The continuously infinite group ∞1 is omitted.
Coordinates | Seitz symbol |
---|---|
a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
-b, a-b, c | x, y, z | { 1 ‖ 3+001 | 0 } |
-a+b, -a, c | x, y, z | { 1 ‖ 3-001 | 0 } |
a-b, -b, -c | x, y, z | { 1 ‖ 2100 | 0 } |
b, a, -c | x, y, z | { 1 ‖ 2110 | 0 } |
-a, -a+b, -c | x, y, z | { 1 ‖ 2010 | 0 } |
-a+b, -a, -c+1/2 | x, y, z | { 1 ‖ -6+001 | 0 0 1/2 } |
a, b, -c+1/2 | x, y, z | { 1 ‖ m001 | 0 0 1/2 } |
-b, a-b, -c+1/2 | x, y, z | { 1 ‖ -6-001 | 0 0 1/2 } |
-a, -a+b, c+1/2 | x, y, z | { 1 ‖ m210 | 0 0 1/2 } |
a-b, -b, c+1/2 | x, y, z | { 1 ‖ m120 | 0 0 1/2 } |
b, a, c+1/2 | x, y, z | { 1 ‖ m1-10 | 0 0 1/2 } |
a-b, a, c+1/2 | -x, -y, -z | { -1 ‖ 6+001 | 0 0 1/2 } |
-a, -b, c+1/2 | -x, -y, -z | { -1 ‖ 2001 | 0 0 1/2 } |
b, -a+b, c+1/2 | -x, -y, -z | { -1 ‖ 6-001 | 0 0 1/2 } |
a, a-b, -c+1/2 | -x, -y, -z | { -1 ‖ 2210 | 0 0 1/2 } |
-a+b, b, -c+1/2 | -x, -y, -z | { -1 ‖ 2120 | 0 0 1/2 } |
-b, -a, -c+1/2 | -x, -y, -z | { -1 ‖ 21-10 | 0 0 1/2 } |
-a, -b, -c | -x, -y, -z | { -1 ‖ -1 | 0 } |
b, -a+b, -c | -x, -y, -z | { -1 ‖ -3+001 | 0 } |
a-b, a, -c | -x, -y, -z | { -1 ‖ -3-001 | 0 } |
-a+b, b, c | -x, -y, -z | { -1 ‖ m100 | 0 } |
-b, -a, c | -x, -y, -z | { -1 ‖ m110 | 0 } |
a, a-b, c | -x, -y, -z | { -1 ‖ m010 | 0 } |
a, b, c | -x, y, z | { m ‖ 1 | 0 } |
-b, a-b, c | -x, y, z | { m ‖ 3+001 | 0 } |
-a+b, -a, c | -x, y, z | { m ‖ 3-001 | 0 } |
a-b, -b, -c | -x, y, z | { m ‖ 2100 | 0 } |
b, a, -c | -x, y, z | { m ‖ 2110 | 0 } |
-a, -a+b, -c | -x, y, z | { m ‖ 2010 | 0 } |
-a+b, -a, -c+1/2 | -x, y, z | { m ‖ -6+001 | 0 0 1/2 } |
a, b, -c+1/2 | -x, y, z | { m ‖ m001 | 0 0 1/2 } |
-b, a-b, -c+1/2 | -x, y, z | { m ‖ -6-001 | 0 0 1/2 } |
-a, -a+b, c+1/2 | -x, y, z | { m ‖ m210 | 0 0 1/2 } |
a-b, -b, c+1/2 | -x, y, z | { m ‖ m120 | 0 0 1/2 } |
b, a, c+1/2 | -x, y, z | { m ‖ m1-10 | 0 0 1/2 } |
a-b, a, c+1/2 | x, -y, -z | { 2 ‖ 6+001 | 0 0 1/2 } |
-a, -b, c+1/2 | x, -y, -z | { 2 ‖ 2001 | 0 0 1/2 } |
b, -a+b, c+1/2 | x, -y, -z | { 2 ‖ 6-001 | 0 0 1/2 } |
a, a-b, -c+1/2 | x, -y, -z | { 2 ‖ 2210 | 0 0 1/2 } |
-a+b, b, -c+1/2 | x, -y, -z | { 2 ‖ 2120 | 0 0 1/2 } |
-b, -a, -c+1/2 | x, -y, -z | { 2 ‖ 21-10 | 0 0 1/2 } |
-a, -b, -c | x, -y, -z | { 2 ‖ -1 | 0 } |
b, -a+b, -c | x, -y, -z | { 2 ‖ -3+001 | 0 } |
a-b, a, -c | x, -y, -z | { 2 ‖ -3-001 | 0 } |
-a+b, b, c | x, -y, -z | { 2 ‖ m100 | 0 } |
-b, -a, c | x, -y, -z | { 2 ‖ m110 | 0 } |
a, a-b, c | x, -y, -z | { 2 ‖ m010 | 0 } |
WP | Site symmetry | Representative |
---|---|---|
2a | $\ce{^{-1}{-3}}\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
2b | $\ce{^{1}{-6}}\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (0,0,1/4 | 0,0,0) |
2c | $\ce{^{1}{-6}}\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/3,2/3,1/4 | 0,0,0) |
2d | $\ce{^{1}{-6}}\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (1/3,2/3,3/4 | 0,0,0) |
