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 ‖ 2001 | 0 } |
b, a, -c | x, y, z | { 1 ‖ 2110 | 0 } |
-b, -a, -c | x, y, z | { 1 ‖ 21-10 | 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 ‖ m100 | 0 } |
a, -b, c | x, y, z | { 1 ‖ m010 | 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 ‖ 2100 | 0 } |
-a, b, -c | -x, -y, -z | { -1 ‖ 2010 | 0 } |
-a, -b, -c | -x, -y, -z | { -1 ‖ -1 | 0 } |
a, b, -c | -x, -y, -z | { -1 ‖ m001 | 0 } |
-b, -a, c | -x, -y, -z | { -1 ‖ m110 | 0 } |
b, a, c | -x, -y, -z | { -1 ‖ m1-10 | 0 } |
a, b, c | -x, y, z | { m ‖ 1 | 0 } |
-a, -b, c | -x, y, z | { m ‖ 2001 | 0 } |
b, a, -c | -x, y, z | { m ‖ 2110 | 0 } |
-b, -a, -c | -x, y, z | { m ‖ 21-10 | 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 ‖ m100 | 0 } |
a, -b, c | -x, y, z | { m ‖ m010 | 0 } |
-b, a, c | x, -y, -z | { 2 ‖ 4+001 | 0 } |
b, -a, c | x, -y, -z | { 2 ‖ 4-001 | 0 } |
a, -b, -c | x, -y, -z | { 2 ‖ 2100 | 0 } |
-a, b, -c | x, -y, -z | { 2 ‖ 2010 | 0 } |
-a, -b, -c | x, -y, -z | { 2 ‖ -1 | 0 } |
a, b, -c | x, -y, -z | { 2 ‖ m001 | 0 } |
-b, -a, c | x, -y, -z | { 2 ‖ m110 | 0 } |
b, a, c | x, -y, -z | { 2 ‖ m1-10 | 0 } |
WP | Site symmetry | Representative |
---|---|---|
1a | $\ce{^{-1}{4}}/\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
1b | $\ce{^{-1}{4}}/\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,0) |
1c | $\ce{^{-1}{4}}/\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (1/2,1/2,0 | 0,0,0) |
1d | $\ce{^{-1}{4}}/\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (1/2,1/2,1/2 | 0,0,0) |
2e | $\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (0,1/2,1/2 | 0,0,0) |
2f | $\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (0,1/2,0 | 0,0,0) |
2g | $\ce{^{-1}{4}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,0) |
2h | $\ce{^{-1}{4}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (1/2,1/2,c | 0,0,0) |
4i | $\ce{^{1}{2}}\ce{^{1}{m}}\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (0,1/2,c | 0,0,z) |
4j | $\ce{^{-1}{m}}.\ce{^{1}{2}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (a,a,0 | 0,0,0) |
4k | $\ce{^{-1}{m}}.\ce{^{1}{2}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (a,a,1/2 | 0,0,0) |
4l | $\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (a,0,0 | 0,0,0) |
4m | $\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (a,0,1/2 | 0,0,0) |
4n | $\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (a,1/2,0 | 0,0,0) |
4o | $\ce{^{-1}{m}}\ce{^{-1}{2}}\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (a,1/2,1/2 | 0,0,0) |
