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 ‖ 2001 | 0 1/2 0 } |
b+3/4, a+1/4, -c+3/4 | x, y, z | { 1 ‖ 2110 | 3/4 1/4 3/4 } |
-b+1/4, -a+1/4, -c+3/4 | x, y, z | { 1 ‖ 21-10 | 1/4 1/4 3/4 } |
-a, -b, -c | x, y, z | { 1 ‖ -1 | 0 } |
a, b+1/2, -c | x, y, z | { 1 ‖ m001 | 0 1/2 0 } |
-b+1/4, -a+3/4, c+1/4 | x, y, z | { 1 ‖ m110 | 1/4 3/4 1/4 } |
b+3/4, a+3/4, c+1/4 | x, y, z | { 1 ‖ m1-10 | 3/4 3/4 1/4 } |
-b+1/4, a+3/4, c+1/4 | -x, -y, -z | { -1 ‖ 4+001 | 1/4 3/4 1/4 } |
b+3/4, -a+3/4, c+1/4 | -x, -y, -z | { -1 ‖ 4-001 | 3/4 3/4 1/4 } |
a, -b, -c | -x, -y, -z | { -1 ‖ 2100 | 0 } |
-a, b+1/2, -c | -x, -y, -z | { -1 ‖ 2010 | 0 1/2 0 } |
b+3/4, -a+1/4, -c+3/4 | -x, -y, -z | { -1 ‖ -4+001 | 3/4 1/4 3/4 } |
-b+1/4, a+1/4, -c+3/4 | -x, -y, -z | { -1 ‖ -4-001 | 1/4 1/4 3/4 } |
-a, b, c | -x, -y, -z | { -1 ‖ m100 | 0 } |
a, -b+1/2, c | -x, -y, -z | { -1 ‖ m010 | 0 1/2 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, c+1/2 | x, y, z | { 1 ‖ 2001 | 1/2 0 1/2 } |
b+1/4, a+3/4, -c+1/4 | x, y, z | { 1 ‖ 2110 | 1/4 3/4 1/4 } |
-b+3/4, -a+3/4, -c+1/4 | x, y, z | { 1 ‖ 21-10 | 3/4 3/4 1/4 } |
-a+1/2, -b+1/2, -c+1/2 | x, y, z | { 1 ‖ -1 | 1/2 1/2 1/2 } |
a+1/2, b, -c+1/2 | x, y, z | { 1 ‖ m001 | 1/2 0 1/2 } |
-b+3/4, -a+1/4, c+3/4 | x, y, z | { 1 ‖ m110 | 3/4 1/4 3/4 } |
b+1/4, a+1/4, c+3/4 | x, y, z | { 1 ‖ m1-10 | 1/4 1/4 3/4 } |
-b+3/4, a+1/4, c+3/4 | -x, -y, -z | { -1 ‖ 4+001 | 3/4 1/4 3/4 } |
b+1/4, -a+1/4, c+3/4 | -x, -y, -z | { -1 ‖ 4-001 | 1/4 1/4 3/4 } |
a+1/2, -b+1/2, -c+1/2 | -x, -y, -z | { -1 ‖ 2100 | 1/2 1/2 1/2 } |
-a+1/2, b, -c+1/2 | -x, -y, -z | { -1 ‖ 2010 | 1/2 0 1/2 } |
b+1/4, -a+3/4, -c+1/4 | -x, -y, -z | { -1 ‖ -4+001 | 1/4 3/4 1/4 } |
-b+3/4, a+3/4, -c+1/4 | -x, -y, -z | { -1 ‖ -4-001 | 3/4 3/4 1/4 } |
-a+1/2, b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m100 | 1/2 1/2 1/2 } |
a+1/2, -b, c+1/2 | -x, -y, -z | { -1 ‖ m010 | 1/2 0 1/2 } |
a, b, c | -x, y, z | { m ‖ 1 | 0 } |
-a, -b+1/2, c | -x, y, z | { m ‖ 2001 | 0 1/2 0 } |
b+3/4, a+1/4, -c+3/4 | -x, y, z | { m ‖ 2110 | 3/4 1/4 3/4 } |
-b+1/4, -a+1/4, -c+3/4 | -x, y, z | { m ‖ 21-10 | 1/4 1/4 3/4 } |
-a, -b, -c | -x, y, z | { m ‖ -1 | 0 } |
a, b+1/2, -c | -x, y, z | { m ‖ m001 | 0 1/2 0 } |
-b+1/4, -a+3/4, c+1/4 | -x, y, z | { m ‖ m110 | 1/4 3/4 1/4 } |
b+3/4, a+3/4, c+1/4 | -x, y, z | { m ‖ m1-10 | 3/4 3/4 1/4 } |
-b+1/4, a+3/4, c+1/4 | x, -y, -z | { 2 ‖ 4+001 | 1/4 3/4 1/4 } |
b+3/4, -a+3/4, c+1/4 | x, -y, -z | { 2 ‖ 4-001 | 3/4 3/4 1/4 } |
a, -b, -c | x, -y, -z | { 2 ‖ 2100 | 0 } |
-a, b+1/2, -c | x, -y, -z | { 2 ‖ 2010 | 0 1/2 0 } |
