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 ‖ 2010 | 0 } |
-a+1/2, b, c | x, y, z | { 1 ‖ m100 | 1/2 0 0 } |
a+1/2, b, -c | x, y, z | { 1 ‖ m001 | 1/2 0 0 } |
a+1/2, -b, -c | -x, -y, -z | { -1 ‖ 2100 | 1/2 0 0 } |
-a+1/2, -b, c | -x, -y, -z | { -1 ‖ 2001 | 1/2 0 0 } |
-a, -b, -c | -x, -y, -z | { -1 ‖ -1 | 0 } |
a, -b, c | -x, -y, -z | { -1 ‖ m010 | 0 } |
a, b, c | -x, y, z | { m ‖ 1 | 0 } |
-a, b, -c | -x, y, z | { m ‖ 2010 | 0 } |
-a+1/2, b, c | -x, y, z | { m ‖ m100 | 1/2 0 0 } |
a+1/2, b, -c | -x, y, z | { m ‖ m001 | 1/2 0 0 } |
a+1/2, -b, -c | x, -y, -z | { 2 ‖ 2100 | 1/2 0 0 } |
-a+1/2, -b, c | x, -y, -z | { 2 ‖ 2001 | 1/2 0 0 } |
-a, -b, -c | x, -y, -z | { 2 ‖ -1 | 0 } |
a, -b, c | x, -y, -z | { 2 ‖ m010 | 0 } |
WP | Site symmetry | Representative |
---|---|---|
2a | $.\ce{^{1}{2}}/\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
2b | $.\ce{^{1}{2}}/\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (0,1/2,0 | 0,0,0) |
2c | $.\ce{^{1}{2}}/\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,0) |
2d | $.\ce{^{1}{2}}/\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (0,1/2,1/2 | 0,0,0) |
2e | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/4,0,c | 0,0,0) |
2f | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/4,1/2,c | 0,0,0) |
4g | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (0,b,0 | 0,0,z) |
4h | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (0,b,1/2 | 0,0,z) |
4i | $.\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (a,0,c | 0,0,0) |
4j | $.\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (a,1/2,c | 0,0,0) |
4k | $\ce{^{1}{m}}..\ce{^{\infty m}{1}} $ | (1/4,b,c | 0,0,z) |
8l | $\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{^{1}{m}}\ce{^{\infty}{1}} $ |
B:(0,v,1/2) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
C:(u,1/2,0) | $ \ce{^{m}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
D:(1/2,v,0) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
Δ:(0,v,0) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
E:(u,1/2,1/2) | $ \ce{^{m}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
G:(1/2,0,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
H:(0,1/2,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
Λ:(0,0,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