4e | $\ce{^{1}{3}}\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,0) |
4f | $\ce{^{1}{3}}\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (1/3,2/3,c | 0,0,0) |
6g | $.\ce{^{1}{2}}/\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (1/2,0,0 | 0,0,0) |
6h | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{\infty m}{1}} $ | (a,2a,1/4 | 0,0,0) |
12i | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (a,0,0 | 0,0,z) |
12j | $\ce{^{1}{m}}..\ce{^{\infty m}{1}} $ | (a,b,1/4 | 0,0,z) |
12k | $.\ce{^{-1}{m}}.\ce{^{\infty m}{1}} $ | (a,2a,c | 0,0,0) |
24l | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
Wavevector-k | Little co-group |
---|---|
A:(0,0,1/2) | $\ce{^{-1}{6/}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
Γ:(0,0,0) | $\ce{^{-1}{6/}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
H:(1/3,1/3,1/2) | $\ce{^{-1}{6/}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
K:(1/3,1/3,0) | $\ce{^{-1}{6/}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
L:(1/2,0,1/2) | $\ce{^{1}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
M:(1/2,0,0) | $\ce{^{1}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
Δ:(0,0,w) | $\ce{^{2}{6/}}\ce{^{m}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
P:(1/3,1/3,w) | $\ce{^{-1}{-3}}\ce{^{1}{1}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
Λ:(u,u,0) | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
Σ:(u,0,0) | $\ce{^{m}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
Q:(u,u,1/2) | $\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
R:(u,0,1/2) | $\ce{^{m}{m}}\ce{^{2}{m}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
U:(1/2,0,w) | $\ce{^{1}{m}}\ce{^{2}{m}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
B:(u,v,0) | $\ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
C:(u,u,w) | $\ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
D:(u,0,w) | $\ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
E:(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(24) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2)⊕Γ_{3}^{S}(2)⊕Γ_{4}^{S}(2)⊕2Γ_{5}^{S}(4)⊕2Γ_{6}^{S}(4) $ | |
A:(0,0,1/2) | A:(0,0,1/2) | $2A_{1}^{S}A_{2}^{S}(8)⊕2A_{3}^{S}(4) $ | |
H:(1/3,1/3,1/2) | H:(1/3,1/3,1/2) | $2H_{1}^{S}(4)⊕2H_{2}^{S}(4)⊕2H_{3}^{S}(4) $ | |
K:(1/3,1/3,0) | K:(1/3,1/3,0) | $K_{1}^{S}(2)⊕K_{2}^{S}(2)⊕K_{3}^{S}(2)⊕K_{4}^{S}(2)⊕2K_{5}^{S}(4)⊕2K_{6}^{S}(4) $ | |
L:(1/2,0,1/2) | L:(1/2,0,1/2) | $6L_{1}^{S}(4) $ | |
M:(1/2,0,0) | M:(1/2,0,0) | $3M_{1}^{S}(2)⊕3M_{2}^{S}(2)⊕3M_{3}^{S}(2)⊕3M_{4}^{S}(2) $ | |
Δ:(0,0,w) | Δ:(0,0,w) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2)⊕4Δ_{3}^{S}(4) $ | |
Λ:(u,u,0) | Λ:(u,u,0) | $3Λ_{1}^{S}(2)⊕3Λ_{2}^{S}(2)⊕3Λ_{3}^{S}(2)⊕3Λ_{4}^{S}(2) $ | |
P:(1/3,1/3,w) | P:(1/3,1/3,w) | $2P_{1}^{S}(2)⊕2P_{2}^{S}(2)⊕4P_{3}^{S}(4) $ | |
Q:(u,u,1/2) | Q:(u,u,1/2) | $6Q_{1}^{S}(4) $ | |
R:(u,0,1/2) | R:(u,0,1/2) | $6R_{1}^{S}R_{2}^{S}(4) $ | |
