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+1/2 | x, y, z | { 1 ‖ 2110 | 0 0 1/2 } |
-b, -a, -c+1/2 | x, y, z | { 1 ‖ 21-10 | 0 0 1/2 } |
b, -a, -c | x, y, z | { 1 ‖ -4+001 | 0 } |
-b, a, -c | x, y, z | { 1 ‖ -4-001 | 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 | -x, -y, -z | { -1 ‖ 4+001 | 0 } |
b, -a, c | -x, -y, -z | { -1 ‖ 4-001 | 0 } |
a, -b, -c+1/2 | -x, -y, -z | { -1 ‖ 2100 | 0 0 1/2 } |
-a, b, -c+1/2 | -x, -y, -z | { -1 ‖ 2010 | 0 0 1/2 } |
-a, -b, -c | -x, -y, -z | { -1 ‖ -1 | 0 } |
a, b, -c | -x, -y, -z | { -1 ‖ m001 | 0 } |
-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, b, c | -x, y, z | { m ‖ 1 | 0 } |
-a, -b, c | -x, y, z | { m ‖ 2001 | 0 } |
b, a, -c+1/2 | -x, y, z | { m ‖ 2110 | 0 0 1/2 } |
-b, -a, -c+1/2 | -x, y, z | { m ‖ 21-10 | 0 0 1/2 } |
b, -a, -c | -x, y, z | { m ‖ -4+001 | 0 } |
-b, a, -c | -x, y, z | { m ‖ -4-001 | 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 | x, -y, -z | { 2 ‖ 4+001 | 0 } |
b, -a, c | x, -y, -z | { 2 ‖ 4-001 | 0 } |
a, -b, -c+1/2 | x, -y, -z | { 2 ‖ 2100 | 0 0 1/2 } |
-a, b, -c+1/2 | x, -y, -z | { 2 ‖ 2010 | 0 0 1/2 } |
-a, -b, -c | x, -y, -z | { 2 ‖ -1 | 0 } |
a, b, -c | x, -y, -z | { 2 ‖ m001 | 0 } |
-b, -a, c+1/2 | x, -y, -z | { 2 ‖ m110 | 0 0 1/2 } |
b, a, c+1/2 | x, -y, -z | { 2 ‖ m1-10 | 0 0 1/2 } |
WP | Site symmetry | Representative |
---|---|---|
2a | $\ce{^{-1}{4}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,1/4 | 0,0,0) |
2b | $\ce{^{-1}{4}}/\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
2c | $\ce{^{-1}{4}}\ce{^{-1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/2,1/2,1/4 | 0,0,0) |
2d | $\ce{^{-1}{4}}/\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (1/2,1/2,0 | 0,0,0) |
4e | $\ce{^{1}{2}}/\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (0,1/2,0 | 0,0,0) |
4f | $\ce{^{1}{2}}\ce{^{-1}{2}}\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (0,1/2,1/4 | 0,0,0) |
4g | $\ce{^{-1}{4}}..\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,0) |
4h | $\ce{^{-1}{4}}..\ce{^{\infty m}{1}} $ | (1/2,1/2,c | 0,0,0) |
8i | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (0,1/2,c | 0,0,z) |
8j | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (a,a,1/4 | 0,0,z) |
8k | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (a,0,1/4 | 0,0,0) |
8l | $.\ce{^{-1}{2}}.\ce{^{\infty m}{1}} $ | (a,1/2,1/4 | 0,0,0) |
8m | $\ce{^{-1}{m}}..\ce{^{\infty m}{1}} $ | (a,b,0 | 0,0,0) |
16n | $\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↑ | A↑G(8) | |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{4}^{S}(2)⊕Γ_{5}^{S}(4) $ | |
