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 ‖ 2100 | 0 } |
-a, b, -c | x, y, z | { 1 ‖ 2010 | 0 } |
-a, -b, c | x, y, z | { 1 ‖ 2001 | 0 } |
c, a, b | x, y, z | { 1 ‖ 3+111 | 0 } |
b, c, a | x, y, z | { 1 ‖ 3-111 | 0 } |
-b, c, -a | x, y, z | { 1 ‖ 3-1-1-1 | 0 } |
-c, -a, b | x, y, z | { 1 ‖ 3+1-1-1 | 0 } |
-b, -c, a | x, y, z | { 1 ‖ 3--11-1 | 0 } |
c, -a, -b | x, y, z | { 1 ‖ 3+-11-1 | 0 } |
b, -c, -a | x, y, z | { 1 ‖ 3--1-11 | 0 } |
-c, a, -b | x, y, z | { 1 ‖ 3+-1-11 | 0 } |
-a+1/2, c+1/2, -b+1/2 | -x, -y, -z | { -1 ‖ -4+100 | 1/2 1/2 1/2 } |
-a+1/2, -c+1/2, b+1/2 | -x, -y, -z | { -1 ‖ -4-100 | 1/2 1/2 1/2 } |
-c+1/2, -b+1/2, a+1/2 | -x, -y, -z | { -1 ‖ -4+010 | 1/2 1/2 1/2 } |
c+1/2, -b+1/2, -a+1/2 | -x, -y, -z | { -1 ‖ -4-010 | 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 } |
-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+1/2, -c+1/2, -b+1/2 | -x, -y, -z | { -1 ‖ m011 | 1/2 1/2 1/2 } |
a+1/2, c+1/2, b+1/2 | -x, -y, -z | { -1 ‖ m01-1 | 1/2 1/2 1/2 } |
-c+1/2, b+1/2, -a+1/2 | -x, -y, -z | { -1 ‖ m101 | 1/2 1/2 1/2 } |
c+1/2, b+1/2, a+1/2 | -x, -y, -z | { -1 ‖ m-101 | 1/2 1/2 1/2 } |
a, b, c | -x, y, z | { m ‖ 1 | 0 } |
a, -b, -c | -x, y, z | { m ‖ 2100 | 0 } |
-a, b, -c | -x, y, z | { m ‖ 2010 | 0 } |
-a, -b, c | -x, y, z | { m ‖ 2001 | 0 } |
c, a, b | -x, y, z | { m ‖ 3+111 | 0 } |
b, c, a | -x, y, z | { m ‖ 3-111 | 0 } |
-b, c, -a | -x, y, z | { m ‖ 3-1-1-1 | 0 } |
-c, -a, b | -x, y, z | { m ‖ 3+1-1-1 | 0 } |
-b, -c, a | -x, y, z | { m ‖ 3--11-1 | 0 } |
c, -a, -b | -x, y, z | { m ‖ 3+-11-1 | 0 } |
b, -c, -a | -x, y, z | { m ‖ 3--1-11 | 0 } |
-c, a, -b | -x, y, z | { m ‖ 3+-1-11 | 0 } |
-a+1/2, c+1/2, -b+1/2 | x, -y, -z | { 2 ‖ -4+100 | 1/2 1/2 1/2 } |
-a+1/2, -c+1/2, b+1/2 | x, -y, -z | { 2 ‖ -4-100 | 1/2 1/2 1/2 } |
-c+1/2, -b+1/2, a+1/2 | x, -y, -z | { 2 ‖ -4+010 | 1/2 1/2 1/2 } |
c+1/2, -b+1/2, -a+1/2 | x, -y, -z | { 2 ‖ -4-010 | 1/2 1/2 1/2 } |
b+1/2, -a+1/2, -c+1/2 | x, -y, -z | { 2 ‖ -4+001 | 1/2 1/2 1/2 } |
-b+1/2, a+1/2, -c+1/2 | x, -y, -z | { 2 ‖ -4-001 | 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 } |
