The continuously infinite group ∞1 is omitted.
Coordinates | Seitz symbol |
---|---|
a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
a+1/2, -b+1/2, -c+1/2 | x, y, z | { 1 ‖ 2100 | 1/2 1/2 1/2 } |
-a+1/2, b+1/2, -c+1/2 | x, y, z | { 1 ‖ 2010 | 1/2 1/2 1/2 } |
-a, -b, c | x, y, z | { 1 ‖ 2001 | 0 } |
-a, -b, -c | -x, -y, -z | { -1 ‖ -1 | 0 } |
-a+1/2, b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m100 | 1/2 1/2 1/2 } |
a+1/2, -b+1/2, c+1/2 | -x, -y, -z | { -1 ‖ m010 | 1/2 1/2 1/2 } |
a, b, -c | -x, -y, -z | { -1 ‖ m001 | 0 } |
a, b, c | -x, y, z | { m ‖ 1 | 0 } |
a+1/2, -b+1/2, -c+1/2 | -x, y, z | { m ‖ 2100 | 1/2 1/2 1/2 } |
-a+1/2, b+1/2, -c+1/2 | -x, y, z | { m ‖ 2010 | 1/2 1/2 1/2 } |
-a, -b, c | -x, y, z | { m ‖ 2001 | 0 } |
-a, -b, -c | x, -y, -z | { 2 ‖ -1 | 0 } |
-a+1/2, b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m100 | 1/2 1/2 1/2 } |
a+1/2, -b+1/2, c+1/2 | x, -y, -z | { 2 ‖ m010 | 1/2 1/2 1/2 } |
a, b, -c | x, -y, -z | { 2 ‖ m001 | 0 } |
WP | Site symmetry | Representative |
---|---|---|
2a | $..\ce{^{1}{2}}/\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
2b | $..\ce{^{1}{2}}/\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (0,0,1/2 | 0,0,0) |
2c | $..\ce{^{1}{2}}/\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (0,1/2,0 | 0,0,0) |
2d | $..\ce{^{1}{2}}/\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (0,1/2,1/2 | 0,0,0) |
4e | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,0,c | 0,0,z) |
4f | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (0,1/2,c | 0,0,z) |
4g | $..\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ | (a,b,0 | 0,0,0) |
8h | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
Wavevector-k | Little co-group |
---|---|
Γ:(0,0,0) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
R:(1/2,1/2,1/2) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
S:(1/2,1/2,0) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
T:(0,1/2,1/2) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
U:(1/2,0,1/2) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
X:(1/2,0,0) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
Y:(0,1/2,0) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
Z:(0,0,1/2) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
A:(u,0,1/2) | $ \ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
B:(0,v,1/2) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
C:(u,1/2,0) | $ \ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
D:(1/2,v,0) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
Δ:(0,v,0) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
E:(u,1/2,1/2) | $ \ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
