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, -b, -c | x, y, z | { 1 ‖ -1 | 0 } |
| a, b, -c | x, y, z | { 1 ‖ m001 | 0 } |
| -b, a, c | -x, -y, -z | { -1 ‖ 4+001 | 0 } |
| b, -a, c | -x, -y, -z | { -1 ‖ 4-001 | 0 } |
| b, -a, -c | -x, -y, -z | { -1 ‖ -4+001 | 0 } |
| -b, a, -c | -x, -y, -z | { -1 ‖ -4-001 | 0 } |
| a+1/2, b+1/2, c+1/2 | x, y, z | { 1 ‖ 1 | 1/2 1/2 1/2 } |
| -a+1/2, -b+1/2, c+1/2 | x, y, z | { 1 ‖ 2001 | 1/2 1/2 1/2 } |
| -a+1/2, -b+1/2, -c+1/2 | x, y, z | { 1 ‖ -1 | 1/2 1/2 1/2 } |
| a+1/2, b+1/2, -c+1/2 | x, y, z | { 1 ‖ m001 | 1/2 1/2 1/2 } |
| -b+1/2, a+1/2, c+1/2 | -x, -y, -z | { -1 ‖ 4+001 | 1/2 1/2 1/2 } |
| b+1/2, -a+1/2, c+1/2 | -x, -y, -z | { -1 ‖ 4-001 | 1/2 1/2 1/2 } |
| b+1/2, -a+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ -4+001 | 1/2 1/2 1/2 } |
| -b+1/2, a+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ -4-001 | 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, -b, -c | -x, y, z | { m ‖ -1 | 0 } |
| a, b, -c | -x, y, z | { m ‖ m001 | 0 } |
| -b, a, c | x, -y, -z | { 2 ‖ 4+001 | 0 } |
| b, -a, c | x, -y, -z | { 2 ‖ 4-001 | 0 } |
| b, -a, -c | x, -y, -z | { 2 ‖ -4+001 | 0 } |
| -b, a, -c | x, -y, -z | { 2 ‖ -4-001 | 0 } |
| a+1/2, b+1/2, c+1/2 | -x, y, z | { m ‖ 1 | 1/2 1/2 1/2 } |
| -a+1/2, -b+1/2, c+1/2 | -x, y, z | { m ‖ 2001 | 1/2 1/2 1/2 } |
| -a+1/2, -b+1/2, -c+1/2 | -x, y, z | { m ‖ -1 | 1/2 1/2 1/2 } |
| a+1/2, b+1/2, -c+1/2 | -x, y, z | { m ‖ m001 | 1/2 1/2 1/2 } |
| -b+1/2, a+1/2, c+1/2 | x, -y, -z | { 2 ‖ 4+001 | 1/2 1/2 1/2 } |
| b+1/2, -a+1/2, c+1/2 | x, -y, -z | { 2 ‖ 4-001 | 1/2 1/2 1/2 } |
| b+1/2, -a+1/2, -c+1/2 | x, -y, -z | { 2 ‖ -4+001 | 1/2 1/2 1/2 } |
| -b+1/2, a+1/2, -c+1/2 | x, -y, -z | { 2 ‖ -4-001 | 1/2 1/2 1/2 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 2a | $\ce{^{-1}{4}}/\ce{^{1}{m}}..\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
| 2b | $\ce{^{-1}{4}}/\ce{^{1}{m}}..\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,0) |
| 4c | $\ce{^{1}{2}}/\ce{^{1}{m}}..\ce{^{\infty m}{1}} $ | (0,1/2,0 | 0,0,z) |
| 4d | $\ce{^{-1}{-4}}..\ce{^{\infty m}{1}} $ | (0,1/2,1/4 | 0,0,0) |
| 4e | $\ce{^{-1}{4}}..\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,0) |
| 8f | $\ce{^{1}{-1}}\ce{^{\infty m}{1}} $ | (1/4,1/4,1/4 | 0,0,z) |
