U-tiling: UQC123
h-net
1 record listed.
| Image |
h-net name |
Orbifold symbol |
Transitivity (Vert,Edge,Face) |
Vertex Degree |
2D Vertex Symbol |
 |
hqc121 |
*2244 |
(2,3,2) |
{8,4} |
{8.3.3.8.8.3.3.8}{3.3.3.3} |
s-nets
3 records listed.
| Surface |
Edge collapse |
Image |
s-net name |
Other names |
Space group |
Space group number |
Symmetry class |
Vertex degree(s) |
Vertices per primitive unit cell |
Transitivity (Vertex, Edge) |
|
P
|
True
|
|
sqc2759
|
|
P42/mmc |
131 |
tetragonal |
{7,4} |
6 |
(2,3) |
|
G
|
False
|
|
sqc3458
|
|
I-42d |
122 |
tetragonal |
{8,4} |
6 |
(2,3) |
|
D
|
False
|
|
sqc391
|
|
P4/mmm |
123 |
tetragonal |
{8,4} |
3 |
(2,3) |
Topological data
| Vertex degrees | {8,4} |
| 2D vertex symbol | {8.3.3.8.8.3.3.8}{3.3.3.3} |
| Dual tiling |  |
D-symbol
Genus-3 version with t-tau cuts labelled
<7.1:80:31 12 13 5 36 17 18 10 16 15 20 26 32 33 25 37 38 30 35 40 71 52 53 45 76 57 58 50 56 55 60 66 72 73 65 77 78 70 75 80,2 4 15 7 9 20 12 14 17 19 22 24 35 27 29 40 32 34 37 39 42 44 55 47 49 60 52 54 57 59 62 64 75 67 69 80 72 74 77 79,41 3 9 10 46 8 51 13 24 25 56 18 29 30 61 23 66 28 71 33 39 40 76 38 43 49 50 48 53 64 65 58 69 70 63 68 73 79 80 78:8 3 3 3 3 8 3 3 3 3,8 4 8 8 8 4> {(0, 17): 't1', (0, 56): 'tau3^-1', (0, 57): 'tau3^-1', (0, 62): 'tau1', (2, 58): 't1*tau2^-1*t3^-1', (2, 59): 't1*tau2^-1*t3^-1', (0, 51): 't2^-1', (0, 52): 't2^-1', (0, 45): 't1^-1*tau2*t3', (0, 35): 't3^-1*tau2^-1*t1', (0, 32): 't3^-1', (0, 36): 't3^-1*tau2^-1*t3^-1', (0, 37): 't3^-1*tau2^-1*t3^-1', (0, 31): 't3^-1', (0, 16): 't1', (0, 61): 'tau1', (2, 18): 't1*tau2^-1*t3^-1', (2, 19): 't1*tau2^-1*t3^-1', (1, 74): 'tau1^-1', (1, 79): 'tau1^-1*t2^-1*tau3*t1*tau2^-1*t3^-1', (1, 59): 'tau3^-1', (1, 54): 't2^-1', (1, 34): 't3^-1', (1, 39): 't3^-1*tau2^-1*t3^-1', (1, 19): 't1', (0, 66): 't3*tau2*t1^-1*tau3^-1*t2*tau1', (0, 67): 't3*tau2*t1^-1*tau3^-1*t2*tau1'}