U-tiling: UQC4187
h-net
1 record listed.
| Image |
h-net name |
Orbifold symbol |
Transitivity (Vert,Edge,Face) |
Vertex Degree |
2D Vertex Symbol |
 |
hqc863 |
*4444 |
(4,4,2) |
{4,4,8,4} |
{5.5.12.12}{12.12.12.12}{5.5.5.5... |
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
|
|
sqc1062
|
|
P4/mmm |
123 |
tetragonal |
{4,6,4} |
6 |
(3,4) |
|
G
|
False
|
|
sqc1829
|
|
I-4 |
82 |
tetragonal |
{4,8,4,4} |
7 |
(4,4) |
|
D
|
False
|
|
sqc1873
|
|
I-4m2 |
119 |
tetragonal |
{4,8,4,4} |
7 |
(4,4) |
Topological data
| Vertex degrees | {4,4,8,4} |
| 2D vertex symbol | {5.5.12.12}{12.12.12.12}{5.5.5.5.5.5.5.5}{5.5.5.5} |
| Dual tiling |  |
D-symbol
Genus-3 version with t-tau cuts labelled
<11.2:64:17 6 19 5 8 25 14 27 13 16 22 21 24 30 29 32 49 38 51 37 40 57 46 59 45 48 54 53 56 62 61 64,2 4 53 7 24 10 12 61 15 32 18 20 29 23 26 28 31 34 36 45 39 56 42 44 47 64 50 52 55 58 60 63,3 18 20 21 22 15 16 11 26 28 29 30 19 39 40 27 47 48 35 50 52 53 54 43 58 60 61 62 51 63 64 59:5 12 5 5 5,4 4 8 4 4 4 4> {(0, 58): 't3^-1*tau2^-1*t3^-1', (2, 60): 't3^-1*tau2^-1*t1*tau3*t2^-1*tau1^-1', (0, 56): 't3^-1*tau2^-1*t3^-1', (2, 57): 't3^-1*tau2^-1*t1*tau3*t2^-1*tau1^-1', (2, 59): 't3^-1*tau2^-1*t1*tau3*t2^-1*tau1^-1', (0, 50): 't3^-1', (2, 53): 'tau1^-1', (0, 48): 't3^-1', (2, 49): 'tau1^-1', (2, 51): 'tau1^-1', (2, 45): 'tau1*t2*tau3^-1*t1^-1*tau2*t3', (2, 47): 't3*tau2*t1^-1', (2, 36): 'tau1', (0, 26): 't1', (2, 30): 't1*tau2^-1*t3^-1', (2, 25): 'tau3^-1', (2, 20): 't2^-1', (2, 21): 't2^-1', (2, 17): 't2^-1', (2, 19): 't2^-1', (2, 12): 'tau3', (2, 13): 'tau3', (0, 8): 't1^-1', (2, 11): 'tau3', (1, 60): 't3^-1*tau2^-1*t1', (1, 63): 't3^-1*tau2^-1*t3^-1', (1, 55): 't3^-1', (1, 31): 't1'}