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 } |
a, b+1/2, c+1/2 | x, y, z | { 1 ‖ 1 | 0 1/2 1/2 } |
a, -b+1/2, -c+1/2 | x, y, z | { 1 ‖ 2100 | 0 1/2 1/2 } |
-a, b+1/2, -c+1/2 | x, y, z | { 1 ‖ 2010 | 0 1/2 1/2 } |
-a, -b+1/2, c+1/2 | x, y, z | { 1 ‖ 2001 | 0 1/2 1/2 } |
a+1/2, b, c+1/2 | x, y, z | { 1 ‖ 1 | 1/2 0 1/2 } |
a+1/2, -b, -c+1/2 | x, y, z | { 1 ‖ 2100 | 1/2 0 1/2 } |
-a+1/2, b, -c+1/2 | x, y, z | { 1 ‖ 2010 | 1/2 0 1/2 } |
-a+1/2, -b, c+1/2 | x, y, z | { 1 ‖ 2001 | 1/2 0 1/2 } |
a+1/2, b+1/2, c | x, y, z | { 1 ‖ 1 | 1/2 1/2 0 } |
a+1/2, -b+1/2, -c | x, y, z | { 1 ‖ 2100 | 1/2 1/2 0 } |
-a+1/2, b+1/2, -c | x, y, z | { 1 ‖ 2010 | 1/2 1/2 0 } |
-a+1/2, -b+1/2, c | x, y, z | { 1 ‖ 2001 | 1/2 1/2 0 } |
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 } |
a, b+1/2, c+1/2 | -x, y, z | { m ‖ 1 | 0 1/2 1/2 } |
a, -b+1/2, -c+1/2 | -x, y, z | { m ‖ 2100 | 0 1/2 1/2 } |
-a, b+1/2, -c+1/2 | -x, y, z | { m ‖ 2010 | 0 1/2 1/2 } |
-a, -b+1/2, c+1/2 | -x, y, z | { m ‖ 2001 | 0 1/2 1/2 } |
a+1/2, b, c+1/2 | -x, y, z | { m ‖ 1 | 1/2 0 1/2 } |
a+1/2, -b, -c+1/2 | -x, y, z | { m ‖ 2100 | 1/2 0 1/2 } |
-a+1/2, b, -c+1/2 | -x, y, z | { m ‖ 2010 | 1/2 0 1/2 } |
-a+1/2, -b, c+1/2 | -x, y, z | { m ‖ 2001 | 1/2 0 1/2 } |
a+1/2, b+1/2, c | -x, y, z | { m ‖ 1 | 1/2 1/2 0 } |
a+1/2, -b+1/2, -c | -x, y, z | { m ‖ 2100 | 1/2 1/2 0 } |
-a+1/2, b+1/2, -c | -x, y, z | { m ‖ 2010 | 1/2 1/2 0 } |
-a+1/2, -b+1/2, c | -x, y, z | { m ‖ 2001 | 1/2 1/2 0 } |
WP | Site symmetry | Representative |
---|---|---|
4a | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,0 |0,0,z) |
4b | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,1/2 |0,0,z) |
4c | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/4,1/4,1/4 |0,0,z) |
4d | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/4,1/4,3/4 |0,0,z) |
8e | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,0,0 |0,0,z) |
8f | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (0,b,0 |0,0,z) |
8g | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,c |0,0,z) |
8h | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/4,1/4,c |0,0,z) |
8i | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (1/4,b,1/4 |0,0,z) |
8j | $\ce{^{1}{2}}..\ce{^{\infty m}{1}} $ | (a,1/4,1/4 |0,0,z) |
16k | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c |0,0,z) |
Wavevector-k | Little co-group |
---|---|
Γ:(0,0,0) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
T:(1,0,0) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
Y:(0,1,0) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