a+1/2, -c+1/2, -b+1/2 | x, -y, -z | { 2 ‖ m011 | 1/2 1/2 1/2 } |
a+1/2, c+1/2, b+1/2 | x, -y, -z | { 2 ‖ m01-1 | 1/2 1/2 1/2 } |
-c+1/2, b+1/2, -a+1/2 | x, -y, -z | { 2 ‖ m101 | 1/2 1/2 1/2 } |
c+1/2, b+1/2, a+1/2 | x, -y, -z | { 2 ‖ m-101 | 1/2 1/2 1/2 } |
WP | Site symmetry | Representative |
---|---|---|
2a | $\ce{^{1}{2}}\ce{^{1}{3}}.\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,z) |
6b | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (0,1/2,1/2 | 0,0,z) |
6c | $\ce{^{-1}{-4}}..\ce{^{\infty m}{1}} $ | (1/4,1/2,0 | 0,0,0) |
6d | $\ce{^{-1}{-4}}..\ce{^{\infty m}{1}} $ | (1/4,0,1/2 | 0,0,0) |
8e | $.\ce{^{1}{3}}.\ce{^{\infty m}{1}} $ | (a,a,a | 0,0,z) |
12f | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,0,0 | 0,0,z) |
12g | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,1/2,0 | 0,0,z) |
12h | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,0,1/2 | 0,0,z) |
24i | $\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}{m}}\ce{^{\infty m}{1}} $ |
R:(1/2,1/2,1/2) | $\ce{^{-1}{-4}}\ce{^{1}{3}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
M:(1/2,1/2,0) | $\ce{^{-1}{-4}}\ce{^{1}{2}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
X:(0,1/2,0) | $\ce{^{-1}{-4}}\ce{^{1}{2}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
Δ:(0,v,0) | $\ce{^{-1}{-4}}\ce{^{m}{2}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
T:(1/2,1/2,w) | $\ce{^{-1}{-4}}\ce{^{m}{2}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
Λ:(u,u,u) | $\ce{^{1}{3}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
S:(u,1/2,u) | $\ce{^{-1}{m}}\ce{^{m}{2}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
Σ:(u,u,0) | $\ce{^{2}{m}}\ce{^{-1}{m}}\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{^{2}{m}}\ce{^{\infty}{1}} $ |
GP:(u,v,w) | $\ce{^{1}{1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
k-vector | k-vector-G↑ | A↑G(2) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2) $ | |
M:(1/2,1/2,0) | M:(1/2,1/2,0) | $M_{1}^{S}(2) $ | |
R:(1/2,1/2,1/2) | R:(1/2,1/2,1/2) | $R_{1}^{S}(2) $ | |
X:(0,1/2,0) | X:(0,1/2,0) | $X_{1}^{S}(2) $ | |
Δ:(0,v,0) | Δ:(0,v,0) | $Δ_{1}^{S}(2) $ | |