G:(1/2,0,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
H:(0,1/2,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
Λ:(0,0,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
P:(1/2,v,1/2) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
Q:(1/2,1/2,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
Σ:(u,0,0) | $ \ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
K:(0,v,w) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
L:(1/2,v,w) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
M:(u,0,w) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
N:(u,1/2,w) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
V:(u,v,0) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
W:(u,v,1/2) | $ \ce{^{m}{2/}}\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(4) |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2) $ |
R:(1/2,1/2,1/2) | R:(1/2,1/2,1/2) | $R_{1}^{S}R_{2}^{S}(4) $ |
S:(1/2,1/2,0) | S:(1/2,1/2,0) | $S_{1}^{S}S_{2}^{S}(4) $ |
T:(0,1/2,1/2) | T:(0,1/2,1/2) | $T_{1}^{S}(4) $ |
U:(1/2,0,1/2) | U:(1/2,0,1/2) | $U_{1}^{S}(4) $ |
X:(1/2,0,0) | X:(1/2,0,0) | $X_{1}^{S}(4) $ |
Y:(0,1/2,0) | Y:(0,1/2,0) | $Y_{1}^{S}(4) $ |
Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}(2)⊕Z_{2}^{S}(2) $ |
A:(u,0,1/2) | A:(u,0,1/2) | $A_{1}^{S}(2)⊕A_{2}^{S}(2) $ |
B:(0,v,1/2) | B:(0,v,1/2) | $B_{1}^{S}(2)⊕B_{2}^{S}(2) $ |
C:(u,1/2,0) | C:(u,1/2,0) | $C_{1}^{S}C_{2}^{S}(4) $ |
D:(1/2,v,0) | D:(1/2,v,0) | $D_{1}^{S}D_{2}^{S}(4) $ |
Δ:(0,v,0) | Δ:(0,v,0) | $Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2) $ |
E:(u,1/2,1/2) | E:(u,1/2,1/2) | $E_{1}^{S}E_{2}^{S}(4) $ |
G:(1/2,0,w) | G:(1/2,0,w) | $G_{1}^{S}G_{2}^{S}(4) $ |
H:(0,1/2,w) | H:(0,1/2,w) | $H_{1}^{S}H_{2}^{S}(4) $ |
Λ:(0,0,w) | Λ:(0,0,w) | $2Λ_{1}^{S}(2) $ |
P:(1/2,v,1/2) | P:(1/2,v,1/2) | $P_{1}^{S}P_{2}^{S}(4) $ |
Q:(1/2,1/2,w) | Q:(1/2,1/2,w) | $Q_{1}^{S}Q_{1}^{S}(4) $ |
Σ:(u,0,0) | Σ:(u,0,0) | $Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2) $ |
K:(0,v,w) | K:(0,v,w) | $2K_{1}^{S}(2) $ |
L:(1/2,v,w) | L:(1/2,v,w) | $L_{1}^{S}L_{1}^{S}(4) $ |
M:(u,0,w) | M:(u,0,w) | $2M_{1}^{S}(2) $ |
N:(u,1/2,w) | N:(u,1/2,w) | $N_{1}^{S}N_{1}^{S}(4) $ |
V:(u,v,0) | V:(u,v,0) | $2V_{1}^{S}(2) $ |
W:(u,v,1/2) | W:(u,v,1/2) | $2W_{1}^{S}(2) $ |
GP:(u,v,w) | GP:(u,v,w) | $2GP_{1}^{S}(2) $ |
k-vector | k-vector-G↑ | A↑G(4) |
Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2) $ |
R:(1/2,1/2,1/2) | R:(1/2,1/2,1/2) | $R_{3}^{S}R_{4}^{S}(4) $ |
S:(1/2,1/2,0) | S:(1/2,1/2,0) | $S_{3}^{S}S_{4}^{S}(4) $ |
T:(0,1/2,1/2) | T:(0,1/2,1/2) | $T_{1}^{S}(4) $ |
U:(1/2,0,1/2) | U:(1/2,0,1/2) | $U_{1}^{S}(4) $ |
X:(1/2,0,0) | X:(1/2,0,0) | $X_{1}^{S}(4) $ |
