(1/2,0,w) | G:(-w,1/2,0) | $2G_{1}^{S}G_{2}^{S}(2) $ | |
| H:(0,1/2,w) | F:(-w,0,-1/2) | $(H)F_{1}^{S}(2)⊕(H)F_{2}^{S}(2) $ | |
| Λ:(0,0,w) | F:(-w,0,0) | $(Λ)F_{1}^{S}(2)⊕(Λ)F_{2}^{S}(2) $ | |
| P:(1/2,v,1/2) | G:(-1/2,1/2,-v) | $(P)G_{1}^{S}G_{2}^{S}(4) $ | |
| Q:(1/2,1/2,w) | G:(-w,1/2,-1/2) | $(Q)G_{1}^{S}G_{2}^{S}(4) $ | |
| Σ:(u,0,0) | Λ:(0,u,0) | $(Σ)Λ_{1}^{S}(2)⊕(Σ)Λ_{2}^{S}(2) $ | |
| K:(0,v,w) | F:(-w,0,-v) | $2(K)F_{1}^{S}(1)⊕2(K)F_{2}^{S}(1)$ | Spin Splitting |
| L:(1/2,v,w) | G:(-w,1/2,-v) | $2(L)G_{1}^{S}G_{2}^{S}(2)$ | Spin Splitting |
| M:(u,0,w) | GP:(-w,u,0) | $2(M)GP_{1}^{S}(2) $ | |
| N:(u,1/2,w) | GP:(-w,u,-1/2) | $2(N)GP_{1}^{S}(2) $ | |
| V:(u,v,0) | GP:(0,u,-v) | $2(V)GP_{1}^{S}(2) $ | |
| W:(u,v,1/2) | GP:(-1/2,u,-v) | $2(W)GP_{1}^{S}(2) $ | |
| GP:(u,v,w) | GP:(-w,u,-v) | $4GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | Ag↑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,-}E_{2}^{S,-}(4) $ | |
| S:(1/2,-1/2,0) | D:(0,1/2,1/2) | $(S)D_{1}^{S,-}D_{2}^{S,-}(4) $ | |
| T:(0,-1/2,-1/2) | A:(1/2,0,1/2) | $(T)A_{1}^{S}(4) $ | |
| U:(1/2,0,-1/2) | C:(1/2,1/2,0) | $(U)C_{1}^{S}(4) $ | |
| X:(1/2,0,0) | Z:(0,1/2,0) | $(X)Z_{1}^{S}(4) $ | |
| Y:(0,-1/2,0) | B:(0,0,1/2) | $(Y)B_{1}^{S}(4) $ | |
| Z:(0,0,-1/2) | Y:(1/2,0,0) | $(Z)Y_{1}^{S,+}(2)⊕(Z)Y_{2}^{S,+}(2) $ | |
| A:(u,0,-1/2) | W:(1/2,u,0) | $(A)W_{1}^{S}(2)⊕(A)W_{2}^{S}(2) $ | |
| B:(0,v,1/2) | F:(-1/2,0,-v) | $(B)F_{1}^{S}(2)⊕(B)F_{2}^{S}(2) $ | |
| C:(u,-1/2,0) | V:(0,u,1/2) | $(C)V_{1}^{S}V_{2}^{S}(4) $ | |
| D:(1/2,v,0) | G:(0,1/2,-v) | $(D)G_{1}^{S}G_{2}^{S}(4) $ | |
| Δ:(0,v,0) | F:(0,0,-v) | $(Δ)F_{1}^{S}(2)⊕(Δ)F_{2}^{S}(2) $ | |
| E:(u,-1/2,-1/2) | U:(1/2,u,1/2) | $(E)U_{1}^{S}U_{2}^{S}(4) $ | |
| G:(1/2,0,w) | G:(-w,1/2,0) | $2G_{1}^{S}G_{2}^{S}(2) $ | |
| H:(0,1/2,w) | F:(-w,0,-1/2) | $(H)F_{1}^{S}(2)⊕(H)F_{2}^{S}(2) $ | |
| Λ:(0,0,w) | F:(-w,0,0) | $(Λ)F_{1}^{S}(2)⊕(Λ)F_{2}^{S}(2) $ | |
| P:(1/2,v,1/2) | G:(-1/2,1/2,-v) | $(P)G_{1}^{S}G_{2}^{S}(4) $ | |
| Q:(1/2,1/2,w) | G:(-w,1/2,-1/2) | $(Q)G_{1}^{S}G_{2}^{S}(4) $ | |
| Σ:(u,0,0) | Λ:(0,u,0) | $(Σ)Λ_{1}^{S}(2)⊕(Σ)Λ_{2}^{S}(2) $ | |
| K:(0,v,w) | F:(-w,0,-v) | $2(K)F_{1}^{S}(1)⊕2(K)F_{2}^{S}(1)$ | Spin Splitting |
