The continuously infinite group ∞1 is omitted.
Coordinates | Seitz symbol |
---|---|
a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
-b, a-b, c | x, y, z | { 1 ‖ 3+001 | 0 } |
-a+b, -a, c | x, y, z | { 1 ‖ 3-001 | 0 } |
a-b, -b, -c | x, y, z | { 1 ‖ 2100 | 0 } |
b, a, -c | x, y, z | { 1 ‖ 2110 | 0 } |
-a, -a+b, -c | x, y, z | { 1 ‖ 2010 | 0 } |
-a, -b, -c | x, y, z | { 1 ‖ -1 | 0 } |
b, -a+b, -c | x, y, z | { 1 ‖ -3+001 | 0 } |
a-b, a, -c | x, y, z | { 1 ‖ -3-001 | 0 } |
-a+b, b, c | x, y, z | { 1 ‖ m100 | 0 } |
-b, -a, c | x, y, z | { 1 ‖ m110 | 0 } |
a, a-b, c | x, y, z | { 1 ‖ m010 | 0 } |
a+2/3, b+1/3, c+1/3 | x, y, z | { 1 ‖ 1 | 2/3 1/3 1/3 } |
-b+2/3, a-b+1/3, c+1/3 | x, y, z | { 1 ‖ 3+001 | 2/3 1/3 1/3 } |
-a+b+2/3, -a+1/3, c+1/3 | x, y, z | { 1 ‖ 3-001 | 2/3 1/3 1/3 } |
a-b+2/3, -b+1/3, -c+1/3 | x, y, z | { 1 ‖ 2100 | 2/3 1/3 1/3 } |
b+2/3, a+1/3, -c+1/3 | x, y, z | { 1 ‖ 2110 | 2/3 1/3 1/3 } |
-a+2/3, -a+b+1/3, -c+1/3 | x, y, z | { 1 ‖ 2010 | 2/3 1/3 1/3 } |
-a+2/3, -b+1/3, -c+1/3 | x, y, z | { 1 ‖ -1 | 2/3 1/3 1/3 } |
b+2/3, -a+b+1/3, -c+1/3 | x, y, z | { 1 ‖ -3+001 | 2/3 1/3 1/3 } |
a-b+2/3, a+1/3, -c+1/3 | x, y, z | { 1 ‖ -3-001 | 2/3 1/3 1/3 } |
-a+b+2/3, b+1/3, c+1/3 | x, y, z | { 1 ‖ m100 | 2/3 1/3 1/3 } |
-b+2/3, -a+1/3, c+1/3 | x, y, z | { 1 ‖ m110 | 2/3 1/3 1/3 } |
a+2/3, a-b+1/3, c+1/3 | x, y, z | { 1 ‖ m010 | 2/3 1/3 1/3 } |
a+1/3, b+2/3, c+2/3 | x, y, z | { 1 ‖ 1 | 1/3 2/3 2/3 } |
-b+1/3, a-b+2/3, c+2/3 | x, y, z | { 1 ‖ 3+001 | 1/3 2/3 2/3 } |
-a+b+1/3, -a+2/3, c+2/3 | x, y, z | { 1 ‖ 3-001 | 1/3 2/3 2/3 } |
a-b+1/3, -b+2/3, -c+2/3 | x, y, z | { 1 ‖ 2100 | 1/3 2/3 2/3 } |
b+1/3, a+2/3, -c+2/3 | x, y, z | { 1 ‖ 2110 | 1/3 2/3 2/3 } |
-a+1/3, -a+b+2/3, -c+2/3 | x, y, z | { 1 ‖ 2010 | 1/3 2/3 2/3 } |
-a+1/3, -b+2/3, -c+2/3 | x, y, z | { 1 ‖ -1 | 1/3 2/3 2/3 } |
b+1/3, -a+b+2/3, -c+2/3 | x, y, z | { 1 ‖ -3+001 | 1/3 2/3 2/3 } |
a-b+1/3, a+2/3, -c+2/3 | x, y, z | { 1 ‖ -3-001 | 1/3 2/3 2/3 } |
-a+b+1/3, b+2/3, c+2/3 | x, y, z | { 1 ‖ m100 | 1/3 2/3 2/3 } |