P:(1/2,v,1/2) | $ \ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
Q:(1/2,1/2,w) | $ \ce{^{1}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
Σ:(u,0,0) | $ \ce{^{m}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
K:(0,v,w) | $ \ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
L:(1/2,v,w) | $ \ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
M:(u,0,w) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
N:(u,1/2,w) | $ \ce{^{m}{2/}}\ce{^{2}{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) | U:(1/2,0,1/2) | $(S)U_{1}^{S}(4) $ |
T:(0,1/2,-1/2) | T:(0,1/2,1/2) | $T_{1}^{S}(2)⊕T_{2}^{S}(2) $ |
U:(1/2,0,-1/2) | S:(1/2,1/2,0) | $(U)S_{1}^{S}(4) $ |
X:(1/2,0,0) | X:(1/2,0,0) | $X_{1}^{S}(4) $ |
Y:(0,1/2,0) | Z:(0,0,1/2) | $(Y)Z_{1}^{S}(2)⊕(Y)Z_{2}^{S}(2) $ |
Z:(0,0,-1/2) | Y:(0,1/2,0) | $(Z)Y_{1}^{S}(2)⊕(Z)Y_{2}^{S}(2) $ |
A:(u,0,-1/2) | C:(u,1/2,0) | $(A)C_{1}^{S}(2)⊕(A)C_{2}^{S}(2) $ |
B:(0,v,-1/2) | H:(0,1/2,v) | $(B)H_{1}^{S}(2)⊕(B)H_{2}^{S}(2) $ |
C:(u,1/2,0) | A:(u,0,1/2) | $(C)A_{1}^{S}(2)⊕(C)A_{2}^{S}(2) $ |
D:(1/2,v,0) | G:(1/2,0,v) | $(D)G_{1}^{S}(4) $ |
Δ:(0,v,0) | Λ:(0,0,v) | $(Δ)Λ_{1}^{S}(2)⊕(Δ)Λ_{2}^{S}(2) $ |
E:(u,1/2,-1/2) | E:(u,1/2,1/2) | $E_{1}^{S}(2)⊕E_{2}^{S}(2) $ |
G:(1/2,0,w) | D:(1/2,-w,0) | $(G)D_{1}^{S}D_{2}^{S}(4) $ |
H:(0,1/2,w) | B:(0,-w,1/2) | $(H)B_{1}^{S}(2)⊕(H)B_{2}^{S}(2) $ |
Λ:(0,0,w) | Δ:(0,-w,0) | $(Λ)Δ_{1}^{S}(2)⊕(Λ)Δ_{2}^{S}(2) $ |
P:(1/2,v,-1/2) | Q:(1/2,1/2,v) | $(P)Q_{1}^{S}(4) $ |
Q:(1/2,1/2,w) | P:(1/2,-w,1/2) | $(Q)P_{1}^{S}P_{2}^{S}(4) $ |
Σ:(u,0,0) | Σ:(u,0,0) | $Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2) $ |
K:(0,v,w) | K:(0,-w,v) | $K_{1}^{S}(2)⊕K_{2}^{S}(2) $ |
L:(1/2,v,w) | L:(1/2,-w,v) | $L_{1}^{S}(2)⊕L_{2}^{S}(2) $ |
M:(u,0,w) | V:(u,-w,0) | $2(M)V_{1}^{S}(2) $ |
N:(u,1/2,w) | W:(u,-w,1/2) | $2(N)W_{1}^{S}(2) $ |
V:(u,v,0) | M:(u,0,v) | $(V)M_{1}^{S}(2)⊕(V)M_{2}^{S}(2) $ |
W:(u,v,-1/2) | N:(u,1/2,v) | $(W)N_{1}^{S}(2)⊕(W)N_{2}^{S}(2) $ |
GP:(u,v,w) | GP:(u,-w,v) | $2GP_{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) | U:(1/2,0,1/2) | $(S)U_{1}^{S}(4) $ |
T:(0,1/2,-1/2) | T:(0,1/2,1/2) | $T_{3}^{S}(2)⊕T_{4}^{S}(2) $ |
U:(1/2,0,-1/2) | S:(1/2,1/2,0) | $(U)S_{1}^{S}(4) $ |
X:(1/2,0,0) | X:(1/2,0,0) | $X_{1}^{S}(4) $ |