Λ:(u,u,u) | Λ:(u,u,u) | $Λ_{1}^{S}(2) $ | |
S:(u,1/2,u) | S:(u,1/2,u) | $S_{1}^{S}(2) $ | |
Σ:(u,u,0) | Σ:(u,u,0) | $Σ_{1}^{S}(2) $ | |
T:(1/2,1/2,w) | T:(1/2,1/2,w) | $T_{1}^{S}(2) $ | |
Z:(u,1/2,0) | Z:(u,1/2,0) | $2 Z_{1}^{S}(1)$ | Spin Splitting |
A:(u,v,0) | A:(u,v,0) | $2A_{1}^{S}(1)$ | Spin Splitting |
B:(u,1/2,w) | B:(u,1/2,w) | $2B_{1}^{S}(1)$ | Spin Splitting |
C:(u,u,w) | C:(u,u,w) | $C_{1}^{S}(2) $ | |
GP:(u,v,w) | GP:(u,v,w) | $2GP_{1}^{S}(1)$ | Spin Splitting |
k-vector | k-vector-G↑ | A↑G(6) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}Γ_{3}^{S}(4) $ | |
M:(1/2,1/2,0) | M:(1/2,1/2,0) | $M_{2}^{S}(2)⊕M_{3}^{S}(2)⊕M_{4}^{S}(2) $ | |
R:(1/2,1/2,1/2) | R:(1/2,1/2,1/2) | $R_{4}^{S}(6) $ | |
X:(0,1/2,0) | X:(0,1/2,0) | $X_{1}^{S}(2)⊕2X_{4}^{S}(2) $ | |
Δ:(0,v,0) | Δ:(0,v,0) | $3Δ_{1}^{S}(2) $ | |
Λ:(u,u,u) | Λ:(u,u,u) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2)⊕Λ_{3}^{S}(2) $ | |
S:(u,1/2,u) | S:(u,1/2,u) | $3S_{1}^{S}(2) $ | |
Σ:(u,u,0) | Σ:(u,u,0) | $3Σ_{1}^{S}(2) $ | |
T:(1/2,1/2,w) | T:(1/2,1/2,w) | $T_{1}^{S}(2)⊕2T_{2}^{S}(2) $ | |
Z:(u,1/2,0) | Z:(u,1/2,0) | $2Z_{1}^{S}(1)⊕4Z_{2}^{S}(1)$ | Spin Splitting |
A:(u,v,0) | A:(u,v,0) | $6A_{1}^{S}(1)$ | Spin Splitting |
B:(u,1/2,w) | B:(u,1/2,w) | $6B_{1}^{S}(1)$ | Spin Splitting |
C:(u,u,w) | C:(u,u,w) | $3C_{1}^{S}(2) $ | |
GP:(u,v,w) | GP:(u,v,w) | $6GP_{1}^{S}(1)$ | Spin Splitting |
k-vector | k-vector-G↑ | A1↑G(8) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{4}^{S}(6) $ | |
M:(1/2,1/2,0) | M:(1/2,1/2,0) | $M_{1}^{S}(2)⊕M_{2}^{S}(2)⊕M_{3}^{S}(2)⊕M_{4}^{S}(2) $ | |
R:(1/2,1/2,1/2) | R:(1/2,1/2,1/2) | $R_{1}^{S}(2)⊕R_{4}^{S}(6) $ | |
X:(0,1/2,0) | X:(0,1/2,0) | $X_{1}^{S}(2)⊕X_{2}^{S}(2)⊕X_{3}^{S}(2)⊕X_{4}^{S}(2) $ | |
Δ:(0,v,0) | Δ:(0,v,0) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $ | |
Λ:(u,u,u) | Λ:(u,u,u) | $2Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2)⊕Λ_{3}^{S}(2) $ | |
S:(u,1/2,u) | S:(u,1/2,u) | $4S_{1}^{S}(2) $ | |
Σ:(u,u,0) | Σ:(u,u,0) | $4Σ_{1}^{S}(2) $ | |
T:(1/2,1/2,w) | T:(1/2,1/2,w) | $2T_{1}^{S}(2)⊕2T_{2}^{S}(2) $ | |
Z:(u,1/2,0) | Z:(u,1/2,0) | $4Z_{1}^{S}(1)⊕4Z_{2}^{S}(1)$ | Spin Splitting |