-b+1/3, -a+2/3, c+2/3 | x, y, z | { 1 ‖ m110 | 1/3 2/3 2/3 } |
a+1/3, a-b+2/3, c+2/3 | x, y, z | { 1 ‖ m010 | 1/3 2/3 2/3 } |
a, b, c | -x, y, z | { m ‖ 1 | 0 } |
-b, a-b, c | -x, y, z | { m ‖ 3+001 | 0 } |
-a+b, -a, c | -x, y, z | { m ‖ 3-001 | 0 } |
a-b, -b, -c | -x, y, z | { m ‖ 2100 | 0 } |
b, a, -c | -x, y, z | { m ‖ 2110 | 0 } |
-a, -a+b, -c | -x, y, z | { m ‖ 2010 | 0 } |
-a, -b, -c | -x, y, z | { m ‖ -1 | 0 } |
b, -a+b, -c | -x, y, z | { m ‖ -3+001 | 0 } |
a-b, a, -c | -x, y, z | { m ‖ -3-001 | 0 } |
-a+b, b, c | -x, y, z | { m ‖ m100 | 0 } |
-b, -a, c | -x, y, z | { m ‖ m110 | 0 } |
a, a-b, c | -x, y, z | { m ‖ m010 | 0 } |
a+2/3, b+1/3, c+1/3 | -x, y, z | { m ‖ 1 | 2/3 1/3 1/3 } |
-b+2/3, a-b+1/3, c+1/3 | -x, y, z | { m ‖ 3+001 | 2/3 1/3 1/3 } |
-a+b+2/3, -a+1/3, c+1/3 | -x, y, z | { m ‖ 3-001 | 2/3 1/3 1/3 } |
a-b+2/3, -b+1/3, -c+1/3 | -x, y, z | { m ‖ 2100 | 2/3 1/3 1/3 } |
b+2/3, a+1/3, -c+1/3 | -x, y, z | { m ‖ 2110 | 2/3 1/3 1/3 } |
-a+2/3, -a+b+1/3, -c+1/3 | -x, y, z | { m ‖ 2010 | 2/3 1/3 1/3 } |
-a+2/3, -b+1/3, -c+1/3 | -x, y, z | { m ‖ -1 | 2/3 1/3 1/3 } |
b+2/3, -a+b+1/3, -c+1/3 | -x, y, z | { m ‖ -3+001 | 2/3 1/3 1/3 } |
a-b+2/3, a+1/3, -c+1/3 | -x, y, z | { m ‖ -3-001 | 2/3 1/3 1/3 } |
-a+b+2/3, b+1/3, c+1/3 | -x, y, z | { m ‖ m100 | 2/3 1/3 1/3 } |
-b+2/3, -a+1/3, c+1/3 | -x, y, z | { m ‖ m110 | 2/3 1/3 1/3 } |
a+2/3, a-b+1/3, c+1/3 | -x, y, z | { m ‖ m010 | 2/3 1/3 1/3 } |
a+1/3, b+2/3, c+2/3 | -x, y, z | { m ‖ 1 | 1/3 2/3 2/3 } |
-b+1/3, a-b+2/3, c+2/3 | -x, y, z | { m ‖ 3+001 | 1/3 2/3 2/3 } |
-a+b+1/3, -a+2/3, c+2/3 | -x, y, z | { m ‖ 3-001 | 1/3 2/3 2/3 } |
a-b+1/3, -b+2/3, -c+2/3 | -x, y, z | { m ‖ 2100 | 1/3 2/3 2/3 } |
b+1/3, a+2/3, -c+2/3 | -x, y, z | { m ‖ 2110 | 1/3 2/3 2/3 } |
-a+1/3, -a+b+2/3, -c+2/3 | -x, y, z | { m ‖ 2010 | 1/3 2/3 2/3 } |
-a+1/3, -b+2/3, -c+2/3 | -x, y, z | { m ‖ -1 | 1/3 2/3 2/3 } |
b+1/3, -a+b+2/3, -c+2/3 | -x, y, z | { m ‖ -3+001 | 1/3 2/3 2/3 } |
a-b+1/3, a+2/3, -c+2/3 | -x, y, z | { m ‖ -3-001 | 1/3 2/3 2/3 } |
-a+b+1/3, b+2/3, c+2/3 | -x, y, z | { m ‖ m100 | 1/3 2/3 2/3 } |
