The continuously infinite group ∞1 is omitted.
Coordinates | Seitz symbol |
---|---|
a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
a, -b+1/2, -c | x, y, z | { 1 ‖ 2100 | 0 1/2 0 } |
a+1/2, -b, c | x, y, z | { 1 ‖ m010 | 1/2 0 0 } |
a+1/2, b+1/2, -c | x, y, z | { 1 ‖ m001 | 1/2 1/2 0 } |
-a+1/2, b, -c | -x, -y, -z | { -1 ‖ 2010 | 1/2 0 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, b+1/2, c | -x, -y, -z | { -1 ‖ m100 | 0 1/2 0 } |
a, b, c | -x, y, z | { m ‖ 1 | 0 } |
a, -b+1/2, -c | -x, y, z | { m ‖ 2100 | 0 1/2 0 } |
a+1/2, -b, c | -x, y, z | { m ‖ m010 | 1/2 0 0 } |
a+1/2, b+1/2, -c | -x, y, z | { m ‖ m001 | 1/2 1/2 0 } |
-a+1/2, b, -c | x, -y, -z | { 2 ‖ 2010 | 1/2 0 0 } |
-a+1/2, -b+1/2, c | x, -y, -z | { 2 ‖ 2001 | 1/2 1/2 0 } |
-a, -b, -c | x, -y, -z | { 2 ‖ -1 | 0 } |
-a, b+1/2, c | x, -y, -z | { 2 ‖ m100 | 0 1/2 0 } |
WP | Site symmetry | Representative |
---|---|---|
2a | $\ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/4,1/4,0 | 0,0,0) |
2b | $\ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (3/4,1/4,0 | 0,0,0) |
2c | $\ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (3/4,1/4,1/2 | 0,0,0) |
2d | $\ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/4,1/4,1/2 | 0,0,0) |
4e | $\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
4f | $\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,0) |
4g | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,1/4,0 | 0,0,z) |
4h | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,1/4,1/2 | 0,0,z) |
4i | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (1/4,b,0 | 0,0,0) |
4j | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (1/4,b,1/2 | 0,0,0) |
4k | $..\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/4,1/4,c | 0,0,0) |
4l | $..\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/4,3/4,c | 0,0,0) |
8m | $\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{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
B:(0,v,1/2) | $ \ce{^{2}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
C:(u,1/2,0) | $ \ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
D:(1/2,v,0) | $ \ce{^{2}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
Δ:(0,v,0) | $ \ce{^{2}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
E:(u,1/2,1/2) | $ \ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
G:(1/2,0,w) | $ \ce{^{2}{m}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
H:(0,1/2,w) | $ \ce{^{2}{m}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
Λ:(0,0,w) | $ \ce{^{2}{m}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
P:(1/2,v,1/2) | $ \ce{^{2}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
Q:(1/2,1/2,w) | $ \ce{^{2}{m}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