Y:(0,1/2,0) | Z:(0,0,1/2) | $(Y)Z_{1}^{S}(2)⊕(Y)Z_{2}^{S}(2) $ |
Z:(0,0,-1/2) | Y:(0,1/2,0) | $(Z)Y_{3}^{S}(2)⊕(Z)Y_{4}^{S}(2) $ |
A:(u,0,-1/2) | C:(u,1/2,0) | $(A)C_{1}^{S}(2)⊕(A)C_{2}^{S}(2) $ |
B:(0,v,-1/2) | H:(0,1/2,v) | $(B)H_{3}^{S}(2)⊕(B)H_{4}^{S}(2) $ |
C:(u,1/2,0) | A:(u,0,1/2) | $(C)A_{1}^{S}(2)⊕(C)A_{2}^{S}(2) $ |
D:(1/2,v,0) | G:(1/2,0,v) | $(D)G_{1}^{S}(4) $ |
Δ:(0,v,0) | Λ:(0,0,v) | $(Δ)Λ_{1}^{S}(2)⊕(Δ)Λ_{2}^{S}(2) $ |
E:(u,1/2,-1/2) | E:(u,1/2,1/2) | $E_{1}^{S}(2)⊕E_{2}^{S}(2) $ |
G:(1/2,0,w) | D:(1/2,-w,0) | $(G)D_{1}^{S}D_{2}^{S}(4) $ |
H:(0,1/2,w) | B:(0,-w,1/2) | $(H)B_{1}^{S}(2)⊕(H)B_{2}^{S}(2) $ |
Λ:(0,0,w) | Δ:(0,-w,0) | $(Λ)Δ_{1}^{S}(2)⊕(Λ)Δ_{2}^{S}(2) $ |
P:(1/2,v,-1/2) | Q:(1/2,1/2,v) | $(P)Q_{1}^{S}(4) $ |
Q:(1/2,1/2,w) | P:(1/2,-w,1/2) | $(Q)P_{1}^{S}P_{2}^{S}(4) $ |
Σ:(u,0,0) | Σ:(u,0,0) | $Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2) $ |
K:(0,v,w) | K:(0,-w,v) | $K_{1}^{S}(2)⊕K_{2}^{S}(2) $ |
L:(1/2,v,w) | L:(1/2,-w,v) | $L_{1}^{S}(2)⊕L_{2}^{S}(2) $ |
M:(u,0,w) | V:(u,-w,0) | $2(M)V_{1}^{S}(2) $ |
N:(u,1/2,w) | W:(u,-w,1/2) | $2(N)W_{1}^{S}(2) $ |
V:(u,v,0) | M:(u,0,v) | $(V)M_{1}^{S}(2)⊕(V)M_{2}^{S}(2) $ |
W:(u,v,-1/2) | N:(u,1/2,v) | $(W)N_{1}^{S}(2)⊕(W)N_{2}^{S}(2) $ |
GP:(u,v,w) | GP:(u,-w,v) | $2GP_{1}^{S}(2) $ |
k-vector | k-vector-G↑ | A'↑G(4) |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{3}^{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) | U:(1/2,0,1/2) | $(S)U_{1}^{S}(4) $ |
T:(0,1/2,-1/2) | T:(0,1/2,1/2) | $T_{1}^{S}(2)⊕T_{3}^{S}(2) $ |
U:(1/2,0,-1/2) | S:(1/2,1/2,0) | $(U)S_{1}^{S}(4) $ |
X:(1/2,0,0) | X:(1/2,0,0) | $X_{1}^{S}(4) $ |
Y:(0,1/2,0) | Z:(0,0,1/2) | $(Y)Z_{1}^{S}(2)⊕(Y)Z_{3}^{S}(2) $ |
Z:(0,0,-1/2) | Y:(0,1/2,0) | $(Z)Y_{1}^{S}(2)⊕(Z)Y_{3}^{S}(2) $ |
A:(u,0,-1/2) | C:(u,1/2,0) | $(A)C_{1}^{S}(2)⊕(A)C_{2}^{S}(2) $ |
B:(0,v,-1/2) | H:(0,1/2,v) | $(B)H_{1}^{S}(2)⊕(B)H_{3}^{S}(2) $ |
C:(u,1/2,0) | A:(u,0,1/2) | $(C)A_{1}^{S}(2)⊕(C)A_{2}^{S}(2) $ |
D:(1/2,v,0) | G:(1/2,0,v) | $(D)G_{1}^{S}(4) $ |
Δ:(0,v,0) | Λ:(0,0,v) | $(Δ)Λ_{1}^{S}(2)⊕(Δ)Λ_{3}^{S}(2) $ |
E:(u,1/2,-1/2) | E:(u,1/2,1/2) | $E_{1}^{S}(2)⊕E_{2}^{S}(2) $ |
G:(1/2,0,w) | D:(1/2,-w,0) | $(G)D_{1}^{S}D_{2}^{S}(4) $ |
H:(0,1/2,w) | B:(0,-w,1/2) | $2 (H)B_{1}^{S}(2) $ |
Λ:(0,0,w) | Δ:(0,-w,0) | $(Λ)Δ_{1}^{S}(2)⊕(Λ)Δ_{2}^{S}(2) $ |