-b+1/3, -a+2/3, c+2/3 | -x, y, z | { m ‖ m110 | 1/3 2/3 2/3 } |
a+1/3, a-b+2/3, c+2/3 | -x, y, z | { m ‖ m010 | 1/3 2/3 2/3 } |
WP | Site symmetry | Representative |
---|---|---|
3a | $\ce{^{1}{-3}}\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (0,0,0 |0,0,z) |
3b | $\ce{^{1}{-3}}\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (0,0,1/2 |0,0,z) |
6c | $\ce{^{1}{3}}\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (0,0,c |0,0,z) |
9d | $.\ce{^{1}{2}}/\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (1/2,0,1/2 |0,0,z) |
9e | $.\ce{^{1}{2}}/\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (1/2,0,0 |0,0,z) |
18f | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (a,0,0 |0,0,z) |
18g | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (a,0,1/2 |0,0,z) |
18h | $.\ce{^{1}{m}}.\ce{^{\infty m}{1}} $ | (a,-a,c |0,0,z) |
36i | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c |0,0,z) |
Wavevector-k | Little co-group |
---|---|
Γ:(0,0,0) | $\ce{^{1}{-3}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
T:(0,0,3/2) | $\ce{^{1}{-3}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
F:(0,1/2,1) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
L:(-1/2,1/2,1/2) | $\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $ |
Λ:(0,0,w) | $\ce{^{m}{-3}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
Σ:(u,-2*u,0) | $\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
Y:(u,u,3/2) | $\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $ |
C:(u,-u,w) | $\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $ |
GP:(u,v,w) | $\ce{^{m}{-1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
k-vector | A1g↑G(1) |
Γ:(0,0,0) | $Γ_{1}^{S,+}(1) $ |
T:(0,0,3/2) | $T_{1}^{S,+}(1) $ |
F:(0,1/2,1) | $F_{1}^{S,+}(1) $ |
L:(-1/2,1/2,1/2) | $L_{1}^{S,+}(1) $ |
Λ:(0,0,w) | $Λ_{1}^{S}(1) $ |
Σ:(u,-2*u,0) | $Σ_{1}^{S}(1) $ |
Y:(u,u,3/2) | $Y_{1}^{S}(1) $ |
C:(u,-u,w) | $C_{1}^{S}(1) $ |
GP:(u,v,w) | $GP_{1}^{S}(1) $ |
k-vector | A1g↑G(1) |
Γ:(0,0,0) | $Γ_{1}^{S,+}(1) $ |
T:(0,0,3/2) | $T_{2}^{S,-}(1) $ |