Σ:(u,0,0) | $ \ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
K:(0,v,w) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
L:(1/2,v,w) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
M:(u,0,w) | $ \ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
N:(u,1/2,w) | $ \ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
V:(u,v,0) | $ \ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
W:(u,v,1/2) | $ \ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
GP:(u,v,w) | $ \ce{^{-1}{-1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
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) | R:(1/2,1/2,1/2) | $R_{1}^{S}(4) $ |
S:(1/2,1/2,0) | T:(0,1/2,1/2) | $(S)T_{1}^{S}(4) $ |
T:(0,1/2,-1/2) | S:(1/2,1/2,0) | $(T)S_{1}^{S}(4) $ |
U:(1/2,0,-1/2) | U:(1/2,0,1/2) | $U_{1}^{S}U_{2}^{S}(4) $ |
X:(1/2,0,0) | Z:(0,0,1/2) | $(X)Z_{1}^{S}Z_{2}^{S}(4) $ |
Y:(0,1/2,0) | Y:(0,1/2,0) | $Y_{1}^{S}(4) $ |
Z:(0,0,-1/2) | X:(1/2,0,0) | $(Z)X_{1}^{S}(2)⊕(Z)X_{2}^{S}(2) $ |
A:(u,0,-1/2) | G:(1/2,0,u) | $(A)G_{1}^{S}(2)⊕(A)G_{2}^{S}(2) $ |
B:(0,v,-1/2) | D:(1/2,v,0) | $(B)D_{1}^{S}(2)⊕(B)D_{2}^{S}(2) $ |
C:(u,1/2,0) | H:(0,1/2,u) | $(C)H_{1}^{S}(4) $ |
D:(1/2,v,0) | B:(0,v,1/2) | $(D)B_{1}^{S}B_{2}^{S}(4) $ |
Δ:(0,v,0) | Δ:(0,v,0) | $Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2) $ |
E:(u,1/2,-1/2) | Q:(1/2,1/2,u) | $(E)Q_{1}^{S}(4) $ |
G:(1/2,0,w) | A:(-w,0,1/2) | $(G)A_{1}^{S}A_{2}^{S}(4) $ |
H:(0,1/2,w) | C:(-w,1/2,0) | $(H)C_{1}^{S}C_{2}^{S}(4) $ |
Λ:(0,0,w) | Σ:(-w,0,0) | $(Λ)Σ_{1}^{S}(2)⊕(Λ)Σ_{2}^{S}(2) $ |
P:(1/2,v,-1/2) | P:(1/2,v,1/2) | $P_{1}^{S}P_{2}^{S}(4) $ |
Q:(1/2,1/2,w) | E:(-w,1/2,1/2) | $(Q)E_{1}^{S}(2)⊕(Q)E_{2}^{S}(2) $ |
Σ:(u,0,0) | Λ:(0,0,u) | $(Σ)Λ_{1}^{S}(2)⊕(Σ)Λ_{2}^{S}(2) $ |
K:(0,v,w) | V:(-w,v,0) | $2(K)V_{1}^{S}(2) $ |
L:(1/2,v,w) | W:(-w,v,1/2) | $2(L)W_{1}^{S}(2) $ |
M:(u,0,w) | M:(-w,0,u) | $M_{1}^{S}(2)⊕M_{2}^{S}(2) $ |
N:(u,1/2,w) | N:(-w,1/2,u) | $N_{1}^{S}(2)⊕N_{2}^{S}(2) $ |
V:(u,v,0) | K:(0,v,u) | $(V)K_{1}^{S}(2)⊕(V)K_{2}^{S}(2) $ |
W:(u,v,-1/2) | L:(1/2,v,u) | $(W)L_{1}^{S}(2)⊕(W)L_{2}^{S}(2) $ |
GP:(u,v,w) | GP:(-w,v,u) | $2 GP_{1}^{S}(2) $ |
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) | R:(1/2,1/2,1/2) | $R_{1}^{S}(4) $ |
S:(1/2,1/2,0) | T:(0,1/2,1/2) | $(S)T_{1}^{S}(4) $ |
T:(0,1/2,-1/2) | S:(1/2,1/2,0) | $(T)S_{1}^{S}(4) $ |
U:(1/2,0,-1/2) | U:(1/2,0,1/2) | $U_{3}^{S}U_{4}^{S}(4) $ |
X:(1/2,0,0) | Z:(0,0,1/2) | $(X)Z_{1}^{S}Z_{2}^{S}(4) $ |
Y:(0,1/2,0) | Y:(0,1/2,0) | $Y_{1}^{S}(4) $ |
Z:(0,0,-1/2) | X:(1/2,0,0) | $(Z)X_{3}^{S}(2)⊕(Z)X_{4}^{S}(2) $ |
A:(u,0,-1/2) | G:(1/2,0,u) | $(A)G_{3}^{S}(2)⊕(A)G_{4}^{S}(2) $ |
B:(0,v,-1/2) | D:(1/2,v,0) | $(B)D_{1}^{S}(2)⊕(B)D_{2}^{S}(2) $ |
C:(u,1/2,0) | H:(0,1/2,u) | $(C)H_{1}^{S}(4) $ |