| L:(1/2,v,w) | G:(-w,1/2,-v) | $2(L)G_{1}^{S}G_{2}^{S}(2)$ | Spin Splitting |
| M:(u,0,w) | GP:(-w,u,0) | $2(M)GP_{1}^{S}(2) $ | |
| N:(u,1/2,w) | GP:(-w,u,-1/2) | $2(N)GP_{1}^{S}(2) $ | |
| V:(u,v,0) | GP:(0,u,-v) | $2(V)GP_{1}^{S}(2) $ | |
| W:(u,v,1/2) | GP:(-1/2,u,-v) | $2(W)GP_{1}^{S}(2) $ | |
| GP:(u,v,w) | GP:(-w,u,-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) | E:(1/2,1/2,1/2) | $(R)E_{1}^{S,+}E_{2}^{S,+}(4)⊕(R)E_{1}^{S,-}E_{2}^{S,-}(4) $ | |
| S:(1/2,-1/2,0) | D:(0,1/2,1/2) | $(S)D_{1}^{S,+}D_{2}^{S,+}(4)⊕(S)D_{1}^{S,-}D_{2}^{S,-}(4) $ | |
| T:(0,-1/2,-1/2) | A:(1/2,0,1/2) | $2(T)A_{1}^{S}(4) $ | |
| U:(1/2,0,-1/2) | C:(1/2,1/2,0) | $2(U)C_{1}^{S}(4) $ | |
| X:(1/2,0,0) | Z:(0,1/2,0) | $2(X)Z_{1}^{S}(4) $ | |
| Y:(0,-1/2,0) | B:(0,0,1/2) | $2(Y)B_{1}^{S}(4) $ | |
| Z:(0,0,-1/2) | Y:(1/2,0,0) | $(Z)Y_{1}^{S,+}(2)⊕(Z)Y_{1}^{S,-}(2)⊕(Z)Y_{2}^{S,+}(2)⊕(Z)Y_{2}^{S,-}(2) $ | |
| A:(u,0,-1/2) | W:(1/2,u,0) | $2(A)W_{1}^{S}(2)⊕2 (A)W_{2}^{S}(2) $ | |
| B:(0,v,1/2) | F:(-1/2,0,-v) | $2(B)F_{1}^{S}(2)⊕2(B)F_{2}^{S}(2) $ | |
| C:(u,-1/2,0) | V:(0,u,1/2) | $2(C)V_{1}^{S}V_{2}^{S}(4) $ | |
| D:(1/2,v,0) | G:(0,1/2,-v) | $2(D)G_{1}^{S}G_{2}^{S}(4) $ | |
| Δ:(0,v,0) | F:(0,0,-v) | $2(Δ)F_{1}^{S}(2)⊕2(Δ)F_{2}^{S}(2) $ | |
| E:(u,-1/2,-1/2) | U:(1/2,u,1/2) | $2(E)U_{1}^{S}U_{2}^{S}(4) $ | |
| G:(1/2,0,w) | G:(-w,1/2,0) | $2G_{1}^{S}G_{2}^{S}(4) $ | |
| H:(0,1/2,w) | F:(-w,0,-1/2) | $2(H)F_{1}^{S}(2)⊕2(H)F_{2}^{S}(2) $ | |
| Λ:(0,0,w) | F:(-w,0,0) | $2(Λ)F_{1}^{S}(2)⊕2(Λ)F_{2}^{S}(2) $ | |
| P:(1/2,v,1/2) | G:(-1/2,1/2,-v) | $2(P)G_{1}^{S}G_{2}^{S}(4) $ | |
| Q:(1/2,1/2,w) | G:(-w,1/2,-1/2) | $2(Q)G_{1}^{S}G_{2}^{S}(4) $ | |
| Σ:(u,0,0) | Λ:(0,u,0) | $2(Σ)Λ_{1}^{S}(2)⊕2(Σ)Λ_{2}^{S}(2) $ | |
| K:(0,v,w) | F:(-w,0,-v) | $4(K)F_{1}^{S}(1)⊕4(K)F_{2}^{S}(1)$ | Spin Splitting |
| L:(1/2,v,w) | G:(-w,1/2,-v) | $4(L)G_{1}^{S}G_{2}^{S}(2)$ | Spin Splitting |
| M:(u,0,w) | GP:(-w,u,0) | $4(M)GP_{1}^{S}(2) $ | |
| N:(u,1/2,w) | GP:(-w,u,-1/2) | $4(N)GP_{1}^{S}(2) $ | |
| V:(u,v,0) | GP:(0,u,-v) | $4(V)GP_{1}^{S}(2) $ | |
| W:(u,v,1/2) | GP:(-1/2,u,-v) | $4(W)GP_{1}^{S}(2) $ | |
| GP:(u,v,w) | GP:(-w,u,-v) | $8GP_{1}^{S}(1)$ | Spin Splitting |