F:(0,1/2,1) | $F_{1}^{S,+}(1) $ |
L:(-1/2,1/2,1/2) | $L_{2}^{S,-}(1) $ |
Λ:(0,0,w) | $Λ_{1}^{S}(1) $ |
Σ:(u,-2*u,0) | $Σ_{1}^{S}(1) $ |
Y:(u,u,3/2) | $Y_{2}^{S}(1) $ |
C:(u,-u,w) | $C_{1}^{S}(1) $ |
GP:(u,v,w) | $GP_{1}^{S}(1) $ |
k-vector | A1↑G(2) |
Γ:(0,0,0) | $Γ_{1}^{S,+}(1)⊕Γ_{2}^{S,-}(1) $ |
T:(0,0,3/2) | $T_{1}^{S,+}(1)⊕T_{2}^{S,-}(1) $ |
F:(0,1/2,1) | $F_{1}^{S,+}(1)⊕F_{2}^{S,-}(1) $ |
L:(-1/2,1/2,1/2) | $L_{1}^{S,+}(1)⊕L_{2}^{S,-}(1) $ |
Λ:(0,0,w) | $2Λ_{1}^{S}(1) $ |
Σ:(u,-2*u,0) | $Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
Y:(u,u,3/2) | $Y_{1}^{S}(1)⊕Y_{2}^{S}(1) $ |
C:(u,-u,w) | $2C_{1}^{S}(1) $ |
GP:(u,v,w) | $2GP_{1}^{S}(1) $ |
k-vector | Ag↑G(3) |
Γ:(0,0,0) | $Γ_{1}^{S,+}(1)⊕Γ_{3}^{S,+}(2) $ |
T:(0,0,3/2) | $T_{2}^{S,-}(1)⊕T_{3}^{S,-}(2) $ |
F:(0,1/2,1) | $F_{1}^{S,+}(1)⊕F_{1}^{S,-}(1)⊕F_{2}^{S,-}(1) $ |
L:(-1/2,1/2,1/2) | $L_{1}^{S,+}(1)⊕L_{2}^{S,+}(1)⊕L_{2}^{S,-}(1) $ |
Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{3}^{S}(2) $ |
Σ:(u,-2*u,0) | $2Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
Y:(u,u,3/2) | $Y_{1}^{S}(1)⊕2Y_{2}^{S}(1) $ |
C:(u,-u,w) | $2C_{1}^{S}(1)⊕C_{2}^{S}(1) $ |
GP:(u,v,w) | $3GP_{1}^{S}(1) $ |
k-vector | Ag↑G(3) |
Γ:(0,0,0) | $Γ_{1}^{S,+}(1)⊕Γ_{3}^{S,+}(2) $ |
T:(0,0,3/2) | $T_{1}^{S,+}(1)⊕T_{3}^{S,+}(2) $ |
F:(0,1/2,1) | $F_{1}^{S,+}(1)⊕F_{1}^{S,-}(1)⊕F_{2}^{S,-}(1) $ |
L:(-1/2,1/2,1/2) | $L_{1}^{S,+}(1)⊕L_{1}^{S,-}(1)⊕L_{2}^{S,-}(1) $ |
Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{3}^{S}(2) $ |
Σ:(u,-2*u,0) | $2Σ_{1}^{S}(1)⊕Σ_{2}^{S}(1) $ |
Y:(u,u,3/2) | $2Y_{1}^{S}(1)⊕Y_{2}^{S}(1) $ |
C:(u,-u,w) | $2C_{1}^{S}(1)⊕C_{2}^{S}(1) $ |
GP:(u,v,w) | $3GP_{1}^{S}(1) $ |
k-vector | A↑G(6) |
Γ:(0,0,0) | $Γ_{1}^{S,+}(1)⊕Γ_{1}^{S,-}(1)⊕Γ_{3}^{S,+}(2)⊕Γ_{3}^{S,-}(2) $ |
T:(0,0,3/2) | $T_{1}^{S,+}(1)⊕T_{1}^{S,-}(1)⊕T_{3}^{S,+}(2)⊕T_{3}^{S,-}(2) $ |
F:(0,1/2,1) | $2F_{1}^{S,+}(1)⊕2F_{1}^{S,-}(1)⊕F_{2}^{S,+}(1)⊕F_{2}^{S,-}(1) $ |
L:(-1/2,1/2,1/2) | $2L_{1}^{S,+}(1)⊕2L_{1}^{S,-}(1)⊕L_{2}^{S,+}(1)⊕L_{2}^{S,-}(1) $ |
Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1)⊕2Λ_{3}^{S}(2) $ |
Σ:(u,-2*u,0) | $4Σ_{1}^{S}(1)⊕2Σ_{2}^{S}(1) $ |
Y:(u,u,3/2) | $4Y_{1}^{S}(1)⊕2Y_{2}^{S}(1) $ |
C:(u,-u,w) | $3C_{1}^{S}(1)⊕3C_{2}^{S}(1) $ |
GP:(u,v,w) | $6GP_{1}^{S}(1) $ |
k-vector | A↑G(6) |
Γ:(0,0,0) | $Γ_{1}^{S,+}(1)⊕Γ_{1}^{S,-}(1)⊕Γ_{3}^{S,+}(2)⊕Γ_{3}^{S,-}(2) $ |
T:(0,0,3/2) | $T_{2}^{S,+}(1)⊕T_{2}^{S,-}(1)⊕T_{3}^{S,+}(2)⊕T_{3}^{S,-}(2) $ |
F:(0,1/2,1) | $2F_{1}^{S,+}(1)⊕2F_{1}^{S,-}(1)⊕F_{2}^{S,+}(1)⊕F_{2}^{S,-}(1) $ |
L:(-1/2,1/2,1/2) | $L_{1}^{S,+}(1)⊕L_{1}^{S,-}(1)⊕2L_{2}^{S,+}(1)⊕2L_{2}^{S,-}(1) $ |
Λ:(0,0,w) | $Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1)⊕2Λ_{3}^{S}(2) $ |
Σ:(u,-2*u,0) | $4Σ_{1}^{S}(1)⊕2Σ_{2}^{S}(1) $ |
Y:(u,u,3/2) | $2Y_{1}^{S}(1)⊕4Y_{2}^{S}(1) $ |
C:(u,-u,w) | $3C_{1}^{S}(1)⊕3C_{2}^{S}(1) $ |
GP:(u,v,w) | $6GP_{1}^{S}(1) $ |
k-vector | A'↑G(6) |
Γ:(0,0,0) | $Γ_{1}^{S,+}(1)⊕Γ_{2}^{S,-}(1)⊕Γ_{3}^{S,+}(2)⊕Γ_{3}^{S,-}(2) $ |
T:(0,0,3/2) | $T_{1}^{S,+}(1)⊕T_{2}^{S,-}(1)⊕T_{3}^{S,+}(2)⊕T_{3}^{S,-}(2) $ |
F:(0,1/2,1) | $2F_{1}^{S,+}(1)⊕F_{1}^{S,-}(1)⊕F_{2}^{S,+}(1)⊕2F_{2}^{S,-}(1) $ |
L:(-1/2,1/2,1/2) | $2L_{1}^{S,+}(1)⊕L_{1}^{S,-}(1)⊕L_{2}^{S,+}(1)⊕2L_{2}^{S,-}(1) $ |
Λ:(0,0,w) | $2Λ_{1}^{S}(1)⊕2Λ_{3}^{S}(2) $ |
Σ:(u,-2*u,0) | $3Σ_{1}^{S}(1)⊕3Σ_{2}^{S}(1) $ |
Y:(u,u,3/2) | $3Y_{1}^{S}(1)⊕3Y_{2}^{S}(1) $ |
C:(u,-u,w) | $4C_{1}^{S}(1)⊕2C_{2}^{S}(1) $ |
GP:(u,v,w) | $6GP_{1}^{S}(1) $ |
k-vector | A↑G(12) | |
Γ:(0,0,0) | $Γ_{1}^{S,+}(1)⊕Γ_{1}^{S,-}(1)⊕Γ_{2}^{S,+}(1)⊕Γ_{2}^{S,-}(1)⊕2Γ_{3}^{S,+}(2)⊕2Γ_{3}^{S,-}(2) $ | |
T:(0,0,3/2) | $T_{1}^{S,+}(1)⊕T_{1}^{S,-}(1)⊕T_{2}^{S,+}(1)⊕T_{2}^{S,-}(1)⊕2T_{3}^{S,+}(2)⊕2T_{3}^{S,-}(2) $ | |
F:(0,1/2,1) | $3F_{1}^{S,+}(1)⊕3F_{1}^{S,-}(1)⊕3F_{2}^{S,+}(1)⊕3F_{2}^{S,-}(1) $ | |
L:(-1/2,1/2,1/2) | $3L_{1}^{S,+}(1)⊕3L_{1}^{S,-}(1)⊕3L_{2}^{S,+}(1)⊕3L_{2}^{S,-}(1) $ | |
Λ:(0,0,w) | $2Λ_{1}^{S}(1)⊕2Λ_{2}^{S}(1)⊕4Λ_{3}^{S}(2) $ | |
Σ:(u,-2*u,0) | $6Σ_{1}^{S}(1)⊕6Σ_{2}^{S}(1) $ | |
Y:(u,u,3/2) | $6Y_{1}^{S}(1)⊕6Y_{2}^{S}(1) $ | |
C:(u,-u,w) | $6C_{1}^{S}(1)⊕6C_{2}^{S}(1) $ | |
GP:(u,v,w) | $12GP_{1}^{S}(1) $ |