8p | $\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (a,b,0 | 0,0,0) |
8q | $\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (a,b,1/2 | 0,0,0) |
8r | $..\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (a,a,c | 0,0,0) |
8s | $.\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (a,0,c | 0,0,z) |
8t | $.\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (a,1/2,c | 0,0,z) |
16u | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
Wavevector-k | Little co-group |
---|---|
A:(1/2,1/2,1/2) | $\ce{^{-1}{4/}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
Γ:(0,0,0) | $\ce{^{-1}{4/}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
M:(1/2,1/2,0) | $\ce{^{-1}{4/}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
Z:(0,0,1/2) | $\ce{^{-1}{4/}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
R:(0,1/2,1/2) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{2}{m}}\ce{^{\infty m}{1}} $ |
X:(0,1/2,0) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{2}{m}}\ce{^{\infty m}{1}} $ |
Λ:(0,0,w) | $\ce{^{2}{4/}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
V:(1/2,1/2,w) | $\ce{^{2}{4/}}\ce{^{-1}{m}}\ce{^{1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
Δ:(0,v,0) | $\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
S:(u,u,1/2) | $\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
Σ:(u,u,0) | $\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
T:(u,1/2,1/2) | $\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
U:(0,v,1/2) | $\ce{^{1}{m}}\ce{^{m}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
W:(0,1/2,w) | $\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
Y:(u,1/2,0) | $\ce{^{m}{m}}\ce{^{1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
B:(0,v,w) | $\ce{^{-1}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
C:(u,u,w) | $\ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
D:(u,v,0) | $\ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
E:(u,v,1/2) | $\ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
F:(u,1/2,w) | $\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↑ | A1↑G(4) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2) $ | |
A:(1/2,1/2,1/2) | A:(1/2,1/2,1/2) | $A_{5}^{S}(4) $ | |
M:(1/2,1/2,0) | M:(1/2,1/2,0) | $M_{5}^{S}(4) $ | |
R:(0,1/2,1/2) | R:(0,1/2,1/2) | $R_{1}^{S}(2)⊕R_{3}^{S}(2) $ | |
X:(0,1/2,0) | X:(0,1/2,0) | $X_{1}^{S}(2)⊕X_{3}^{S}(2) $ | |
Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}(2)⊕Z_{2}^{S}(2) $ | |
Δ:(0,v,0) | Δ:(0,v,0) | $2Δ_{1}^{S}(2) $ | |
Λ:(0,0,w) | Λ:(0,0,w) | $2Λ_{1}^{S}(2) $ | |