| 8g | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (0,1/2,c | 0,0,z) |
| 8h | $\ce{^{1}{m}}..\ce{^{\infty m}{1}} $ | (a,b,0 | 0,0,z) |
| 16i | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
| Wavevector-k | Little co-group |
|---|---|
| Γ:(0,0,0) | $\ce{^{-1}{4/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| M:(1,1,1) | $\ce{^{-1}{4/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| P:(1/2,1/2,1/2) | $\ce{^{-1}{4/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| X:(1/2,1/2,0) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
| N:(1/2,0,1/2) | $\ce{^{1}{-1}}\ce{^{\infty m}{1}} $ |
| Λ:(0,0,w) | $\ce{^{2}{4/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| W:(1/2,1/2,w) | $\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
| Q:(1/2,v,1/2) | $\ce{^{m}{-1}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Y:(u,1-u,0) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| Δ:(u,u,0) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
| A:(u,u,w) | $\ce{^{m}{-1}}\ce{^{\infty}{1}} $ |
| B:(u,0,w) | $\ce{^{m}{-1}}\ce{^{\infty}{1}} $ |
| C:(u,v,0) | $\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(2) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S,+}(2) $ | |
| M:(0,0,1) | Y:(0,1,0) | $(M)Y_{1}^{S,+}(2) $ | |
| N:(1/2,0,1/2) | V:(1/2,1/2,0) | $2 (N)V_{1}^{S,+}(1)$ | Spin Splitting |
| P:(1/2,-1/2,3/2) | U:(0,3/2,1/2) | $(P)U_{2}^{S}(2) $ | |
| X:(1/2,-1/2,1) | M:(0,1,1/2) | $2(X)M_{2}^{S,-}(1)$ | Spin Splitting |
| A:(u,u,w) | GP:(2*u,w,-u) | $2(A)GP_{1}^{S}(1)$ | Spin Splitting |
| B:(u,0,w) | GP:(u,w,0) | $2(B)GP_{1}^{S}(1)$ | Spin Splitting |
| C:(u,v,0) | B:(u+v,0,-v) | $2(C)B_{1}^{S}(1)$ | Spin Splitting |
| Δ:(u,u,0) | B:(2*u,0,-u) | $2(Δ)B_{1}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,w,0) | $Λ_{1}^{S}(2) $ | |
| Q:(1/2,v,1/2) | GP:(1/2+v,1/2,-v) | $2(Q)GP_{1}^{S}(1)$ | Spin Splitting |
| Σ:(u,0,0) | B:(u,0,0) | $2(Σ)B_{1}^{S}(1)$ | Spin Splitting |
| W:(1/2,-1/2,1+w) | U:(0,1+w,1/2) | $2(W)U_{2}^{S}(1)$ | Spin Splitting |
| Y:(u,1-u,0) | B:(1,0,-1+u) | $2(Y)B_{1}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u+v,w,-v) | $2GP_{1}^{S}(1)$ | 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) $ | |
| M:(0,0,1) | Y:(0,1,0) | $(M)Y_{1}^{S,-}(2)⊕(M)Y_{2}^{S,-}(2) $ | |