P:(1/2,v,-1/2) | Q:(1/2,1/2,v) | $(P)Q_{1}^{S}(4) $ |
Q:(1/2,1/2,w) | P:(1/2,-w,1/2) | $(Q)P_{1}^{S}P_{2}^{S}(4) $ |
Σ:(u,0,0) | Σ:(u,0,0) | $Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2) $ |
K:(0,v,w) | K:(0,-w,v) | $2 K_{1}^{S}(2) $ |
L:(1/2,v,w) | L:(1/2,-w,v) | $L_{1}^{S}(2)⊕L_{2}^{S}(2) $ |
M:(u,0,w) | V:(u,-w,0) | $2(M)V_{1}^{S}(2) $ |
N:(u,1/2,w) | W:(u,-w,1/2) | $2(N)W_{1}^{S}(2) $ |
V:(u,v,0) | M:(u,0,v) | $(V)M_{1}^{S}(2)⊕(V)M_{2}^{S}(2) $ |
W:(u,v,-1/2) | N:(u,1/2,v) | $(W)N_{1}^{S}(2)⊕(W)N_{2}^{S}(2) $ |
GP:(u,v,w) | GP:(u,-w,v) | $2GP_{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) | U:(1/2,0,1/2) | $2(S)U_{1}^{S}(4) $ |
T:(0,1/2,-1/2) | T:(0,1/2,1/2) | $T_{1}^{S}(2)⊕T_{2}^{S}(2)⊕T_{3}^{S}(2)⊕T_{4}^{S}(2) $ |
U:(1/2,0,-1/2) | S:(1/2,1/2,0) | $2(U)S_{1}^{S}(4) $ |
X:(1/2,0,0) | X:(1/2,0,0) | $2X_{1}^{S}(4) $ |
Y:(0,1/2,0) | Z:(0,0,1/2) | $(Y)Z_{1}^{S}(2)⊕(Y)Z_{2}^{S}(2)⊕(Y)Z_{3}^{S}(2)⊕(Y)Z_{4}^{S}(2) $ |
Z:(0,0,-1/2) | Y:(0,1/2,0) | $(Z)Y_{1}^{S}(2)⊕(Z)Y_{2}^{S}(2)⊕(Z)Y_{3}^{S}(2)⊕(Z)Y_{4}^{S}(2) $ |
A:(u,0,-1/2) | C:(u,1/2,0) | $2(A)C_{1}^{S}(2)⊕2(A)C_{2}^{S}(2) $ |
B:(0,v,-1/2) | H:(0,1/2,v) | $(B)H_{1}^{S}(2)⊕(B)H_{2}^{S}(2)⊕(B)H_{3}^{S}(2)⊕(B)H_{4}^{S}(2) $ |
C:(u,1/2,0) | A:(u,0,1/2) | $2(C)A_{1}^{S}(2)⊕2(C)A_{2}^{S}(2) $ |
D:(1/2,v,0) | G:(1/2,0,v) | $2(D)G_{1}^{S}(4) $ |
Δ:(0,v,0) | Λ:(0,0,v) | $(Δ)Λ_{1}^{S}(2)⊕(Δ)Λ_{2}^{S}(2)⊕(Δ)Λ_{3}^{S}(2)⊕(Δ)Λ_{4}^{S}(2) $ |
E:(u,1/2,-1/2) | E:(u,1/2,1/2) | $2E_{1}^{S}(2)⊕2E_{2}^{S}(2) $ |
G:(1/2,0,w) | D:(1/2,-w,0) | $2(G)D_{1}^{S}D_{2}^{S}(4) $ |
H:(0,1/2,w) | B:(0,-w,1/2) | $2(H)B_{1}^{S}(2)⊕2(H)B_{2}^{S}(2) $ |
Λ:(0,0,w) | Δ:(0,-w,0) | $2(Λ)Δ_{1}^{S}(2)⊕2(Λ)Δ_{2}^{S}(2) $ |
P:(1/2,v,-1/2) | Q:(1/2,1/2,v) | $2(P)Q_{1}^{S}(4) $ |
Q:(1/2,1/2,w) | P:(1/2,-w,1/2) | $2(Q)P_{1}^{S}P_{2}^{S}(4) $ |
Σ:(u,0,0) | Σ:(u,0,0) | $2Σ_{1}^{S}(2)⊕2Σ_{2}^{S}(2) $ |
K:(0,v,w) | K:(0,-w,v) | $2K_{1}^{S}(2)⊕2K_{2}^{S}(2) $ |
L:(1/2,v,w) | L:(1/2,-w,v) | $2L_{1}^{S}(2)⊕2L_{2}^{S}(2) $ |
M:(u,0,w) | V:(u,-w,0) | $4(M)V_{1}^{S}(2) $ |
N:(u,1/2,w) | W:(u,-w,1/2) | $4(N)W_{1}^{S}(2) $ |
V:(u,v,0) | M:(u,0,v) | $2(V)M_{1}^{S}(2)⊕2(V)M_{2}^{S}(2) $ |
W:(u,v,-1/2) | N:(u,1/2,v) | $2(W)N_{1}^{S}(2)⊕2(W)N_{2}^{S}(2) $ |
GP:(u,v,w) | GP:(u,-w,v) | $4GP_{1}^{S}(2) $ |