Σ:(u,0,0) | Σ:(u,0,0) | $6Σ_{1}^{S}(2)⊕6Σ_{2}^{S}(2) $ | |
U:(1/2,0,w) | U:(1/2,0,w) | $6U_{1}^{S}(2)⊕6U_{2}^{S}(2) $ | |
B:(u,v,0) | B:(u,v,0) | $6B_{1}^{S}(2)⊕6B_{2}^{S}(2) $ | |
C:(u,u,w) | C:(u,u,w) | $6C_{1}^{S}(2)⊕6C_{2}^{S}(2) $ | |
D:(u,0,w) | D:(u,0,w) | $12D_{1}^{S}(2) $ | |
E:(u,v,1/2) | E:(u,v,1/2) | $6E_{1}^{S}(2)⊕6E_{2}^{S}(2) $ | |
GP:(u,v,w) | GP:(u,v,w) | $12GP_{1}^{S}(2) $ |
k-vector | k-vector-G↑ | A↑G(12) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2)⊕Γ_{5}^{S}(4)⊕Γ_{6}^{S}(4) $ | |
A:(0,0,1/2) | A:(0,0,1/2) | $A_{1}^{S}A_{2}^{S}(8)⊕A_{3}^{S}(4) $ | |
H:(1/3,1/3,1/2) | H:(1/3,1/3,1/2) | $H_{1}^{S}(4)⊕H_{2}^{S}(4)⊕H_{3}^{S}(4) $ | |
K:(1/3,1/3,0) | K:(1/3,1/3,0) | $K_{1}^{S}(2)⊕K_{2}^{S}(2)⊕K_{5}^{S}(4)⊕K_{6}^{S}(4) $ | |
L:(1/2,0,1/2) | L:(1/2,0,1/2) | $3L_{1}^{S}(4) $ | |
M:(1/2,0,0) | M:(1/2,0,0) | $2M_{1}^{S}(2)⊕2M_{2}^{S}(2)⊕M_{3}^{S}(2)⊕M_{4}^{S}(2) $ | |
Δ:(0,0,w) | Δ:(0,0,w) | $Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2)⊕2Δ_{3}^{S}(4) $ | |
Λ:(u,u,0) | Λ:(u,u,0) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2)⊕Λ_{3}^{S}(2)⊕Λ_{4}^{S}(2) $ | |
P:(1/3,1/3,w) | P:(1/3,1/3,w) | $P_{1}^{S}(2)⊕P_{2}^{S}(2)⊕2P_{3}^{S}(4) $ | |
Q:(u,u,1/2) | Q:(u,u,1/2) | $3Q_{1}^{S}(4) $ | |
R:(u,0,1/2) | R:(u,0,1/2) | $3R_{1}^{S}R_{2}^{S}(4) $ | |
Σ:(u,0,0) | Σ:(u,0,0) | $3Σ_{1}^{S}(2)⊕3Σ_{2}^{S}(2) $ | |
U:(1/2,0,w) | U:(1/2,0,w) | $3U_{1}^{S}(2)⊕3U_{2}^{S}(2) $ | |
B:(u,v,0) | B:(u,v,0) | $3B_{1}^{S}(2)⊕3B_{2}^{S}(2) $ | |
C:(u,u,w) | C:(u,u,w) | $3C_{1}^{S}(2)⊕3C_{2}^{S}(2) $ | |
D:(u,0,w) | D:(u,0,w) | $6D_{1}^{S}(2) $ | |
E:(u,v,1/2) | E:(u,v,1/2) | $3E_{1}^{S}(2)⊕3E_{2}^{S}(2) $ | |
GP:(u,v,w) | GP:(u,v,w) | $6GP_{1}^{S}(2) $ |
k-vector | k-vector-G↑ | A'↑G(12) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{4}^{S}(2)⊕2Γ_{5}^{S}(4) $ | |
A:(0,0,1/2) | A:(0,0,1/2) | $A_{1}^{S}A_{2}^{S}(8)⊕A_{3}^{S}(4) $ | |
H:(1/3,1/3,1/2) | H:(1/3,1/3,1/2) | $H_{1}^{S}(4)⊕H_{2}^{S}(4)⊕H_{3}^{S}(4) $ | |
K:(1/3,1/3,0) | K:(1/3,1/3,0) | $K_{1}^{S}(2)⊕K_{4}^{S}(2)⊕2K_{5}^{S}(4) $ | |
L:(1/2,0,1/2) | L:(1/2,0,1/2) | $3L_{1}^{S}(4) $ | |
M:(1/2,0,0) | M:(1/2,0,0) | $3M_{1}^{S}(2)⊕3M_{4}^{S}(2) $ | |
Δ:(0,0,w) | Δ:(0,0,w) | $Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2)⊕2Δ_{3}^{S}(4) $ | |
Λ:(u,u,0) | Λ:(u,u,0) | $3Λ_{1}^{S}(2)⊕3Λ_{4}^{S}(2) $ | |
P:(1/3,1/3,w) | P:(1/3,1/3,w) | $P_{1}^{S}(2)⊕P_{2}^{S}(2)⊕2P_{3}^{S}(4) $ | |
Q:(u,u,1/2) | Q:(u,u,1/2) | $3Q_{1}^{S}(4) $ | |
R:(u,0,1/2) | R:(u,0,1/2) | $3R_{1}^{S}R_{2}^{S}(4) $ | |
Σ:(u,0,0) | Σ:(u,0,0) | $6Σ_{1}^{S}(2) $ | |
U:(1/2,0,w) | U:(1/2,0,w) | $3U_{1}^{S}(2)⊕3U_{2}^{S}(2) $ | |
B:(u,v,0) | B:(u,v,0) | $6B_{1}^{S}(2) $ | |
C:(u,u,w) | C:(u,u,w) | $3C_{1}^{S}(2)⊕3C_{2}^{S}(2) $ | |
D:(u,0,w) | D:(u,0,w) | $6D_{1}^{S}(2) $ | |
E:(u,v,1/2) | E:(u,v,1/2) | $3E_{1}^{S}(2)⊕3E_{2}^{S}(2) $ | |
GP:(u,v,w) | GP:(u,v,w) | $6GP_{1}^{S}(2) $ |