The continuously infinite group ∞1 is omitted.
Coordinates | Seitz symbol |
---|---|
a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
a+3/4, -c+3/4, b+1/4 | x, y, z | { 1 ‖ 4+100 | 3/4 3/4 1/4 } |
a+1/4, c+3/4, -b+3/4 | x, y, z | { 1 ‖ 4-100 | 1/4 3/4 3/4 } |
c+1/4, b+3/4, -a+3/4 | x, y, z | { 1 ‖ 4+010 | 1/4 3/4 3/4 } |
-c+3/4, b+1/4, a+3/4 | x, y, z | { 1 ‖ 4-010 | 3/4 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+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 | x, y, z | { 1 ‖ 2100 | 1/2 1/2 0 } |
-a, b+1/2, -c+1/2 | x, y, z | { 1 ‖ 2010 | 0 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+3/4 | x, y, z | { 1 ‖ 2110 | 1/4 3/4 3/4 } |
-b+1/4, -a+1/4, -c+1/4 | x, y, z | { 1 ‖ 21-10 | 1/4 1/4 1/4 } |
-a+3/4, c+1/4, b+3/4 | x, y, z | { 1 ‖ 2011 | 3/4 1/4 3/4 } |
-a+1/4, -c+1/4, -b+1/4 | x, y, z | { 1 ‖ 201-1 | 1/4 1/4 1/4 } |
c+3/4, -b+3/4, a+1/4 | x, y, z | { 1 ‖ 2101 | 3/4 3/4 1/4 } |
-c+1/4, -b+1/4, -a+1/4 | x, y, z | { 1 ‖ 2-101 | 1/4 1/4 1/4 } |
c, a, b | x, y, z | { 1 ‖ 3+111 | 0 } |
b, c, a | x, y, z | { 1 ‖ 3-111 | 0 } |
-b, c+1/2, -a+1/2 | x, y, z | { 1 ‖ 3-1-1-1 | 0 1/2 1/2 } |
-c+1/2, -a, b+1/2 | x, y, z | { 1 ‖ 3+1-1-1 | 1/2 0 1/2 } |
-b+1/2, -c, a+1/2 | x, y, z | { 1 ‖ 3--11-1 | 1/2 0 1/2 } |
c+1/2, -a+1/2, -b | x, y, z | { 1 ‖ 3+-11-1 | 1/2 1/2 0 } |
b+1/2, -c+1/2, -a | x, y, z | { 1 ‖ 3--1-11 | 1/2 1/2 0 } |
-c, a+1/2, -b+1/2 | x, y, z | { 1 ‖ 3+-1-11 | 0 1/2 1/2 } |
a, b, c | -x, y, z | { m ‖ 1 | 0 } |
a+3/4, -c+3/4, b+1/4 | -x, y, z | { m ‖ 4+100 | 3/4 3/4 1/4 } |
a+1/4, c+3/4, -b+3/4 | -x, y, z | { m ‖ 4-100 | 1/4 3/4 3/4 } |
c+1/4, b+3/4, -a+3/4 | -x, y, z | { m ‖ 4+010 | 1/4 3/4 3/4 } |
-c+3/4, b+1/4, a+3/4 | -x, y, z | { m ‖ 4-010 | 3/4 1/4 3/4 } |
-b+3/4, a+1/4, c+3/4 | -x, y, z | { m ‖ 4+001 | 3/4 1/4 3/4 } |
b+3/4, -a+3/4, c+1/4 | -x, y, z | { m ‖ 4-001 | 3/4 3/4 1/4 } |
a+1/2, -b+1/2, -c | -x, y, z | { m ‖ 2100 | 1/2 1/2 0 } |
-a, b+1/2, -c+1/2 | -x, y, z | { m ‖ 2010 | 0 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+3/4 | -x, y, z | { m ‖ 2110 | 1/4 3/4 3/4 } |
-b+1/4, -a+1/4, -c+1/4 | -x, y, z | { m ‖ 21-10 | 1/4 1/4 1/4 } |
-a+3/4, c+1/4, b+3/4 | -x, y, z | { m ‖ 2011 | 3/4 1/4 3/4 } |
-a+1/4, -c+1/4, -b+1/4 | -x, y, z | { m ‖ 201-1 | 1/4 1/4 1/4 } |
c+3/4, -b+3/4, a+1/4 | -x, y, z | { m ‖ 2101 | 3/4 3/4 1/4 } |
-c+1/4, -b+1/4, -a+1/4 | -x, y, z | { m ‖ 2-101 | 1/4 1/4 1/4 } |
c, a, b | -x, y, z | { m ‖ 3+111 | 0 } |
b, c, a | -x, y, z | { m ‖ 3-111 | 0 } |
-b, c+1/2, -a+1/2 | -x, y, z | { m ‖ 3-1-1-1 | 0 1/2 1/2 } |
-c+1/2, -a, b+1/2 | -x, y, z | { m ‖ 3+1-1-1 | 1/2 0 1/2 } |
-b+1/2, -c, a+1/2 | -x, y, z | { m ‖ 3--11-1 | 1/2 0 1/2 } |
c+1/2, -a+1/2, -b | -x, y, z | { m ‖ 3+-11-1 | 1/2 1/2 0 } |