| N:(1/2,0,1/2) | V:(1/2,1/2,0) | $2(N)V_{1}^{S,+}(1)⊕2(N)V_{1}^{S,-}(1)$ | Spin Splitting |
| P:(1/2,-1/2,3/2) | U:(0,3/2,1/2) | $(P)U_{1}^{S}(2)⊕(P)U_{2}^{S}(2) $ | |
| X:(1/2,-1/2,1) | M:(0,1,1/2) | $2 (X)M_{1}^{S,-}(1)⊕2(X)M_{2}^{S,-}(1)$ | Spin Splitting |
| A:(u,u,w) | GP:(2*u,w,-u) | $4(A)GP_{1}^{S}(1)$ | Spin Splitting |
| B:(u,0,w) | GP:(u,w,0) | $4(B)GP_{1}^{S}(1)$ | Spin Splitting |
| C:(u,v,0) | B:(u+v,0,-v) | $2(C)B_{1}^{S}(1)⊕2(C)B_{2}^{S}(1)$ | Spin Splitting |
| Δ:(u,u,0) | B:(2*u,0,-u) | $2(Δ)B_{1}^{S}(1)⊕2(Δ)B_{2}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,w,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
| Q:(1/2,v,1/2) | GP:(1/2+v,1/2,-v) | $4(Q)GP_{1}^{S}(1)$ | Spin Splitting |
| Σ:(u,0,0) | B:(u,0,0) | $2(Σ)B_{1}^{S}(1)⊕2(Σ)B_{2}^{S}(1)$ | Spin Splitting |
| W:(1/2,-1/2,1+w) | U:(0,1+w,1/2) | $2(W)U_{1}^{S}(1)⊕2(W)U_{2}^{S}(1)$ | Spin Splitting |
| Y:(u,1-u,0) | B:(1,0,-1+u) | $2(Y)B_{1}^{S}(1)⊕2(Y)B_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u+v,w,-v) | $4GP_{1}^{S}(1)$ | Spin Splitting |
| k-vector | k-vector-G↑ | A↑G(4) | |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2) $ | |
| M:(0,0,1) | Y:(0,1,0) | $(M)Y_{1}^{S,+}(2)⊕(M)Y_{1}^{S,-}(2) $ | |
| N:(1/2,0,1/2) | V:(1/2,1/2,0) | $2(N)V_{1}^{S,+}(1)⊕2(N)V_{1}^{S,-}(1)$ | Spin Splitting |
| P:(1/2,-1/2,3/2) | U:(0,3/2,1/2) | $2(P)U_{2}^{S}(2) $ | |
| X:(1/2,-1/2,1) | M:(0,1,1/2) | $2 (X)M_{2}^{S,+}(1)⊕2(X)M_{2}^{S,-}(1)$ | Spin Splitting |
| A:(u,u,w) | GP:(2*u,w,-u) | $4(A)GP_{1}^{S}(1)$ | Spin Splitting |
| B:(u,0,w) | GP:(u,w,0) | $4(B)GP_{1}^{S}(1)$ | Spin Splitting |
| C:(u,v,0) | B:(u+v,0,-v) | $2(C)B_{1}^{S}(1)⊕2(C)B_{2}^{S}(1)$ | Spin Splitting |
| Δ:(u,u,0) | B:(2*u,0,-u) | $2(Δ)B_{1}^{S}(1)⊕2(Δ)B_{2}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,w,0) | $2 Λ_{1}^{S}(2) $ | |
| Q:(1/2,v,1/2) | GP:(1/2+v,1/2,-v) | $4(Q)GP_{1}^{S}(1)$ | Spin Splitting |
| Σ:(u,0,0) | B:(u,0,0) | $2(Σ)B_{1}^{S}(1)⊕2(Σ)B_{2}^{S}(1)$ | Spin Splitting |
| W:(1/2,-1/2,1+w) | U:(0,1+w,1/2) | $4(W)U_{2}^{S}(1)$ | Spin Splitting |
| Y:(u,1-u,0) | B:(1,0,-1+u) | $2(Y)B_{1}^{S}(1)⊕2(Y)B_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u+v,w,-v) | $4GP_{1}^{S}(1)$ | 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) $ | |
