The continuously infinite group ∞1 is omitted.
Coordinates | Seitz symbol |
---|---|
a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
-b, a, c | x, y, z | { 1 ‖ 4+001 | 0 } |
b, -a, c | x, y, z | { 1 ‖ 4-001 | 0 } |
-a, -b, c | x, y, z | { 1 ‖ 2001 | 0 } |
-a, b, c+1/2 | x, y, z | { 1 ‖ m100 | 0 0 1/2 } |
a, -b, c+1/2 | x, y, z | { 1 ‖ m010 | 0 0 1/2 } |
-b, -a, c+1/2 | x, y, z | { 1 ‖ m110 | 0 0 1/2 } |
b, a, c+1/2 | x, y, z | { 1 ‖ m1-10 | 0 0 1/2 } |
a+1/2, b+1/2, c+1/2 | x, y, z | { 1 ‖ 1 | 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+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 | x, y, z | { 1 ‖ m100 | 1/2 1/2 0 } |
a+1/2, -b+1/2, c | x, y, z | { 1 ‖ m010 | 1/2 1/2 0 } |
-b+1/2, -a+1/2, c | x, y, z | { 1 ‖ m110 | 1/2 1/2 0 } |
b+1/2, a+1/2, c | x, y, z | { 1 ‖ m1-10 | 1/2 1/2 0 } |
a, b, c+1/2 | -x, -y, -z | { -1 ‖ 1 | 0 0 1/2 } |
-b, a, c+1/2 | -x, -y, -z | { -1 ‖ 4+001 | 0 0 1/2 } |
b, -a, c+1/2 | -x, -y, -z | { -1 ‖ 4-001 | 0 0 1/2 } |
-a, -b, c+1/2 | -x, -y, -z | { -1 ‖ 2001 | 0 0 1/2 } |
-a, b, c | -x, -y, -z | { -1 ‖ m100 | 0 } |
a, -b, c | -x, -y, -z | { -1 ‖ m010 | 0 } |
-b, -a, c | -x, -y, -z | { -1 ‖ m110 | 0 } |
b, a, c | -x, -y, -z | { -1 ‖ m1-10 | 0 } |
a+1/2, b+1/2, c | -x, -y, -z | { -1 ‖ 1 | 1/2 1/2 0 } |
-b+1/2, a+1/2, c | -x, -y, -z | { -1 ‖ 4+001 | 1/2 1/2 0 } |
b+1/2, -a+1/2, c | -x, -y, -z | { -1 ‖ 4-001 | 1/2 1/2 0 } |
-a+1/2, -b+1/2, c | -x, -y, -z | { -1 ‖ 2001 | 1/2 1/2 0 } |
-a+1/2, b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m100 | 1/2 1/2 1/2 } |
a+1/2, -b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m010 | 1/2 1/2 1/2 } |
-b+1/2, -a+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m110 | 1/2 1/2 1/2 } |
b+1/2, a+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m1-10 | 1/2 1/2 1/2 } |
a, b, c | -x, y, z | { m ‖ 1 | 0 } |
-b, a, c | -x, y, z | { m ‖ 4+001 | 0 } |
b, -a, c | -x, y, z | { m ‖ 4-001 | 0 } |
-a, -b, c | -x, y, z | { m ‖ 2001 | 0 } |
-a, b, c+1/2 | -x, y, z | { m ‖ m100 | 0 0 1/2 } |
a, -b, c+1/2 | -x, y, z | { m ‖ m010 | 0 0 1/2 } |
-b, -a, c+1/2 | -x, y, z | { m ‖ m110 | 0 0 1/2 } |
b, a, c+1/2 | -x, y, z | { m ‖ m1-10 | 0 0 1/2 } |
a+1/2, b+1/2, c+1/2 | -x, y, z | { m ‖ 1 | 1/2 1/2 1/2 } |
-b+1/2, a+1/2, c+1/2 | -x, y, z | { m ‖ 4+001 | 1/2 1/2 1/2 } |
