The continuously infinite group ∞1 is omitted.
| Coordinates | Seitz symbol |
|---|---|
| a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
| -a+1/2, -b, c+1/2 | x, y, z | { 1 ‖ 2001 | 1/2 0 1/2 } |
| -a, -b, -c | x, y, z | { 1 ‖ -1 | 0 } |
| a+1/2, b, -c+1/2 | x, y, z | { 1 ‖ m001 | 1/2 0 1/2 } |
| a+1/2, -b+1/2, -c | -x, -y, -z | { -1 ‖ 2100 | 1/2 1/2 0 } |
| -a, b+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ 2010 | 0 1/2 1/2 } |
| -a+1/2, b+1/2, c | -x, -y, -z | { -1 ‖ m100 | 1/2 1/2 0 } |
| a, -b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m010 | 0 1/2 1/2 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| -a+1/2, -b, c+1/2 | -x, y, z | { m ‖ 2001 | 1/2 0 1/2 } |
| -a, -b, -c | -x, y, z | { m ‖ -1 | 0 } |
| a+1/2, b, -c+1/2 | -x, y, z | { m ‖ m001 | 1/2 0 1/2 } |
| a+1/2, -b+1/2, -c | x, -y, -z | { 2 ‖ 2100 | 1/2 1/2 0 } |
| -a, b+1/2, -c+1/2 | x, -y, -z | { 2 ‖ 2010 | 0 1/2 1/2 } |
| -a+1/2, b+1/2, c | x, -y, -z | { 2 ‖ m100 | 1/2 1/2 0 } |
| a, -b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m010 | 0 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}} $ | (0,0,1/2 | 0,0,z) |
| 8c | $\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{^{-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}} $ |
| C:(u,1/2,0) | $ \ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| D:(1/2,v,0) | $ \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}} $ |
| E:(u,1/2,1/2) | $ \ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| G:(1/2,0,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| H:(0,1/2,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}} $ |
| P:(1/2,v,1/2) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Q:(1/2,1/2,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}} $ |
| K:(0,v,w) | $ \ce{^{-1}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| L:(1/2,v,w) | $ \ce{^{-1}{2/}}\ce{^{2}{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{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| W:(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↑ | 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) | A:(1/2,0,1/2) | $(S)A_{1}^{S}(4) $ | |
| T:(0,-1/2,-1/2) | C:(1/2,1/2,0) | $(T)C_{1}^{S}(4) $ | |
| U:(1/2,0,-1/2) | D:(0,1/2,1/2) | $(U)D_{1}^{S,+}D_{2}^{S,+}(4) $ | |