A:(u,v,0) | A:(u,v,0) | $8A_{1}^{S}(1)$ | Spin Splitting |
B:(u,1/2,w) | B:(u,1/2,w) | $8B_{1}^{S}(1)$ | Spin Splitting |
C:(u,u,w) | C:(u,u,w) | $4C_{1}^{S}(2) $ | |
GP:(u,v,w) | GP:(u,v,w) | $8GP_{1}^{S}(1)$ | Spin Splitting |
k-vector | k-vector-G↑ | A↑G(12) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}Γ_{3}^{S}(4)⊕Γ_{4}^{S}(6) $ | |
M:(1/2,1/2,0) | M:(1/2,1/2,0) | $3 M_{1}^{S}(2)⊕M_{2}^{S}(2)⊕M_{3}^{S}(2)⊕M_{4}^{S}(2) $ | |
R:(1/2,1/2,1/2) | R:(1/2,1/2,1/2) | $R_{1}^{S}(4)⊕R_{2}^{S}R_{3}^{S}(4)⊕R_{4}^{S}(6) $ | |
X:(0,1/2,0) | X:(0,1/2,0) | $3 X_{1}^{S}(2)⊕X_{2}^{S}(2)⊕X_{3}^{S}(2)⊕X_{4}^{S}(2) $ | |
Δ:(0,v,0) | Δ:(0,v,0) | $4Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $ | |
Λ:(u,u,u) | Λ:(u,u,u) | $2Λ_{1}^{S}(2)⊕2 Λ_{2}^{S}(2)⊕2 Λ_{3}^{S}(2) $ | |
S:(u,1/2,u) | S:(u,1/2,u) | $6S_{1}^{S}(2) $ | |
Σ:(u,u,0) | Σ:(u,u,0) | $6Σ_{1}^{S}(2) $ | |
T:(1/2,1/2,w) | T:(1/2,1/2,w) | $4T_{1}^{S}(2)⊕2T_{2}^{S}(2) $ | |
Z:(u,1/2,0) | Z:(u,1/2,0) | $8Z_{1}^{S}(1)⊕4Z_{2}^{S}(1)$ | Spin Splitting |
A:(u,v,0) | A:(u,v,0) | $12A_{1}^{S}(1)$ | Spin Splitting |
B:(u,1/2,w) | B:(u,1/2,w) | $12B_{1}^{S}(1)$ | Spin Splitting |
C:(u,u,w) | C:(u,u,w) | $6C_{1}^{S}(2) $ | |
GP:(u,v,w) | GP:(u,v,w) | $12GP_{1}^{S}(1)$ | Spin Splitting |
k-vector | k-vector-G↑ | A↑G(12) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}Γ_{3}^{S}(4)⊕Γ_{4}^{S}(6) $ | |
M:(1/2,1/2,0) | M:(1/2,1/2,0) | $M_{1}^{S}(2)⊕M_{2}^{S}(2)⊕M_{3}^{S}(2)⊕3 M_{4}^{S}(2) $ | |
R:(1/2,1/2,1/2) | R:(1/2,1/2,1/2) | $2 R_{4}^{S}(6) $ | |
X:(0,1/2,0) | X:(0,1/2,0) | $2 X_{1}^{S}(2)⊕2 X_{2}^{S}(2)⊕2X_{4}^{S}(2) $ | |
Δ:(0,v,0) | Δ:(0,v,0) | $4Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $ | |
Λ:(u,u,u) | Λ:(u,u,u) | $2Λ_{1}^{S}(2)⊕2 Λ_{2}^{S}(2)⊕2 Λ_{3}^{S}(2) $ | |
S:(u,1/2,u) | S:(u,1/2,u) | $6S_{1}^{S}(2) $ | |
Σ:(u,u,0) | Σ:(u,u,0) | $6Σ_{1}^{S}(2) $ | |
T:(1/2,1/2,w) | T:(1/2,1/2,w) | $2T_{1}^{S}(2)⊕4T_{2}^{S}(2) $ | |
Z:(u,1/2,0) | Z:(u,1/2,0) | $4Z_{1}^{S}(1)⊕8Z_{2}^{S}(1)$ | Spin Splitting |
A:(u,v,0) | A:(u,v,0) | $12A_{1}^{S}(1)$ | Spin Splitting |
B:(u,1/2,w) | B:(u,1/2,w) | $12B_{1}^{S}(1)$ | Spin Splitting |