b+1/2, -c+1/2, -a | -x, y, z | { m ‖ 3--1-11 | 1/2 1/2 0 } |
-c, a+1/2, -b+1/2 | -x, y, z | { m ‖ 3+-1-11 | 0 1/2 1/2 } |
WP | Site symmetry | Representative |
---|---|---|
4a | $.\ce{^{1}{3}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/8,1/8,1/8 |0,0,z) |
4b | $.\ce{^{1}{3}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (5/8,5/8,5/8 |0,0,z) |
8c | $.\ce{^{1}{3}}.\ce{^{\infty m}{1}} $ | (a,a,a |0,0,z) |
12d | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/8,b,-b+1/4 |0,0,z) |
24e | $\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}{3}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
R:(1/2,1/2,1/2) | $\ce{^{1}{4}}\ce{^{1}{3}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
M:(1/2,1/2,0) | $\ce{^{1}{4}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
X:(0,1/2,0) | $\ce{^{1}{4}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
Δ:(0,v,0) | $\ce{^{1}{4}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
T:(1/2,1/2,w) | $\ce{^{1}{4}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
Λ:(u,u,u) | $\ce{^{1}{3}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
S:(u,1/2,u) | $\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
Σ:(u,u,0) | $\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
Z:(u,1/2,0) | $\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
A:(u,v,0) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
B:(u,1/2,w) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
C:(u,u,w) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
GP:(u,v,w) | $\ce{^{1}{1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
k-vector | A↑G(12) |
Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{3}^{S}(2)⊕Γ_{4}^{S}(3)⊕2Γ_{5}^{S}(3) $ |
R:(1/2,1/2,1/2) | $R_{1}^{S}R_{2}^{S}(4)⊕2R_{3}^{S}(4) $ |
M:(1/2,1/2,0) | $2M_{1}^{S}M_{4}^{S}(2)⊕M_{2}^{S}M_{3}^{S}(2)⊕3M_{5}^{S}(2) $ |
X:(0,1/2,0) | $3X_{1}^{S}(2)⊕3X_{2}^{S}(2) $ |
Δ:(0,v,0) | $3Δ_{1}^{S}(1)⊕3Δ_{2}^{S}(1)⊕3Δ_{3}^{S}(1)⊕3Δ_{4}^{S}(1) $ |
T:(1/2,1/2,w) | $3T_{1}^{S}T_{2}^{S}(2)⊕3T_{3}^{S}T_{4}^{S}(2) $ |
Λ:(u,u,u) | $4Λ_{1}^{S}(1)⊕4Λ_{2}^{S}(1)⊕4Λ_{3}^{S}(1) $ |
S:(u,1/2,u) | $6S_{1}^{S}S_{2}^{S}(2) $ |
Σ:(u,u,0) | $7Σ_{1}^{S}(1)⊕5Σ_{2}^{S}(1) $ |
Z:(u,1/2,0) | $6Z_{1}^{S}Z_{2}^{S}(2) $ |
A:(u,v,0) | $12A_{1}^{S}(1) $ |
B:(u,1/2,w) | $6B_{1}^{S}B_{1}^{S}(2) $ |
C:(u,u,w) | $12C_{1}^{S}(1) $ |
GP:(u,v,w) | $12GP_{1}^{S}(1) $ |
k-vector | A↑G(24) |
Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}(1)⊕2Γ_{3}^{S}(2)⊕3Γ_{4}^{S}(3)⊕3Γ_{5}^{S}(3) $ |
R:(1/2,1/2,1/2) | $2R_{1}^{S}R_{2}^{S}(4)⊕4R_{3}^{S}(4) $ |
M:(1/2,1/2,0) | $3M_{1}^{S}M_{4}^{S}(2)⊕3M_{2}^{S}M_{3}^{S}(2)⊕6M_{5}^{S}(2) $ |
X:(0,1/2,0) | $6X_{1}^{S}(2)⊕6X_{2}^{S}(2) $ |