| X:(1/2,0,0) | B:(0,0,1/2) | $(X)B_{1}^{S}(4) $ | |
| Y:(0,-1/2,0) | Y:(1/2,0,0) | $Y_{1}^{S,+}(2)⊕Y_{2}^{S,+}(2) $ | |
| Z:(0,0,-1/2) | Z:(0,1/2,0) | $Z_{1}^{S}(4) $ | |
| A:(u,0,-1/2) | G:(0,1/2,u) | $(A)G_{1}^{S}G_{2}^{S}(4) $ | |
| B:(0,v,-1/2) | G:(-v,1/2,0) | $(B)G_{1}^{S}G_{2}^{S}(4) $ | |
| C:(u,1/2,0) | F:(-1/2,0,u) | $(C)F_{1}^{S}(2)⊕(C)F_{2}^{S}(2) $ | |
| D:(1/2,v,0) | F:(-v,0,1/2) | $(D)F_{1}^{S}(2)⊕(D)F_{2}^{S}(2) $ | |
| Δ:(0,v,0) | F:(-v,0,0) | $(Δ)F_{1}^{S}(2)⊕(Δ)F_{2}^{S}(2) $ | |
| E:(u,1/2,-1/2) | G:(-1/2,1/2,u) | $(E)G_{1}^{S}G_{2}^{S}(4) $ | |
| G:(1/2,0,w) | V:(0,-w,1/2) | $(G)V_{1}^{S}V_{2}^{S}(4) $ | |
| H:(0,-1/2,w) | W:(1/2,-w,0) | $(H)W_{1}^{S}(2)⊕(H)W_{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:(-v,1/2,1/2) | $(P)G_{1}^{S}G_{2}^{S}(4) $ | |
| Q:(1/2,-1/2,w) | U:(1/2,-w,1/2) | $(Q)U_{1}^{S}U_{2}^{S}(4) $ | |
| Σ:(u,0,0) | F:(0,0,u) | $(Σ)F_{1}^{S}(2)⊕(Σ)F_{2}^{S}(2) $ | |
| K:(0,v,w) | GP:(-v,-w,0) | $2(K)GP_{1}^{S}(2) $ | |
| L:(1/2,v,w) | GP:(-v,-w,1/2) | $2(L)GP_{1}^{S}(2) $ | |
| M:(u,0,w) | GP:(0,-w,u) | $2(M)GP_{1}^{S}(2) $ | |
| N:(u,1/2,w) | GP:(-1/2,-w,u) | $2(N)GP_{1}^{S}(2) $ | |
| V:(u,v,0) | F:(-v,0,u) | $2(V)F_{1}^{S}(1)⊕2(V)F_{2}^{S}(1)$ | Spin Splitting |
| W:(u,v,-1/2) | G:(-v,1/2,u) | $2(W)G_{1}^{S}G_{2}^{S}(2)$ | Spin Splitting |
| GP:(u,v,w) | GP:(-v,-w,u) | $4GP_{1}^{S}(1)$ | 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) | A:(1/2,0,1/2) | $(S)A_{1}^{S}(4) $ | |
| T:(0,-1/2,-1/2) | C:(1/2,1/2,0) | $(T)C_{1}^{S}(4) $ | |
| U:(1/2,0,-1/2) | D:(0,1/2,1/2) | $(U)D_{1}^{S,-}D_{2}^{S,-}(4) $ | |
| X:(1/2,0,0) | B:(0,0,1/2) | $(X)B_{1}^{S}(4) $ | |
| Y:(0,-1/2,0) | Y:(1/2,0,0) | $Y_{1}^{S,+}(2)⊕Y_{2}^{S,+}(2) $ | |
| Z:(0,0,-1/2) | Z:(0,1/2,0) | $Z_{1}^{S}(4) $ | |
| A:(u,0,-1/2) | G:(0,1/2,u) | $(A)G_{1}^{S}G_{2}^{S}(4) $ | |
| B:(0,v,-1/2) | G:(-v,1/2,0) | $(B)G_{1}^{S}G_{2}^{S}(4) $ | |
| C:(u,1/2,0) | F:(-1/2,0,u) | $(C)F_{1}^{S}(2)⊕(C)F_{2}^{S}(2) $ | |
| D:(1/2,v,0) | F:(-v,0,1/2) | $(D)F_{1}^{S}(2)⊕(D)F_{2}^{S}(2) $ | |
| Δ:(0,v,0) | F:(-v,0,0) | $(Δ)F_{1}^{S}(2)⊕(Δ)F_{2}^{S}(2) $ | |
| E:(u,1/2,-1/2) | G:(-1/2,1/2,u) | $(E)G_{1}^{S}G_{2}^{S}(4) $ | |
| G:(1/2,0,w) | V:(0,-w,1/2) | $(G)V_{1}^{S}V_{2}^{S}(4) $ | |