C:(u,u,w) | C:(u,u,w) | $6C_{1}^{S}(2) $ | |
GP:(u,v,w) | GP:(u,v,w) | $12GP_{1}^{S}(1)$ | Spin Splitting |
k-vector | k-vector-G↑ | A↑G(12) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}Γ_{3}^{S}(4)⊕Γ_{4}^{S}(6) $ | |
M:(1/2,1/2,0) | M:(1/2,1/2,0) | $M_{1}^{S}(2)⊕M_{2}^{S}(2)⊕3 M_{3}^{S}(2)⊕M_{4}^{S}(2) $ | |
R:(1/2,1/2,1/2) | R:(1/2,1/2,1/2) | $2 R_{4}^{S}(6) $ | |
X:(0,1/2,0) | X:(0,1/2,0) | $2 X_{1}^{S}(2)⊕2 X_{3}^{S}(2)⊕2X_{4}^{S}(2) $ | |
Δ:(0,v,0) | Δ:(0,v,0) | $4Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $ | |
Λ:(u,u,u) | Λ:(u,u,u) | $2Λ_{1}^{S}(2)⊕2 Λ_{2}^{S}(2)⊕2 Λ_{3}^{S}(2) $ | |
S:(u,1/2,u) | S:(u,1/2,u) | $6S_{1}^{S}(2) $ | |
Σ:(u,u,0) | Σ:(u,u,0) | $6Σ_{1}^{S}(2) $ | |
T:(1/2,1/2,w) | T:(1/2,1/2,w) | $2T_{1}^{S}(2)⊕4T_{2}^{S}(2) $ | |
Z:(u,1/2,0) | Z:(u,1/2,0) | $8Z_{1}^{S}(1)⊕4Z_{2}^{S}(1)$ | Spin Splitting |
A:(u,v,0) | A:(u,v,0) | $12A_{1}^{S}(1)$ | Spin Splitting |
B:(u,1/2,w) | B:(u,1/2,w) | $12B_{1}^{S}(1)$ | Spin Splitting |
C:(u,u,w) | C:(u,u,w) | $6C_{1}^{S}(2) $ | |
GP:(u,v,w) | GP:(u,v,w) | $12GP_{1}^{S}(1)$ | Spin Splitting |
k-vector | k-vector-G↑ | A↑G(24) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}Γ_{3}^{S}(4)⊕3 Γ_{4}^{S}(6) $ | |
M:(1/2,1/2,0) | M:(1/2,1/2,0) | $3 M_{1}^{S}(2)⊕3 M_{2}^{S}(2)⊕3 M_{3}^{S}(2)⊕3 M_{4}^{S}(2) $ | |
R:(1/2,1/2,1/2) | R:(1/2,1/2,1/2) | $R_{1}^{S}(2)⊕R_{2}^{S}R_{3}^{S}(4)⊕3R_{4}^{S}(6) $ | |
X:(0,1/2,0) | X:(0,1/2,0) | $3 X_{1}^{S}(2)⊕3 X_{2}^{S}(2)⊕3 X_{3}^{S}(2)⊕3 X_{4}^{S}(2) $ | |
Δ:(0,v,0) | Δ:(0,v,0) | $6Δ_{1}^{S}(2)⊕6Δ_{2}^{S}(2) $ | |
Λ:(u,u,u) | Λ:(u,u,u) | $4Λ_{1}^{S}(2)⊕4 Λ_{2}^{S}(2)⊕4 Λ_{3}^{S}(2) $ | |
S:(u,1/2,u) | S:(u,1/2,u) | $12S_{1}^{S}(2) $ | |
Σ:(u,u,0) | Σ:(u,u,0) | $12Σ_{1}^{S}(2) $ | |
T:(1/2,1/2,w) | T:(1/2,1/2,w) | $6T_{1}^{S}(2)⊕6T_{2}^{S}(2) $ | |
Z:(u,1/2,0) | Z:(u,1/2,0) | $12Z_{1}^{S}(1)⊕12Z_{2}^{S}(1)$ | Spin Splitting |
A:(u,v,0) | A:(u,v,0) | $24A_{1}^{S}(1)$ | Spin Splitting |
B:(u,1/2,w) | B:(u,1/2,w) | $24B_{1}^{S}(1)$ | Spin Splitting |
C:(u,u,w) | C:(u,u,w) | $12C_{1}^{S}(2) $ | |
GP:(u,v,w) | GP:(u,v,w) | $24GP_{1}^{S}(1)$ | Spin Splitting |