b+1/2, -a+1/2, c+1/2 | -x, y, z | { m ‖ 4-001 | 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 | -x, y, z | { m ‖ m100 | 1/2 1/2 0 } |
a+1/2, -b+1/2, c | -x, y, z | { m ‖ m010 | 1/2 1/2 0 } |
-b+1/2, -a+1/2, c | -x, y, z | { m ‖ m110 | 1/2 1/2 0 } |
b+1/2, a+1/2, c | -x, y, z | { m ‖ m1-10 | 1/2 1/2 0 } |
a, b, c+1/2 | x, -y, -z | { 2 ‖ 1 | 0 0 1/2 } |
-b, a, c+1/2 | x, -y, -z | { 2 ‖ 4+001 | 0 0 1/2 } |
b, -a, c+1/2 | x, -y, -z | { 2 ‖ 4-001 | 0 0 1/2 } |
-a, -b, c+1/2 | x, -y, -z | { 2 ‖ 2001 | 0 0 1/2 } |
-a, b, c | x, -y, -z | { 2 ‖ m100 | 0 } |
a, -b, c | x, -y, -z | { 2 ‖ m010 | 0 } |
-b, -a, c | x, -y, -z | { 2 ‖ m110 | 0 } |
b, a, c | x, -y, -z | { 2 ‖ m1-10 | 0 } |
a+1/2, b+1/2, c | x, -y, -z | { 2 ‖ 1 | 1/2 1/2 0 } |
-b+1/2, a+1/2, c | x, -y, -z | { 2 ‖ 4+001 | 1/2 1/2 0 } |
b+1/2, -a+1/2, c | x, -y, -z | { 2 ‖ 4-001 | 1/2 1/2 0 } |
-a+1/2, -b+1/2, c | x, -y, -z | { 2 ‖ 2001 | 1/2 1/2 0 } |
-a+1/2, b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m100 | 1/2 1/2 1/2 } |
a+1/2, -b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m010 | 1/2 1/2 1/2 } |
-b+1/2, -a+1/2, c+1/2 | x, -y, -z | { 2 ‖ m110 | 1/2 1/2 1/2 } |
b+1/2, a+1/2, c+1/2 | x, -y, -z | { 2 ‖ m1-10 | 1/2 1/2 1/2 } |
WP | Site symmetry | Representative |
---|---|---|
4a | $\ce{^{1}{4}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,0) |
4b | $\ce{^{-1}{4}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (0,1/2,c | 0,0,0) |
8c | $\ce{^{-1}{2}}.\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (1/4,1/4,c | 0,0,0) |
16d | $.\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (0,b,c | 0,0,0) |
16e | $..\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (a,a,c | 0,0,0) |
16f | $..\ce{^{1}{m}}\ce{^{\infty m}{1}} $ | (a,a+1/2,c | 0,0,z) |
32g | $\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{^{\infty /mm}{1}} $ |
M:(1,1,1) | $\ce{^{1}{4}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
P:(1/2,1/2,1/2) | $\ce{^{m}{4}}\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
X:(1/2,1/2,0) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{2}}\ce{^{\infty /mm}{1}} $ |
N:(1/2,0,1/2) | $\ce{^{1}{m}}\ce{^{\infty /mm}{1}} $ |
Λ:(0,0,w) | $\ce{^{1}{4}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
Δ:(u,u,0) | $\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