Z:(0,0,1) | $\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{1}{2}}\ce{^{\infty m}{1}} $ |
L:(1/2,1/2,1/2) | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ |
A:(u,0,1) | $\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
B:(0,v,1) | $\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
Δ:(0,v,0) | $\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
H:(0,1,w) | $\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
Λ:(0,0,w) | $\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{1}{2}}\ce{^{\infty}{1}} $ |
Σ:(u,0,0) | $\ce{^{1}{2}}\ce{^{m}{2}}\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
E:(0,v,w) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
J:(u,0,w) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
M:(u,v,0) | $\ce{^{m}{2}}\ce{^{\infty}{1}} $ |
GP:(u,v,w) | $\ce{^{1}{1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
k-vector | A↑G(1) |
Γ:(0,0,0) | $Γ_{1}^{S}(1) $ |
T:(1,0,0) | $T_{1}^{S}(1) $ |
Y:(0,1,0) | $Y_{1}^{S}(1) $ |
Z:(0,0,1) | $Z_{1}^{S}(1) $ |
L:(1/2,1/2,1/2) | $L_{1}^{S}(1) $ |
A:(u,0,1) | $A_{1}^{S}(1) $ |
B:(0,v,1) | $B_{1}^{S}(1) $ |
Δ:(0,v,0) | $Δ_{1}^{S}(1) $ |
H:(0,1,w) | $H_{1}^{S}(1) $ |
Λ:(0,0,w) | $Λ_{1}^{S}(1) $ |
Σ:(u,0,0) | $Σ_{1}^{S}(1) $ |
E:(0,v,w) | $E_{1}^{S}(1) $ |
J:(u,0,w) | $J_{1}^{S}(1) $ |
M:(u,v,0) | $M_{1}^{S}(1) $ |
GP:(u,v,w) | $GP_{1}^{S}(1) $ |
k-vector | A↑G(1) |
Γ:(0,0,0) | $Γ_{1}^{S}(1) $ |
T:(1,0,0) | $T_{1}^{S}(1) $ |
Y:(0,1,0) | $Y_{1}^{S}(1) $ |
Z:(0,0,1) | $Z_{1}^{S}(1) $ |
L:(1/2,1/2,1/2) | $L_{1}^{S}(1) $ |
A:(u,0,1) | $A_{1}^{S}(1) $ |
B:(0,v,1) | $B_{1}^{S}(1) $ |
Δ:(0,v,0) | $Δ_{1}^{S}(1) $ |
H:(0,1,w) | $H_{1}^{S}(1) $ |
Λ:(0,0,w) | $Λ_{1}^{S}(1) $ |
Σ:(u,0,0) | $Σ_{1}^{S}(1) $ |
E:(0,v,w) | $E_{1}^{S}(1) $ |
J:(u,0,w) | $J_{1}^{S}(1) $ |
M:(u,v,0) | $M_{1}^{S}(1) $ |
GP:(u,v,w) | $GP_{1}^{S}(1) $ |
k-vector | A↑G(1) |
Γ:(0,0,0) | $Γ_{1}^{S}(1) $ |
T:(1,0,0) | $T_{3}^{S}(1) $ |
Y:(0,1,0) | $Y_{4}^{S}(1) $ |
Z:(0,0,1) | $Z_{2}^{S}(1) $ |
L:(1/2,1/2,1/2) | $L_{1}^{S}(1) $ |
A:(u,0,1) | $A_{2}^{S}(1) $ |
B:(0,v,1) | $B_{2}^{S}(1) $ |
Δ:(0,v,0) | $Δ_{1}^{S}(1) $ |
H:(0,1,w) | $H_{2}^{S}(1) $ |
Λ:(0,0,w) | $Λ_{1}^{S}(1) $ |
Σ:(u,0,0) | $Σ_{1}^{S}(1) $ |
E:(0,v,w) | $E_{1}^{S}(1) $ |
J:(u,0,w) | $J_{1}^{S}(1) $ |
M:(u,v,0) | $M_{1}^{S}(1) $ |
GP:(u,v,w) | $GP_{1}^{S}(1) $ |
k-vector | A↑G(1) |
Γ:(0,0,0) | $Γ_{1}^{S}(1) $ |
T:(1,0,0) | $T_{3}^{S}(1) $ |
Y:(0,1,0) | $Y_{4}^{S}(1) $ |
Z:(0,0,1) | $Z_{2}^{S}(1) $ |
L:(1/2,1/2,1/2) | $L_{1}^{S}(1) $ |