D:(1/2,v,0) | B:(0,v,1/2) | $(D)B_{1}^{S}B_{2}^{S}(4) $ |
Δ:(0,v,0) | Δ:(0,v,0) | $Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2) $ |
E:(u,1/2,-1/2) | Q:(1/2,1/2,u) | $(E)Q_{1}^{S}(4) $ |
G:(1/2,0,w) | A:(-w,0,1/2) | $(G)A_{1}^{S}A_{2}^{S}(4) $ |
H:(0,1/2,w) | C:(-w,1/2,0) | $(H)C_{1}^{S}C_{2}^{S}(4) $ |
Λ:(0,0,w) | Σ:(-w,0,0) | $(Λ)Σ_{1}^{S}(2)⊕(Λ)Σ_{2}^{S}(2) $ |
P:(1/2,v,-1/2) | P:(1/2,v,1/2) | $P_{1}^{S}P_{2}^{S}(4) $ |
Q:(1/2,1/2,w) | E:(-w,1/2,1/2) | $(Q)E_{1}^{S}(2)⊕(Q)E_{2}^{S}(2) $ |
Σ:(u,0,0) | Λ:(0,0,u) | $(Σ)Λ_{1}^{S}(2)⊕(Σ)Λ_{2}^{S}(2) $ |
K:(0,v,w) | V:(-w,v,0) | $2(K)V_{1}^{S}(2) $ |
L:(1/2,v,w) | W:(-w,v,1/2) | $2(L)W_{1}^{S}(2) $ |
M:(u,0,w) | M:(-w,0,u) | $M_{1}^{S}(2)⊕M_{2}^{S}(2) $ |
N:(u,1/2,w) | N:(-w,1/2,u) | $N_{1}^{S}(2)⊕N_{2}^{S}(2) $ |
V:(u,v,0) | K:(0,v,u) | $(V)K_{1}^{S}(2)⊕(V)K_{2}^{S}(2) $ |
W:(u,v,-1/2) | L:(1/2,v,u) | $(W)L_{1}^{S}(2)⊕(W)L_{2}^{S}(2) $ |
GP:(u,v,w) | GP:(-w,v,u) | $2 GP_{1}^{S}(2) $ |
k-vector | k-vector-G↑ | A↑G(8) |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2)⊕Γ_{3}^{S}(2)⊕Γ_{4}^{S}(2) $ |
R:(1/2,1/2,-1/2) | R:(1/2,1/2,1/2) | $2R_{1}^{S}(4) $ |
S:(1/2,1/2,0) | T:(0,1/2,1/2) | $2(S)T_{1}^{S}(4) $ |
T:(0,1/2,-1/2) | S:(1/2,1/2,0) | $2(T)S_{1}^{S}(4) $ |
U:(1/2,0,-1/2) | U:(1/2,0,1/2) | $U_{1}^{S}U_{2}^{S}(4)⊕U_{3}^{S}U_{4}^{S}(4) $ |
X:(1/2,0,0) | Z:(0,0,1/2) | $(X)Z_{1}^{S}Z_{2}^{S}(4)⊕(X)Z_{3}^{S}Z_{4}^{S}(4) $ |
Y:(0,1/2,0) | Y:(0,1/2,0) | $2Y_{1}^{S}(4) $ |
Z:(0,0,-1/2) | X:(1/2,0,0) | $(Z)X_{1}^{S}(2)⊕(Z)X_{2}^{S}(2)⊕(Z)X_{3}^{S}(2)⊕(Z)X_{4}^{S}(2) $ |
A:(u,0,-1/2) | G:(1/2,0,u) | $(A)G_{1}^{S}(2)⊕(A)G_{2}^{S}(2)⊕(A)G_{3}^{S}(2)⊕(A)G_{4}^{S}(2) $ |
B:(0,v,-1/2) | D:(1/2,v,0) | $2(B)D_{1}^{S}(2)⊕2(B)D_{2}^{S}(2) $ |
C:(u,1/2,0) | H:(0,1/2,u) | $2(C)H_{1}^{S}(4) $ |
D:(1/2,v,0) | B:(0,v,1/2) | $2(D)B_{1}^{S}B_{2}^{S}(4) $ |
Δ:(0,v,0) | Δ:(0,v,0) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $ |
E:(u,1/2,-1/2) | Q:(1/2,1/2,u) | $2(E)Q_{1}^{S}(4) $ |
G:(1/2,0,w) | A:(-w,0,1/2) | $2(G)A_{1}^{S}A_{2}^{S}(4) $ |
H:(0,1/2,w) | C:(-w,1/2,0) | $2(H)C_{1}^{S}C_{2}^{S}(4) $ |
Λ:(0,0,w) | Σ:(-w,0,0) | $2(Λ)Σ_{1}^{S}(2)⊕2(Λ)Σ_{2}^{S}(2) $ |
P:(1/2,v,-1/2) | P:(1/2,v,1/2) | $2P_{1}^{S}P_{2}^{S}(4) $ |
Q:(1/2,1/2,w) | E:(-w,1/2,1/2) | $2(Q)E_{1}^{S}(2)⊕2(Q)E_{2}^{S}(2) $ |
Σ:(u,0,0) | Λ:(0,0,u) | $(Σ)Λ_{1}^{S}(2)⊕(Σ)Λ_{2}^{S}(2)⊕(Σ)Λ_{3}^{S}(2)⊕(Σ)Λ_{4}^{S}(2) $ |
K:(0,v,w) | V:(-w,v,0) | $4(K)V_{1}^{S}(2) $ |
L:(1/2,v,w) | W:(-w,v,1/2) | $4(L)W_{1}^{S}(2) $ |
M:(u,0,w) | M:(-w,0,u) | $2M_{1}^{S}(2)⊕2M_{2}^{S}(2) $ |
N:(u,1/2,w) | N:(-w,1/2,u) | $2N_{1}^{S}(2)⊕2N_{2}^{S}(2) $ |
V:(u,v,0) | K:(0,v,u) | $2(V)K_{1}^{S}(2)⊕2(V)K_{2}^{S}(2) $ |
W:(u,v,-1/2) | L:(1/2,v,u) | $2(W)L_{1}^{S}(2)⊕2(W)L_{2}^{S}(2) $ |
GP:(u,v,w) | GP:(-w,v,u) | $4 GP_{1}^{S}(2) $ |