S:(u,u,1/2) | S:(u,u,1/2) | $S_{1}^{S}(2)⊕S_{2}^{S}(2) $ | |
Σ:(u,u,0) | Σ:(u,u,0) | $Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2) $ | |
T:(u,1/2,1/2) | T:(u,1/2,1/2) | $T_{1}^{S}(2)⊕T_{2}^{S}(2) $ | |
U:(0,v,1/2) | U:(0,v,1/2) | $2U_{1}^{S}(2) $ | |
V:(1/2,1/2,w) | V:(1/2,1/2,w) | $V_{3}^{S}V_{4}^{S}(4) $ | |
W:(0,1/2,w) | W:(0,1/2,w) | $W_{1}^{S}(2)⊕W_{3}^{S}(2) $ | |
Y:(u,1/2,0) | Y:(u,1/2,0) | $Y_{1}^{S}(2)⊕Y_{2}^{S}(2) $ | |
B:(0,v,w) | B:(0,v,w) | $2B_{1}^{S}(2) $ | |
C:(u,u,w) | C:(u,u,w) | $2C_{1}^{S}(2) $ | |
D:(u,v,0) | D:(u,v,0) | $2D_{1}^{S}(2) $ | |
E:(u,v,1/2) | E:(u,v,1/2) | $2E_{1}^{S}(2) $ | |
F:(u,1/2,w) | F:(u,1/2,w) | $F_{1}^{S}(2)⊕F_{2}^{S}(2) $ | |
GP:(u,v,w) | GP:(u,v,w) | $2GP_{1}^{S}(2) $ |
k-vector | k-vector-G↑ | A'↑G(8) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2)⊕Γ_{5}^{S}(4) $ | |
A:(1/2,1/2,1/2) | A:(1/2,1/2,1/2) | $A_{1}^{S}(2)⊕A_{2}^{S}(2)⊕A_{5}^{S}(4) $ | |
M:(1/2,1/2,0) | M:(1/2,1/2,0) | $M_{1}^{S}(2)⊕M_{2}^{S}(2)⊕M_{5}^{S}(4) $ | |
R:(0,1/2,1/2) | R:(0,1/2,1/2) | $2R_{1}^{S}(2)⊕R_{3}^{S}(2)⊕R_{4}^{S}(2) $ | |
X:(0,1/2,0) | X:(0,1/2,0) | $2X_{1}^{S}(2)⊕X_{3}^{S}(2)⊕X_{4}^{S}(2) $ | |
Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}(2)⊕Z_{2}^{S}(2)⊕Z_{5}^{S}(4) $ | |
Δ:(0,v,0) | Δ:(0,v,0) | $3Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2) $ | |
Λ:(0,0,w) | Λ:(0,0,w) | $2Λ_{1}^{S}(2)⊕Λ_{3}^{S}Λ_{4}^{S}(4) $ | |
S:(u,u,1/2) | S:(u,u,1/2) | $2S_{1}^{S}(2)⊕2S_{2}^{S}(2) $ | |
Σ:(u,u,0) | Σ:(u,u,0) | $2Σ_{1}^{S}(2)⊕2Σ_{2}^{S}(2) $ | |
T:(u,1/2,1/2) | T:(u,1/2,1/2) | $3T_{1}^{S}(2)⊕T_{2}^{S}(2) $ | |
U:(0,v,1/2) | U:(0,v,1/2) | $3U_{1}^{S}(2)⊕U_{2}^{S}(2) $ | |
V:(1/2,1/2,w) | V:(1/2,1/2,w) | $2V_{1}^{S}(2)⊕V_{3}^{S}V_{4}^{S}(4) $ | |
W:(0,1/2,w) | W:(0,1/2,w) | $2W_{1}^{S}(2)⊕W_{3}^{S}(2)⊕W_{4}^{S}(2) $ | |
Y:(u,1/2,0) | Y:(u,1/2,0) | $3Y_{1}^{S}(2)⊕Y_{2}^{S}(2) $ | |
B:(0,v,w) | B:(0,v,w) | $3B_{1}^{S}(2)⊕B_{2}^{S}(2) $ | |
C:(u,u,w) | C:(u,u,w) | $4C_{1}^{S}(2) $ | |
D:(u,v,0) | D:(u,v,0) | $4D_{1}^{S}(2) $ | |
E:(u,v,1/2) | E:(u,v,1/2) | $4E_{1}^{S}(2) $ | |
F:(u,1/2,w) | F:(u,1/2,w) | $3F_{1}^{S}(2)⊕F_{2}^{S}(2) $ | |
GP:(u,v,w) | GP:(u,v,w) | $4GP_{1}^{S}(2) $ |
k-vector | k-vector-G↑ | A'↑G(8) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2)⊕Γ_{5}^{S}(4) $ | |
A:(1/2,1/2,1/2) | A:(1/2,1/2,1/2) | $A_{3}^{S}(2)⊕A_{4}^{S}(2)⊕A_{5}^{S}(4) $ | |
M:(1/2,1/2,0) | M:(1/2,1/2,0) | $M_{3}^{S}(2)⊕M_{4}^{S}(2)⊕M_{5}^{S}(4) $ | |
R:(0,1/2,1/2) | R:(0,1/2,1/2) | $R_{1}^{S}(2)⊕R_{2}^{S}(2)⊕2R_{3}^{S}(2) $ | |
X:(0,1/2,0) | X:(0,1/2,0) | $X_{1}^{S}(2)⊕X_{2}^{S}(2)⊕2X_{3}^{S}(2) $ | |
Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}(2)⊕Z_{2}^{S}(2)⊕Z_{5}^{S}(4) $ | |
Δ:(0,v,0) | Δ:(0,v,0) | $3Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2) $ | |
Λ:(0,0,w) | Λ:(0,0,w) | $2Λ_{1}^{S}(2)⊕Λ_{3}^{S}Λ_{4}^{S}(4) $ | |
S:(u,u,1/2) | S:(u,u,1/2) | $2S_{1}^{S}(2)⊕2S_{2}^{S}(2) $ | |
Σ:(u,u,0) | Σ:(u,u,0) | $2Σ_{1}^{S}(2)⊕2Σ_{2}^{S}(2) $ | |
T:(u,1/2,1/2) | T:(u,1/2,1/2) | $T_{1}^{S}(2)⊕3T_{2}^{S}(2) $ | |
U:(0,v,1/2) | U:(0,v,1/2) | $3U_{1}^{S}(2)⊕U_{2}^{S}(2) $ | |
V:(1/2,1/2,w) | V:(1/2,1/2,w) | $2V_{2}^{S}(2)⊕V_{3}^{S}V_{4}^{S}(4) $ | |
W:(0,1/2,w) | W:(0,1/2,w) | $W_{1}^{S}(2)⊕W_{2}^{S}(2)⊕2W_{3}^{S}(2) $ | |
Y:(u,1/2,0) | Y:(u,1/2,0) | $Y_{1}^{S}(2)⊕3Y_{2}^{S}(2) $ | |
B:(0,v,w) | B:(0,v,w) | $3B_{1}^{S}(2)⊕B_{2}^{S}(2) $ | |
C:(u,u,w) | C:(u,u,w) | $4C_{1}^{S}(2) $ | |
D:(u,v,0) | D:(u,v,0) | $4D_{1}^{S}(2) $ | |
E:(u,v,1/2) | E:(u,v,1/2) | $4E_{1}^{S}(2) $ | |
F:(u,1/2,w) | F:(u,1/2,w) | $F_{1}^{S}(2)⊕3F_{2}^{S}(2) $ | |
GP:(u,v,w) | GP:(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_{2}^{S}(2)⊕Γ_{3}^{S}(2)⊕Γ_{4}^{S}(2)⊕2Γ_{5}^{S}(4) $ | |
A:(1/2,1/2,1/2) | A:(1/2,1/2,1/2) | $A_{1}^{S}(2)⊕A_{2}^{S}(2)⊕A_{3}^{S}(2)⊕A_{4}^{S}(2)⊕2A_{5}^{S}(4) $ | |
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)⊕2M_{5}^{S}(4) $ | |
R:(0,1/2,1/2) | R:(0,1/2,1/2) | $2R_{1}^{S}(2)⊕2R_{2}^{S}(2)⊕2R_{3}^{S}(2)⊕2R_{4}^{S}(2) $ | |
X:(0,1/2,0) | X:(0,1/2,0) | $2X_{1}^{S}(2)⊕2X_{2}^{S}(2)⊕2X_{3}^{S}(2)⊕2X_{4}^{S}(2) $ | |
Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}(2)⊕Z_{2}^{S}(2)⊕Z_{3}^{S}(2)⊕Z_{4}^{S}(2)⊕2Z_{5}^{S}(4) $ | |
Δ:(0,v,0) | Δ:(0,v,0) | $4Δ_{1}^{S}(2)⊕4Δ_{2}^{S}(2) $ | |
Λ:(0,0,w) | Λ:(0,0,w) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2)⊕2Λ_{3}^{S}Λ_{4}^{S}(4) $ | |
S:(u,u,1/2) | S:(u,u,1/2) | $4S_{1}^{S}(2)⊕4S_{2}^{S}(2) $ | |
Σ:(u,u,0) | Σ:(u,u,0) | $4Σ_{1}^{S}(2)⊕4Σ_{2}^{S}(2) $ | |
T:(u,1/2,1/2) | T:(u,1/2,1/2) | $4T_{1}^{S}(2)⊕4T_{2}^{S}(2) $ | |
U:(0,v,1/2) | U:(0,v,1/2) | $4U_{1}^{S}(2)⊕4U_{2}^{S}(2) $ | |
V:(1/2,1/2,w) | V:(1/2,1/2,w) | $2V_{1}^{S}(2)⊕2V_{2}^{S}(2)⊕2V_{3}^{S}V_{4}^{S}(4) $ | |
W:(0,1/2,w) | W:(0,1/2,w) | $2W_{1}^{S}(2)⊕2W_{2}^{S}(2)⊕2W_{3}^{S}(2)⊕2W_{4}^{S}(2) $ | |
Y:(u,1/2,0) | Y:(u,1/2,0) | $4Y_{1}^{S}(2)⊕4Y_{2}^{S}(2) $ | |
B:(0,v,w) | B:(0,v,w) | $4B_{1}^{S}(2)⊕4B_{2}^{S}(2) $ | |
C:(u,u,w) | C:(u,u,w) | $8C_{1}^{S}(2) $ | |
D:(u,v,0) | D:(u,v,0) | $8D_{1}^{S}(2) $ | |
E:(u,v,1/2) | E:(u,v,1/2) | $8E_{1}^{S}(2) $ | |
F:(u,1/2,w) | F:(u,1/2,w) | $4F_{1}^{S}(2)⊕4F_{2}^{S}(2) $ | |
GP:(u,v,w) | GP:(u,v,w) | $8GP_{1}^{S}(2) $ |