U-tiling: UQC581
h-net
1 record listed.
| Image |
h-net name |
Orbifold symbol |
Transitivity (Vert,Edge,Face) |
Vertex Degree |
2D Vertex Symbol |
 |
hqc384 |
*2244 |
(2,3,3) |
{8,12} |
{4.3.3.3.4.3.3.3}{3.3.3.3.3.3.3.... |
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
|
|
sqc5786
|
|
P42/mmc |
131 |
tetragonal |
{10,8} |
6 |
(2,3) |
|
G
|
False
|
|
sqc6464
|
|
I-42d |
122 |
tetragonal |
{12,8} |
6 |
(2,4) |
|
D
|
False
|
|
sqc1160
|
|
P4/mmm |
123 |
tetragonal |
{8,12} |
3 |
(2,3) |
Topological data
| Vertex degrees | {8,12} |
| 2D vertex symbol | {4.3.3.3.4.3.3.3}{3.3.3.3.3.3.3.3.3.3.3.3} |
| Dual tiling |  |
D-symbol
Genus-3 version with t-tau cuts labelled
<41.1:112:57 4 5 20 21 64 11 12 27 28 71 18 19 78 25 26 85 32 33 48 49 92 39 40 55 56 99 46 47 106 53 54 60 61 76 77 67 68 83 84 74 75 81 82 88 89 104 105 95 96 111 112 102 103 109 110,2 17 60 6 14 9 24 67 13 16 74 20 35 23 81 27 42 30 45 88 34 37 52 95 41 44 102 48 56 51 109 55 58 73 62 70 65 80 69 72 76 91 79 83 98 86 101 90 93 108 97 100 104 112 107 111,43 3 5 7 50 10 12 14 22 17 19 21 24 26 28 36 31 33 35 38 40 42 45 47 49 52 54 56 99 59 61 63 106 66 68 70 78 73 75 77 80 82 84 92 87 89 91 94 96 98 101 103 105 108 110 112:3 3 4 3 3 3 3 3 3 3 3 3 3 3 4 3 3 3,12 8 8 8 8 12> {(0, 103): 'tau1^-1', (0, 62): 't2', (2, 7): 't1^-1*tau2*t3', (0, 55): 't3^-1*tau2^-1*t3^-1', (1, 37): 't3*tau2*t3', (0, 33): 't3', (0, 26): 't1', (0, 48): 't3^-1', (0, 104): 'tau1^-1', (0, 97): 't3*tau2*t1^-1*tau3^-1*t2*tau1', (1, 72): 't2^-1', (1, 107): 'tau1^-1*t2^-1*tau3*t1*tau2^-1*t3^-1', (0, 27): 't1', (1, 44): 't3^-1', (0, 82): 'tau3^-1', (1, 79): 'tau3^-1', (1, 9): 't1^-1', (2, 63): 't1^-1*tau2*t3', (1, 97): 't3*tau2*t1^-1', (0, 61): 't2', (0, 83): 'tau3^-1', (1, 27): 't1*tau2^-1*t3^-1', (1, 100): 'tau1^-1', (0, 54): 't3^-1*tau2^-1*t3^-1', (0, 110): 'tau1^-1*t2^-1*tau3*t1*tau2^-1*t3^-1', }