A:(1/2,1/2,1/2) | A:(1/2,1/2,1/2) | $A_{1}^{S}A_{4}^{S}(4)⊕A_{5}^{S}(4) $ | |
M:(1/2,1/2,0) | M:(1/2,1/2,0) | $M_{1}^{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}R_{2}^{S}(4)⊕R_{3}^{S}R_{4}^{S}(4) $ | |
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) $ | |
Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}Z_{4}^{S}(4)⊕Z_{5}^{S}(4) $ | |
Δ:(0,v,0) | Δ:(0,v,0) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $ | |
Λ:(0,0,w) | Λ:(0,0,w) | $Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2)⊕Λ_{3}^{S}Λ_{4}^{S}(4) $ | |
S:(u,u,1/2) | S:(u,u,1/2) | $3S_{1}^{S}(2)⊕S_{2}^{S}(2) $ | |
Σ:(u,u,0) | Σ:(u,u,0) | $3Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2) $ | |
T:(u,1/2,1/2) | T:(u,1/2,1/2) | $2T_{1}^{S}T_{2}^{S}(4) $ | |
U:(0,v,1/2) | U:(0,v,1/2) | $2U_{1}^{S}U_{2}^{S}(4) $ | |
V:(1/2,1/2,w) | V:(1/2,1/2,w) | $V_{1}^{S}(2)⊕V_{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)⊕W_{3}^{S}(2)⊕W_{4}^{S}(2) $ | |
Y:(u,1/2,0) | Y:(u,1/2,0) | $2Y_{1}^{S}(2)⊕2Y_{2}^{S}(2) $ | |
B:(0,v,w) | B:(0,v,w) | $2B_{1}^{S}(2)⊕2B_{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) | $2F_{1}^{S}(2)⊕2F_{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_{3}^{S}(2)⊕Γ_{4}^{S}(2) $ | |
A:(1/2,1/2,1/2) | A:(1/2,1/2,1/2) | $A_{1}^{S}A_{4}^{S}(4)⊕A_{2}^{S}A_{3}^{S}(4) $ | |
M:(1/2,1/2,0) | M:(1/2,1/2,0) | $2M_{5}^{S}(4) $ | |
R:(0,1/2,1/2) | R:(0,1/2,1/2) | $R_{1}^{S}R_{2}^{S}(4)⊕R_{3}^{S}R_{4}^{S}(4) $ | |
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) $ | |
Z:(0,0,1/2) | Z:(0,0,1/2) | $2Z_{5}^{S}(4) $ | |
Δ:(0,v,0) | Δ:(0,v,0) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $ | |
Λ:(0,0,w) | Λ:(0,0,w) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2) $ | |
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) | $2T_{1}^{S}T_{2}^{S}(4) $ | |
U:(0,v,1/2) | U:(0,v,1/2) | $2U_{1}^{S}U_{2}^{S}(4) $ | |
V:(1/2,1/2,w) | V:(1/2,1/2,w) | $2V_{3}^{S}V_{4}^{S}(4) $ | |
W:(0,1/2,w) | W:(0,1/2,w) | $W_{1}^{S}(2)⊕W_{2}^{S}(2)⊕W_{3}^{S}(2)⊕W_{4}^{S}(2) $ | |
Y:(u,1/2,0) | Y:(u,1/2,0) | $2Y_{1}^{S}(2)⊕2Y_{2}^{S}(2) $ | |
B:(0,v,w) | B:(0,v,w) | $2B_{1}^{S}(2)⊕2B_{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) | $2F_{1}^{S}(2)⊕2F_{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}A_{4}^{S}(4)⊕A_{2}^{S}A_{3}^{S}(4)⊕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}R_{2}^{S}(4)⊕2R_{3}^{S}R_{4}^{S}(4) $ | |
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}Z_{4}^{S}(4)⊕Z_{2}^{S}Z_{3}^{S}(4)⊕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}T_{2}^{S}(4) $ | |
U:(0,v,1/2) | U:(0,v,1/2) | $4U_{1}^{S}U_{2}^{S}(4) $ | |
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) $ |