b+3/4, -a+1/4, -c+3/4 | x, -y, -z | { 2 ‖ -4+001 | 3/4 1/4 3/4 } |
-b+1/4, a+1/4, -c+3/4 | x, -y, -z | { 2 ‖ -4-001 | 1/4 1/4 3/4 } |
-a, b, c | x, -y, -z | { 2 ‖ m100 | 0 } |
a, -b+1/2, c | x, -y, -z | { 2 ‖ m010 | 0 1/2 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, c+1/2 | -x, y, z | { m ‖ 2001 | 1/2 0 1/2 } |
b+1/4, a+3/4, -c+1/4 | -x, y, z | { m ‖ 2110 | 1/4 3/4 1/4 } |
-b+3/4, -a+3/4, -c+1/4 | -x, y, z | { m ‖ 21-10 | 3/4 3/4 1/4 } |
-a+1/2, -b+1/2, -c+1/2 | -x, y, z | { m ‖ -1 | 1/2 1/2 1/2 } |
a+1/2, b, -c+1/2 | -x, y, z | { m ‖ m001 | 1/2 0 1/2 } |
-b+3/4, -a+1/4, c+3/4 | -x, y, z | { m ‖ m110 | 3/4 1/4 3/4 } |
b+1/4, a+1/4, c+3/4 | -x, y, z | { m ‖ m1-10 | 1/4 1/4 3/4 } |
-b+3/4, a+1/4, c+3/4 | x, -y, -z | { 2 ‖ 4+001 | 3/4 1/4 3/4 } |
b+1/4, -a+1/4, c+3/4 | x, -y, -z | { 2 ‖ 4-001 | 1/4 1/4 3/4 } |
a+1/2, -b+1/2, -c+1/2 | x, -y, -z | { 2 ‖ 2100 | 1/2 1/2 1/2 } |
-a+1/2, b, -c+1/2 | x, -y, -z | { 2 ‖ 2010 | 1/2 0 1/2 } |
b+1/4, -a+3/4, -c+1/4 | x, -y, -z | { 2 ‖ -4+001 | 1/4 3/4 1/4 } |
-b+3/4, a+3/4, -c+1/4 | x, -y, -z | { 2 ‖ -4-001 | 3/4 3/4 1/4 } |
-a+1/2, b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m100 | 1/2 1/2 1/2 } |
a+1/2, -b, c+1/2 | x, -y, -z | { 2 ‖ m010 | 1/2 0 1/2 } |
WP | Site symmetry | Representative |
---|---|---|
4a | $\ce{^{-1}{-4}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,3/4,1/8 | 0,0,0) |
4b | $\ce{^{-1}{-4}}\ce{^{-1}{m}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,1/4,3/8 | 0,0,0) |
8c | $.\ce{^{-1}{2}}/\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
8d | $.\ce{^{-1}{2}}/\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,0) |
8e | $\ce{^{1}{2}}\ce{^{-1}{m}}\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (0,1/4,c | 0,0,0) |
16f | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (a,0,0 | 0,0,0) |
16g | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (a,a+1/4,7/8 | 0,0,z) |
16h | $.\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (0,b,c | 0,0,0) |
32i | $\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{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
M:(1,1,1) | $\ce{^{-1}{4/}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
P:(1/2,1/2,1/2) | $\ce{^{-1}{4/}}\ce{^{m}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
X:(1/2,1/2,0) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
N:(1/2,0,1/2) | $\ce{^{2}{2/}}\ce{^{2}{m}}\ce{^{\infty m}{1}} $ |
Λ:(0,0,w) | $\ce{^{2}{4/}}\ce{^{m}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
Δ:(u,u,0) | $\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