| M:(0,0,1) | Y:(0,1,0) | $(M)Y_{1}^{S,+}(2)⊕(M)Y_{2}^{S,-}(2) $ | |
| N:(1/2,0,1/2) | V:(1/2,1/2,0) | $2(N)V_{1}^{S,+}(1)⊕2(N)V_{1}^{S,-}(1)$ | Spin Splitting |
| P:(1/2,-1/2,3/2) | U:(0,3/2,1/2) | $(P)U_{1}^{S}(2)⊕(P)U_{2}^{S}(2) $ | |
| X:(1/2,-1/2,1) | M:(0,1,1/2) | $2 (X)M_{1}^{S,+}(1)⊕2(X)M_{2}^{S,-}(1)$ | Spin Splitting |
| A:(u,u,w) | GP:(2*u,w,-u) | $4(A)GP_{1}^{S}(1)$ | Spin Splitting |
| B:(u,0,w) | GP:(u,w,0) | $4(B)GP_{1}^{S}(1)$ | Spin Splitting |
| C:(u,v,0) | B:(u+v,0,-v) | $4(C)B_{1}^{S}(1)$ | Spin Splitting |
| Δ:(u,u,0) | B:(2*u,0,-u) | $4(Δ)B_{1}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,w,0) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $ | |
| Q:(1/2,v,1/2) | GP:(1/2+v,1/2,-v) | $4(Q)GP_{1}^{S}(1)$ | Spin Splitting |
| Σ:(u,0,0) | B:(u,0,0) | $4(Σ)B_{1}^{S}(1)$ | Spin Splitting |
| W:(1/2,-1/2,1+w) | U:(0,1+w,1/2) | $2(W)U_{1}^{S}(2)⊕2 (W)U_{2}^{S}(1)$ | Spin Splitting |
| Y:(u,1-u,0) | B:(1,0,-1+u) | $4(Y)B_{1}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u+v,w,-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) $ | |
| M:(0,0,1) | Y:(0,1,0) | $(M)Y_{1}^{S,+}(2)⊕(M)Y_{1}^{S,-}(2)⊕(M)Y_{2}^{S,+}(2)⊕(M)Y_{2}^{S,-}(2) $ | |
| N:(1/2,0,1/2) | V:(1/2,1/2,0) | $4(N)V_{1}^{S,+}(1)⊕4(N)V_{1}^{S,-}(1)$ | Spin Splitting |
| P:(1/2,-1/2,3/2) | U:(0,3/2,1/2) | $2(P)U_{1}^{S}(2)⊕2(P)U_{2}^{S}(2) $ | |
| X:(1/2,-1/2,1) | M:(0,1,1/2) | $2(X)M_{1}^{S,+}(1)⊕2(X)M_{1}^{S,-}(1)⊕2(X)M_{2}^{S,+}(1)⊕2(X)M_{2}^{S,-}(1)$ | Spin Splitting |
| A:(u,u,w) | GP:(2*u,w,-u) | $8(A)GP_{1}^{S}(1)$ | Spin Splitting |
| B:(u,0,w) | GP:(u,w,0) | $8(B)GP_{1}^{S}(1)$ | Spin Splitting |
| C:(u,v,0) | B:(u+v,0,-v) | $4(C)B_{1}^{S}(1)⊕4(C)B_{2}^{S}(1)$ | Spin Splitting |
| Δ:(u,u,0) | B:(2*u,0,-u) | $4(Δ)B_{1}^{S}(1)⊕4(Δ)B_{2}^{S}(1)$ | Spin Splitting |
| Λ:(0,0,w) | Λ:(0,w,0) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2) $ | |
| Q:(1/2,v,1/2) | GP:(1/2+v,1/2,-v) | $8(Q)GP_{1}^{S}(1)$ | Spin Splitting |
| Σ:(u,0,0) | B:(u,0,0) | $4(Σ)B_{1}^{S}(1)⊕4(Σ)B_{2}^{S}(1)$ | Spin Splitting |
| W:(1/2,-1/2,1+w) | U:(0,1+w,1/2) | $4(W)U_{1}^{S}(1)⊕4(W)U_{2}^{S}(1)$ | Spin Splitting |
| Y:(u,1-u,0) | B:(1,0,-1+u) | $4(Y)B_{1}^{S}(1)⊕4(Y)B_{2}^{S}(1)$ | Spin Splitting |
| GP:(u,v,w) | GP:(u+v,w,-v) | $8GP_{1}^{S}(1)$ | Spin Splitting |