| H:(0,-1/2,w) | W:(1/2,-w,0) | $(H)W_{1}^{S}(2)⊕(H)W_{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:(-v,1/2,1/2) | $(P)G_{1}^{S}G_{2}^{S}(4) $ | |
| Q:(1/2,-1/2,w) | U:(1/2,-w,1/2) | $(Q)U_{1}^{S}U_{2}^{S}(4) $ | |
| Σ:(u,0,0) | F:(0,0,u) | $(Σ)F_{1}^{S}(2)⊕(Σ)F_{2}^{S}(2) $ | |
| K:(0,v,w) | GP:(-v,-w,0) | $2(K)GP_{1}^{S}(2) $ | |
| L:(1/2,v,w) | GP:(-v,-w,1/2) | $2(L)GP_{1}^{S}(2) $ | |
| M:(u,0,w) | GP:(0,-w,u) | $2(M)GP_{1}^{S}(2) $ | |
| N:(u,1/2,w) | GP:(-1/2,-w,u) | $2(N)GP_{1}^{S}(2) $ | |
| V:(u,v,0) | F:(-v,0,u) | $2(V)F_{1}^{S}(1)⊕2(V)F_{2}^{S}(1)$ | Spin Splitting |
| W:(u,v,-1/2) | G:(-v,1/2,u) | $2(W)G_{1}^{S}G_{2}^{S}(2)$ | Spin Splitting |
| GP:(u,v,w) | GP:(-v,-w,u) | $4GP_{1}^{S}(1)$ | 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) | A:(1/2,0,1/2) | $2(S)A_{1}^{S}(4) $ | |
| T:(0,-1/2,-1/2) | C:(1/2,1/2,0) | $2(T)C_{1}^{S}(4) $ | |
| U:(1/2,0,-1/2) | D:(0,1/2,1/2) | $(U)D_{1}^{S,+}D_{2}^{S,+}(4)⊕(U)D_{1}^{S,-}D_{2}^{S,-}(4) $ | |
| X:(1/2,0,0) | B:(0,0,1/2) | $2(X)B_{1}^{S}(4) $ | |
| Y:(0,-1/2,0) | 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) | $2Z_{1}^{S}(4) $ | |
| A:(u,0,-1/2) | G:(0,1/2,u) | $2(A)G_{1}^{S}G_{2}^{S}(4) $ | |
| B:(0,v,-1/2) | G:(-v,1/2,0) | $2(B)G_{1}^{S}G_{2}^{S}(4) $ | |
| C:(u,1/2,0) | F:(-1/2,0,u) | $2(C)F_{1}^{S}(2)⊕2(C)F_{2}^{S}(2) $ | |
| D:(1/2,v,0) | F:(-v,0,1/2) | $2(D)F_{1}^{S}(2)⊕2(D)F_{2}^{S}(2) $ | |
| Δ:(0,v,0) | F:(-v,0,0) | $2(Δ)F_{1}^{S}(2)⊕2(Δ)F_{2}^{S}(2) $ | |
| E:(u,1/2,-1/2) | G:(-1/2,1/2,u) | $2(E)G_{1}^{S}G_{2}^{S}(4) $ | |
| G:(1/2,0,w) | V:(0,-w,1/2) | $2(G)V_{1}^{S}V_{2}^{S}(4) $ | |
| H:(0,-1/2,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) $ | |
| P:(1/2,v,-1/2) | G:(-v,1/2,1/2) | $2(P)G_{1}^{S}G_{2}^{S}(4) $ | |
| Q:(1/2,-1/2,w) | U:(1/2,-w,1/2) | $2(Q)U_{1}^{S}U_{2}^{S}(4) $ | |
| Σ:(u,0,0) | F:(0,0,u) | $2(Σ)F_{1}^{S}(2)⊕2(Σ)F_{2}^{S}(2) $ | |
| K:(0,v,w) | GP:(-v,-w,0) | $4(K)GP_{1}^{S}(2) $ | |
| L:(1/2,v,w) | GP:(-v,-w,1/2) | $4(L)GP_{1}^{S}(2) $ | |
| M:(u,0,w) | GP:(0,-w,u) | $4(M)GP_{1}^{S}(2) $ | |
| N:(u,1/2,w) | GP:(-1/2,-w,u) | $4(N)GP_{1}^{S}(2) $ | |
| V:(u,v,0) | F:(-v,0,u) | $4(V)F_{1}^{S}(1)⊕4(V)F_{2}^{S}(1)$ | Spin Splitting |
| W:(u,v,-1/2) | G:(-v,1/2,u) | $4(W)G_{1}^{S}G_{2}^{S}(2)$ | Spin Splitting |
| GP:(u,v,w) | GP:(-v,-w,u) | $8GP_{1}^{S}(1)$ | Spin Splitting |