Q:(1/2,v,1/2) | $\ce{^{m}{m}}\ce{^{\infty 2}{1}} $ |
Σ:(u,0,0) | $\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
W:(1/2,1/2,w) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{1}{2}}\ce{^{\infty 2}{1}} $ |
Y:(u,1-u,0) | $\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
A:(u,u,w) | $\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
B:(u,0,w) | $\ce{^{1}{m}}\ce{^{\infty 2}{1}} $ |
C:(u,v,0) | $\ce{^{m}{2}}\ce{^{\infty 2}{1}} $ |
GP:(u,v,w) | $\ce{^{1}{1}}\ce{^{\infty 2}{1}} $ |
Spin Brillouin Zone
k-vector | A'↑G(8) |
Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{3}^{S}(2)⊕Γ_{5}^{S}(4) $ |
M:(1,1,1) | $M_{2}^{S}(2)⊕M_{4}^{S}(2)⊕M_{5}^{S}(4) $ |
P:(1/2,1/2,1/2) | $P_{1}^{S}P_{2}^{S}(4)⊕P_{4}^{S}P_{4}^{S}(4) $ |
X:(1/2,1/2,0) | $X_{1}^{S}(2)⊕X_{2}^{S}(2)⊕2X_{4}^{S}(2) $ |
N:(1/2,0,1/2) | $2N_{1}^{S}N_{2}^{S}(4) $ |
Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{3}^{S}(2)⊕Λ_{5}^{S}(4) $ |
Δ:(u,u,0) | $3Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2) $ |
Q:(1/2,v,1/2) | $2Q_{1}^{S}Q_{1}^{S}(4) $ |
Σ:(u,0,0) | $2Σ_{1}^{S}(2)⊕2Σ_{2}^{S}(2) $ |
W:(1/2,1/2,w) | $W_{1}^{S}(2)⊕W_{2}^{S}(2)⊕2W_{4}^{S}(2) $ |
Y:(u,1-u,0) | $Y_{1}^{S}(2)⊕3Y_{2}^{S}(2) $ |
A:(u,u,w) | $3A_{1}^{S}(2)⊕A_{2}^{S}(2) $ |
B:(u,0,w) | $2B_{1}^{S}(2)⊕2B_{2}^{S}(2) $ |
C:(u,v,0) | $4C_{1}^{S}(2) $ |
GP:(u,v,w) | $4GP_{1}^{S}(2) $ |
k-vector | A↑G(16) |
Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2)⊕Γ_{3}^{S}(2)⊕Γ_{4}^{S}(2)⊕2Γ_{5}^{S}(4) $ |
M:(1,1,1) | $M_{1}^{S}(2)⊕M_{2}^{S}(2)⊕M_{3}^{S}(2)⊕M_{4}^{S}(2)⊕2M_{5}^{S}(4) $ |
P:(1/2,1/2,1/2) | $2P_{1}^{S}P_{2}^{S}(4)⊕P_{3}^{S}P_{3}^{S}(4)⊕P_{4}^{S}P_{4}^{S}(4) $ |
X:(1/2,1/2,0) | $2X_{1}^{S}(2)⊕2X_{2}^{S}(2)⊕2X_{3}^{S}(2)⊕2X_{4}^{S}(2) $ |
N:(1/2,0,1/2) | $4N_{1}^{S}N_{2}^{S}(4) $ |
Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2)⊕Λ_{3}^{S}(2)⊕Λ_{4}^{S}(2)⊕2Λ_{5}^{S}(4) $ |
Δ:(u,u,0) | $4Δ_{1}^{S}(2)⊕4Δ_{2}^{S}(2) $ |
Q:(1/2,v,1/2) | $4Q_{1}^{S}Q_{1}^{S}(4) $ |
Σ:(u,0,0) | $4Σ_{1}^{S}(2)⊕4Σ_{2}^{S}(2) $ |
W:(1/2,1/2,w) | $2W_{1}^{S}(2)⊕2W_{2}^{S}(2)⊕2W_{3}^{S}(2)⊕2W_{4}^{S}(2) $ |
Y:(u,1-u,0) | $4Y_{1}^{S}(2)⊕4Y_{2}^{S}(2) $ |
A:(u,u,w) | $4A_{1}^{S}(2)⊕4A_{2}^{S}(2) $ |
B:(u,0,w) | $4B_{1}^{S}(2)⊕4B_{2}^{S}(2) $ |
C:(u,v,0) | $8C_{1}^{S}(2) $ |
GP:(u,v,w) | $8GP_{1}^{S}(2) $ |