Δ:(0,v,0) | $6Δ_{1}^{S}(1)⊕6Δ_{2}^{S}(1)⊕6Δ_{3}^{S}(1)⊕6Δ_{4}^{S}(1) $ |
T:(1/2,1/2,w) | $6T_{1}^{S}T_{2}^{S}(2)⊕6T_{3}^{S}T_{4}^{S}(2) $ |
Λ:(u,u,u) | $8Λ_{1}^{S}(1)⊕8Λ_{2}^{S}(1)⊕8Λ_{3}^{S}(1) $ |
S:(u,1/2,u) | $12S_{1}^{S}S_{2}^{S}(2) $ |
Σ:(u,u,0) | $12Σ_{1}^{S}(1)⊕12Σ_{2}^{S}(1) $ |
Z:(u,1/2,0) | $12Z_{1}^{S}Z_{2}^{S}(2) $ |
A:(u,v,0) | $24A_{1}^{S}(1) $ |
B:(u,1/2,w) | $12B_{1}^{S}B_{1}^{S}(2) $ |
C:(u,u,w) | $24C_{1}^{S}(1) $ |
GP:(u,v,w) | $24GP_{1}^{S}(1) $ |
k-vector | A1↑G(4) |
Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{5}^{S}(3) $ |
R:(1/2,1/2,1/2) | $R_{3}^{S}(4) $ |
M:(1/2,1/2,0) | $M_{1}^{S}M_{4}^{S}(2)⊕M_{5}^{S}(2) $ |
X:(0,1/2,0) | $X_{1}^{S}(2)⊕X_{2}^{S}(2) $ |
Δ:(0,v,0) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1)⊕Δ_{3}^{S}(1)⊕Δ_{4}^{S}(1) $ |
T:(1/2,1/2,w) | $T_{1}^{S}T_{2}^{S}(2)⊕T_{3}^{S}T_{4}^{S}(2) $ |
Λ:(u,u,u) | $2Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1)⊕Λ_{3}^{S}(1) $ |
S:(u,1/2,u) | $2S_{1}^{S}S_{2}^{S}(2) $ |
Σ:(u,u,0) | $3Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
Z:(u,1/2,0) | $2Z_{1}^{S}Z_{2}^{S}(2) $ |
A:(u,v,0) | $4A_{1}^{S}(1) $ |
B:(u,1/2,w) | $2B_{1}^{S}B_{1}^{S}(2) $ |
C:(u,u,w) | $4C_{1}^{S}(1) $ |
GP:(u,v,w) | $4GP_{1}^{S}(1) $ |
k-vector | A1↑G(4) |
Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{5}^{S}(3) $ |
R:(1/2,1/2,1/2) | $R_{3}^{S}(4) $ |
M:(1/2,1/2,0) | $M_{1}^{S}M_{4}^{S}(2)⊕M_{5}^{S}(2) $ |
X:(0,1/2,0) | $X_{1}^{S}(2)⊕X_{2}^{S}(2) $ |
Δ:(0,v,0) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1)⊕Δ_{3}^{S}(1)⊕Δ_{4}^{S}(1) $ |
T:(1/2,1/2,w) | $T_{1}^{S}T_{2}^{S}(2)⊕T_{3}^{S}T_{4}^{S}(2) $ |
Λ:(u,u,u) | $2Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1)⊕Λ_{3}^{S}(1) $ |
S:(u,1/2,u) | $2S_{1}^{S}S_{2}^{S}(2) $ |
Σ:(u,u,0) | $3Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
Z:(u,1/2,0) | $2Z_{1}^{S}Z_{2}^{S}(2) $ |
A:(u,v,0) | $4A_{1}^{S}(1) $ |
B:(u,1/2,w) | $2B_{1}^{S}B_{1}^{S}(2) $ |
C:(u,u,w) | $4C_{1}^{S}(1) $ |
GP:(u,v,w) | $4GP_{1}^{S}(1) $ |
k-vector | A1↑G(8) |
Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}(1)⊕Γ_{4}^{S}(3)⊕Γ_{5}^{S}(3) $ |
R:(1/2,1/2,1/2) | $2R_{3}^{S}(4) $ |
M:(1/2,1/2,0) | $M_{1}^{S}M_{4}^{S}(2)⊕M_{2}^{S}M_{3}^{S}(2)⊕2M_{5}^{S}(2) $ |
X:(0,1/2,0) | $2X_{1}^{S}(2)⊕2X_{2}^{S}(2) $ |
Δ:(0,v,0) | $2Δ_{1}^{S}(1)⊕2Δ_{2}^{S}(1)⊕2Δ_{3}^{S}(1)⊕2Δ_{4}^{S}(1) $ |
T:(1/2,1/2,w) | $2T_{1}^{S}T_{2}^{S}(2)⊕2T_{3}^{S}T_{4}^{S}(2) $ |
Λ:(u,u,u) | $4Λ_{1}^{S}(1)⊕2Λ_{2}^{S}(1)⊕2Λ_{3}^{S}(1) $ |
S:(u,1/2,u) | $4S_{1}^{S}S_{2}^{S}(2) $ |
Σ:(u,u,0) | $4Σ_{1}^{S}(1)⊕4Σ_{2}^{S}(1) $ |
Z:(u,1/2,0) | $4Z_{1}^{S}Z_{2}^{S}(2) $ |
A:(u,v,0) | $8A_{1}^{S}(1) $ |
B:(u,1/2,w) | $4B_{1}^{S}B_{1}^{S}(2) $ |
C:(u,u,w) | $8C_{1}^{S}(1) $ |
GP:(u,v,w) | $8GP_{1}^{S}(1) $ |