A:(u,0,1) | $A_{2}^{S}(1) $ |
B:(0,v,1) | $B_{2}^{S}(1) $ |
Δ:(0,v,0) | $Δ_{1}^{S}(1) $ |
H:(0,1,w) | $H_{2}^{S}(1) $ |
Λ:(0,0,w) | $Λ_{1}^{S}(1) $ |
Σ:(u,0,0) | $Σ_{1}^{S}(1) $ |
E:(0,v,w) | $E_{1}^{S}(1) $ |
J:(u,0,w) | $J_{1}^{S}(1) $ |
M:(u,v,0) | $M_{1}^{S}(1) $ |
GP:(u,v,w) | $GP_{1}^{S}(1) $ |
k-vector | A↑G(2) |
Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{3}^{S}(1) $ |
T:(1,0,0) | $T_{1}^{S}(1)⊕T_{3}^{S}(1) $ |
Y:(0,1,0) | $Y_{1}^{S}(1)⊕Y_{3}^{S}(1) $ |
Z:(0,0,1) | $Z_{1}^{S}(1)⊕Z_{3}^{S}(1) $ |
L:(1/2,1/2,1/2) | $2L_{1}^{S}(1) $ |
A:(u,0,1) | $2A_{1}^{S}(1) $ |
B:(0,v,1) | $B_{1}^{S}(1)⊕B_{2}^{S}(1) $ |
Δ:(0,v,0) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1) $ |
H:(0,1,w) | $H_{1}^{S}(1)⊕H_{2}^{S}(1) $ |
Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $ |
Σ:(u,0,0) | $2Σ_{1}^{S}(1) $ |
E:(0,v,w) | $2E_{1}^{S}(1) $ |
J:(u,0,w) | $2J_{1}^{S}(1) $ |
M:(u,v,0) | $2M_{1}^{S}(1) $ |
GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
k-vector | A↑G(2) |
Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{4}^{S}(1) $ |
T:(1,0,0) | $T_{1}^{S}(1)⊕T_{4}^{S}(1) $ |
Y:(0,1,0) | $Y_{1}^{S}(1)⊕Y_{4}^{S}(1) $ |
Z:(0,0,1) | $Z_{1}^{S}(1)⊕Z_{4}^{S}(1) $ |
L:(1/2,1/2,1/2) | $2L_{1}^{S}(1) $ |
A:(u,0,1) | $A_{1}^{S}(1)⊕A_{2}^{S}(1) $ |
B:(0,v,1) | $2B_{1}^{S}(1) $ |
Δ:(0,v,0) | $2Δ_{1}^{S}(1) $ |
H:(0,1,w) | $H_{1}^{S}(1)⊕H_{2}^{S}(1) $ |
Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $ |
Σ:(u,0,0) | $Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
E:(0,v,w) | $2E_{1}^{S}(1) $ |
J:(u,0,w) | $2J_{1}^{S}(1) $ |
M:(u,v,0) | $2M_{1}^{S}(1) $ |
GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
k-vector | A↑G(2) |
Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}(1) $ |
T:(1,0,0) | $T_{1}^{S}(1)⊕T_{2}^{S}(1) $ |
Y:(0,1,0) | $Y_{1}^{S}(1)⊕Y_{2}^{S}(1) $ |
Z:(0,0,1) | $Z_{1}^{S}(1)⊕Z_{2}^{S}(1) $ |
L:(1/2,1/2,1/2) | $2L_{1}^{S}(1) $ |
A:(u,0,1) | $A_{1}^{S}(1)⊕A_{2}^{S}(1) $ |
B:(0,v,1) | $B_{1}^{S}(1)⊕B_{2}^{S}(1) $ |
Δ:(0,v,0) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1) $ |
H:(0,1,w) | $2H_{1}^{S}(1) $ |
Λ:(0,0,w) | $2Λ_{1}^{S}(1) $ |
Σ:(u,0,0) | $Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
E:(0,v,w) | $2E_{1}^{S}(1) $ |
J:(u,0,w) | $2J_{1}^{S}(1) $ |
M:(u,v,0) | $2M_{1}^{S}(1) $ |
GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
k-vector | A↑G(2) |
Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}(1) $ |
T:(1,0,0) | $T_{3}^{S}(1)⊕T_{4}^{S}(1) $ |
Y:(0,1,0) | $Y_{3}^{S}(1)⊕Y_{4}^{S}(1) $ |
Z:(0,0,1) | $Z_{1}^{S}(1)⊕Z_{2}^{S}(1) $ |