Y:(0,1/2,0) | Y:(0,1/2,0) | $Y_{1}^{S}(4) $ |
Z:(0,0,1/2) | Z:(0,0,1/2) | $Z_{1}^{S}(2)⊕Z_{2}^{S}(2) $ |
A:(u,0,1/2) | A:(u,0,1/2) | $A_{1}^{S}(2)⊕A_{2}^{S}(2) $ |
B:(0,v,1/2) | B:(0,v,1/2) | $B_{1}^{S}(2)⊕B_{2}^{S}(2) $ |
C:(u,1/2,0) | C:(u,1/2,0) | $C_{1}^{S}C_{2}^{S}(4) $ |
D:(1/2,v,0) | D:(1/2,v,0) | $D_{1}^{S}D_{2}^{S}(4) $ |
Δ:(0,v,0) | Δ:(0,v,0) | $Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2) $ |
E:(u,1/2,1/2) | E:(u,1/2,1/2) | $E_{1}^{S}E_{2}^{S}(4) $ |
G:(1/2,0,w) | G:(1/2,0,w) | $G_{1}^{S}G_{2}^{S}(4) $ |
H:(0,1/2,w) | H:(0,1/2,w) | $H_{1}^{S}H_{2}^{S}(4) $ |
Λ:(0,0,w) | Λ:(0,0,w) | $2Λ_{1}^{S}(2) $ |
P:(1/2,v,1/2) | P:(1/2,v,1/2) | $P_{1}^{S}P_{2}^{S}(4) $ |
Q:(1/2,1/2,w) | Q:(1/2,1/2,w) | $Q_{2}^{S}Q_{2}^{S}(4) $ |
Σ:(u,0,0) | Σ:(u,0,0) | $Σ_{1}^{S}(2)⊕Σ_{2}^{S}(2) $ |
K:(0,v,w) | K:(0,v,w) | $2K_{1}^{S}(2) $ |
L:(1/2,v,w) | L:(1/2,v,w) | $L_{1}^{S}L_{1}^{S}(4) $ |
M:(u,0,w) | M:(u,0,w) | $2M_{1}^{S}(2) $ |
N:(u,1/2,w) | N:(u,1/2,w) | $N_{1}^{S}N_{1}^{S}(4) $ |
V:(u,v,0) | V:(u,v,0) | $2V_{1}^{S}(2) $ |
W:(u,v,1/2) | W:(u,v,1/2) | $2W_{1}^{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_{3}^{S}(2)⊕Γ_{4}^{S}(2) $ |
R:(1/2,1/2,1/2) | R:(1/2,1/2,1/2) | $R_{1}^{S}R_{2}^{S}(4)⊕R_{3}^{S}R_{4}^{S}(4) $ |
S:(1/2,1/2,0) | S:(1/2,1/2,0) | $S_{1}^{S}S_{2}^{S}(4)⊕S_{3}^{S}S_{4}^{S}(4) $ |
T:(0,1/2,1/2) | T:(0,1/2,1/2) | $2T_{1}^{S}(4) $ |
U:(1/2,0,1/2) | U:(1/2,0,1/2) | $2U_{1}^{S}(4) $ |
X:(1/2,0,0) | X:(1/2,0,0) | $2X_{1}^{S}(4) $ |
Y:(0,1/2,0) | Y:(0,1/2,0) | $2Y_{1}^{S}(4) $ |
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) $ |
A:(u,0,1/2) | A:(u,0,1/2) | $2A_{1}^{S}(2)⊕2A_{2}^{S}(2) $ |
B:(0,v,1/2) | B:(0,v,1/2) | $2B_{1}^{S}(2)⊕2B_{2}^{S}(2) $ |
C:(u,1/2,0) | C:(u,1/2,0) | $2C_{1}^{S}C_{2}^{S}(4) $ |
D:(1/2,v,0) | D:(1/2,v,0) | $2D_{1}^{S}D_{2}^{S}(4) $ |
Δ:(0,v,0) | Δ:(0,v,0) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $ |
E:(u,1/2,1/2) | E:(u,1/2,1/2) | $2E_{1}^{S}E_{2}^{S}(4) $ |
G:(1/2,0,w) | G:(1/2,0,w) | $2G_{1}^{S}G_{2}^{S}(4) $ |
H:(0,1/2,w) | H:(0,1/2,w) | $2H_{1}^{S}H_{2}^{S}(4) $ |
Λ:(0,0,w) | Λ:(0,0,w) | $2Λ_{1}^{S}(2)⊕2Λ_{2}^{S}(2) $ |
P:(1/2,v,1/2) | P:(1/2,v,1/2) | $2P_{1}^{S}P_{2}^{S}(4) $ |
Q:(1/2,1/2,w) | Q:(1/2,1/2,w) | $Q_{1}^{S}Q_{1}^{S}(4)⊕Q_{2}^{S}Q_{2}^{S}(4) $ |
Σ:(u,0,0) | Σ:(u,0,0) | $2Σ_{1}^{S}(2)⊕2Σ_{2}^{S}(2) $ |
K:(0,v,w) | K:(0,v,w) | $4K_{1}^{S}(2) $ |
L:(1/2,v,w) | L:(1/2,v,w) | $2L_{1}^{S}L_{1}^{S}(4) $ |
M:(u,0,w) | M:(u,0,w) | $4M_{1}^{S}(2) $ |
N:(u,1/2,w) | N:(u,1/2,w) | $2N_{1}^{S}N_{1}^{S}(4) $ |
V:(u,v,0) | V:(u,v,0) | $4V_{1}^{S}(2) $ |
W:(u,v,1/2) | W:(u,v,1/2) | $4W_{1}^{S}(2) $ |
GP:(u,v,w) | GP:(u,v,w) | $4GP_{1}^{S}(2) $ |