Q:(1/2,v,1/2) | $\ce{^{2}{2/}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
Σ:(u,0,0) | $\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
W:(1/2,1/2,w) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
Y:(u,1-u,0) | $\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
A:(u,u,w) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
B:(u,0,w) | $\ce{^{-1}{2/}}\ce{^{2}{m}}\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↑ | A↑G(8) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2)⊕Γ_{4}^{S,+}(2)⊕Γ_{4}^{S,-}(2) $ | |
M:(0,0,1) | Z:(0,0,1) | $(M)Z_{1}^{S}(4)⊕(M)Z_{2}^{S}(4) $ | |
N:(1/2,0,1/2) | L:(1/2,1/2,1/2) | $2(N)L_{1}^{S,+}(2)⊕2(N)L_{1}^{S,-}(2) $ | |
P:(1/2,1/2,1/2) | H:(0,1,1/2) | $2(P)H_{1}^{S}(4) $ | |
X:(1/2,1/2,0) | Y:(0,1,0) | $2(X)Y_{1}^{S}(4) $ | |
Δ:(u,u,0) | Δ:(0,2*u,0) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $ | |
Λ:(0,0,w) | Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2)⊕Λ_{3}^{S}(2)⊕Λ_{4}^{S}(2) $ | |
Q:(1/2,v,1/2) | GP:(1/2-v,1/2+v,1/2) | $4(Q)GP_{1}^{S}(2) $ | |
Σ:(u,0,0) | M:(u,u,0) | $2(Σ)M_{1}^{S}(2)⊕2(Σ)M_{2}^{S}(2) $ | |
W:(1/2,1/2,w) | H:(0,1,w) | $2(W)H_{1}^{S}(4) $ | |
Y:(u,-u,1) | A:(2*u,0,1) | $2(Y)A_{1}^{S}(4) $ | |
A:(u,u,w) | E:(0,2*u,w) | $2(A)E_{1}^{S}(2)⊕2(A)E_{2}^{S}(2) $ | |
B:(u,0,w) | GP:(u,u,w) | $4(B)GP_{1}^{S}(2) $ | |
C:(u,v,0) | M:(u-v,u+v,0) | $2(C)M_{1}^{S}(2)⊕2(C)M_{2}^{S}(2) $ | |
GP:(u,v,w) | GP:(u-v,u+v,w) | $4GP_{1}^{S}(2) $ |
k-vector | k-vector-G↑ | A↑G(16) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2)⊕Γ_{2}^{S,+}(2)⊕Γ_{2}^{S,-}(2)⊕Γ_{3}^{S,+}(2)⊕Γ_{3}^{S,-}(2)⊕Γ_{4}^{S,+}(2)⊕Γ_{4}^{S,-}(2) $ | |
M:(0,0,1) | Z:(0,0,1) | $2(M)Z_{1}^{S}(4)⊕2(M)Z_{2}^{S}(4) $ | |
N:(1/2,0,1/2) | L:(1/2,1/2,1/2) | $4(N)L_{1}^{S,+}(2)⊕4(N)L_{1}^{S,-}(2) $ | |
P:(1/2,1/2,1/2) | H:(0,1,1/2) | $4(P)H_{1}^{S}(4) $ | |
X:(1/2,1/2,0) | Y:(0,1,0) | $2(X)Y_{1}^{S}(4)⊕2(X)Y_{2}^{S}(4) $ | |
Δ:(u,u,0) | Δ:(0,2*u,0) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2)⊕2Δ_{3}^{S}(2)⊕2Δ_{4}^{S}(2) $ | |
Λ:(0,0,w) | Λ:(0,0,w) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2)⊕2Λ_{3}^{S}(2)⊕2Λ_{4}^{S}(2) $ | |
Q:(1/2,v,1/2) | GP:(1/2-v,1/2+v,1/2) | $8(Q)GP_{1}^{S}(2) $ | |
Σ:(u,0,0) | M:(u,u,0) | $4(Σ)M_{1}^{S}(2)⊕4(Σ)M_{2}^{S}(2) $ | |
W:(1/2,1/2,w) | H:(0,1,w) | $4(W)H_{1}^{S}(4) $ | |
Y:(u,-u,1) | A:(2*u,0,1) | $4(Y)A_{1}^{S}(4) $ | |
A:(u,u,w) | E:(0,2*u,w) | $4(A)E_{1}^{S}(2)⊕4(A)E_{2}^{S}(2) $ | |
B:(u,0,w) | GP:(u,u,w) | $8(B)GP_{1}^{S}(2) $ | |
C:(u,v,0) | M:(u-v,u+v,0) | $4(C)M_{1}^{S}(2)⊕4(C)M_{2}^{S}(2) $ | |
GP:(u,v,w) | GP:(u-v,u+v,w) | $8GP_{1}^{S}(2) $ |