L:(1/2,1/2,1/2) | $2L_{1}^{S}(1) $ |
A:(u,0,1) | $A_{1}^{S}(1)⊕A_{2}^{S}(1) $ |
B:(0,v,1) | $B_{1}^{S}(1)⊕B_{2}^{S}(1) $ |
Δ:(0,v,0) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1) $ |
H:(0,1,w) | $2H_{2}^{S}(1) $ |
Λ:(0,0,w) | $2Λ_{1}^{S}(1) $ |
Σ:(u,0,0) | $Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
E:(0,v,w) | $2E_{1}^{S}(1) $ |
J:(u,0,w) | $2J_{1}^{S}(1) $ |
M:(u,v,0) | $2M_{1}^{S}(1) $ |
GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
k-vector | A↑G(2) |
Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{4}^{S}(1) $ |
T:(1,0,0) | $T_{2}^{S}(1)⊕T_{3}^{S}(1) $ |
Y:(0,1,0) | $Y_{1}^{S}(1)⊕Y_{4}^{S}(1) $ |
Z:(0,0,1) | $Z_{2}^{S}(1)⊕Z_{3}^{S}(1) $ |
L:(1/2,1/2,1/2) | $2L_{1}^{S}(1) $ |
A:(u,0,1) | $A_{1}^{S}(1)⊕A_{2}^{S}(1) $ |
B:(0,v,1) | $2B_{2}^{S}(1) $ |
Δ:(0,v,0) | $2Δ_{1}^{S}(1) $ |
H:(0,1,w) | $H_{1}^{S}(1)⊕H_{2}^{S}(1) $ |
Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $ |
Σ:(u,0,0) | $Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
E:(0,v,w) | $2E_{1}^{S}(1) $ |
J:(u,0,w) | $2J_{1}^{S}(1) $ |
M:(u,v,0) | $2M_{1}^{S}(1) $ |
GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
k-vector | A↑G(2) |
Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{3}^{S}(1) $ |
T:(1,0,0) | $T_{1}^{S}(1)⊕T_{3}^{S}(1) $ |
Y:(0,1,0) | $Y_{2}^{S}(1)⊕Y_{4}^{S}(1) $ |
Z:(0,0,1) | $Z_{2}^{S}(1)⊕Z_{4}^{S}(1) $ |
L:(1/2,1/2,1/2) | $2L_{1}^{S}(1) $ |
A:(u,0,1) | $2A_{2}^{S}(1) $ |
B:(0,v,1) | $B_{1}^{S}(1)⊕B_{2}^{S}(1) $ |
Δ:(0,v,0) | $Δ_{1}^{S}(1)⊕Δ_{2}^{S}(1) $ |
H:(0,1,w) | $H_{1}^{S}(1)⊕H_{2}^{S}(1) $ |
Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $ |
Σ:(u,0,0) | $2Σ_{1}^{S}(1) $ |
E:(0,v,w) | $2E_{1}^{S}(1) $ |
J:(u,0,w) | $2J_{1}^{S}(1) $ |
M:(u,v,0) | $2M_{1}^{S}(1) $ |
GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
k-vector | A↑G(4) |
Γ:(0,0,0) | $Γ_{1}^{S}(1)⊕Γ_{2}^{S}(1)⊕Γ_{3}^{S}(1)⊕Γ_{4}^{S}(1) $ |
T:(1,0,0) | $T_{1}^{S}(1)⊕T_{2}^{S}(1)⊕T_{3}^{S}(1)⊕T_{4}^{S}(1) $ |
Y:(0,1,0) | $Y_{1}^{S}(1)⊕Y_{2}^{S}(1)⊕Y_{3}^{S}(1)⊕Y_{4}^{S}(1) $ |
Z:(0,0,1) | $Z_{1}^{S}(1)⊕Z_{2}^{S}(1)⊕Z_{3}^{S}(1)⊕Z_{4}^{S}(1) $ |
L:(1/2,1/2,1/2) | $4L_{1}^{S}(1) $ |
A:(u,0,1) | $2A_{1}^{S}(1)⊕2A_{2}^{S}(1) $ |
B:(0,v,1) | $2B_{1}^{S}(1)⊕2B_{2}^{S}(1) $ |
Δ:(0,v,0) | $2Δ_{1}^{S}(1)⊕2Δ_{2}^{S}(1) $ |
H:(0,1,w) | $2H_{1}^{S}(1)⊕2H_{2}^{S}(1) $ |
Λ:(0,0,w) | $2Λ_{1}^{S}(1)⊕2Λ_{2}^{S}(1) $ |
Σ:(u,0,0) | $2Σ_{1}^{S}(1)⊕2Σ_{2}^{S}(1) $ |
E:(0,v,w) | $4E_{1}^{S}(1) $ |
J:(u,0,w) | $4J_{1}^{S}(1) $ |
M:(u,v,0) | $4M_{1}^{S}(1) $ |
GP:(u,v,w) | $4GP_{1}^{S}(1) $ |