U-tiling: UQC3341
h-net
1 record listed.
| Image |
h-net name |
Orbifold symbol |
Transitivity (Vert,Edge,Face) |
Vertex Degree |
2D Vertex Symbol |
 |
hqc453 |
*2244 |
(3,4,2) |
{4,16,4} |
{4.4.4.4}{4.3.3.4.4.3.3.4.4.3.3.... |
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
|
|
sqc4028
|
|
P42/mmc |
131 |
tetragonal |
{3,12,4} |
8 |
(3,4) |
|
G
|
False
|
|
sqc6225
|
|
I-42d |
122 |
tetragonal |
{4,16,4} |
8 |
(3,4) |
|
D
|
False
|
|
sqc1126
|
|
P-42m |
111 |
tetragonal |
{4,16,4} |
4 |
(3,4) |
Topological data
| Vertex degrees | {4,16,4} |
| 2D vertex symbol | {4.4.4.4}{4.3.3.4.4.3.3.4.4.3.3.4.4.3.3.4}{3.3.3.3} |
| Dual tiling |  |
D-symbol
Genus-3 version with t-tau cuts labelled
<27.1:112:43 3 46 47 7 50 10 53 54 14 22 17 25 26 21 24 28 36 31 39 40 35 38 42 45 49 52 56 99 59 102 103 63 106 66 109 110 70 78 73 81 82 77 80 84 92 87 95 96 91 94 98 101 105 108 112,2 4 6 49 9 11 13 56 16 18 20 28 23 25 27 30 32 34 42 37 39 41 44 46 48 51 53 55 58 60 62 105 65 67 69 112 72 74 76 84 79 81 83 86 88 90 98 93 95 97 100 102 104 107 109 111,57 9 10 5 20 21 64 12 27 28 71 30 31 19 78 37 38 26 85 33 48 49 92 40 55 56 99 51 52 47 106 54 65 66 61 76 77 68 83 84 86 87 75 93 94 82 89 104 105 96 111 112 107 108 103 110:4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3,4 16 4 4 4 4 16 4> {(2, 61): 't2', (2, 62): 't2', (0, 63): 't1^-1*tau2*t3', (2, 54): 't3^-1*tau2^-1*t3^-1', (2, 55): 't3^-1*tau2^-1*t3^-1', (2, 48): 't3^-1', (0, 52): 't3^-1*tau2^-1*t1', (0, 53): 't3^-1*tau2^-1*t1', (2, 47): 't3^-1', (1, 111): 't3^-1*tau2^-1*t1', (2, 36): 't3*tau2*t1^-1', (2, 37): 't3*tau2*t1^-1', (2, 12): 't1^-1', (2, 13): 't1^-1', (0, 7): 't1^-1*tau2*t3', (1, 55): 't3^-1*tau2^-1*t1', (2, 110): 'tau1^-1*t2^-1*tau3*t1*tau2^-1*t3^-1', (2, 104): 'tau1^-1', (0, 109): 't3^-1*tau2^-1*t1', (2, 103): 'tau1^-1', (2, 97): 't3*tau2*t1^-1*tau3^-1*t2*tau1', (2, 92): 't3*tau2*t1^-1', (2, 82): 'tau3^-1', (2, 83): 'tau3^-1', (2, 79): 't1*tau2^-1*t3^-1', (0, 66): 't1^-1*tau2*t3'}