U-tiling: UQC680
h-net
1 record listed.
| Image |
h-net name |
Orbifold symbol |
Transitivity (Vert,Edge,Face) |
Vertex Degree |
2D Vertex Symbol |
 |
hqc573 |
*22222 |
(2,5,3) |
{6,4} |
{4.4.4.4.4.4}{4.4.4.4} |
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
|
|
sqc6829
|
|
P4/mmm |
123 |
tetragonal |
{4,5} |
12 |
(2,5) |
|
G
|
False
|
|
sqc7654
|
|
I4122 |
98 |
tetragonal |
{4,6} |
12 |
(2,5) |
|
D
|
False
|
|
sqc1916
|
|
P4222 |
93 |
tetragonal |
{4,6} |
6 |
(2,5) |
Topological data
| Vertex degrees | {6,4} |
| 2D vertex symbol | {4.4.4.4.4.4}{4.4.4.4} |
| Dual tiling |  |
D-symbol
Genus-3 version with t-tau cuts labelled
<19.4:128:9 3 12 13 22 23 40 11 30 31 48 25 19 28 29 56 27 72 57 35 60 61 54 55 73 43 76 77 70 71 81 51 84 85 59 86 87 104 89 67 92 93 75 94 95 112 83 120 91 128 105 99 108 109 118 119 107 126 127 121 115 124 125 123,2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128,17 74 75 5 7 80 25 58 59 13 15 64 90 91 21 23 96 82 83 29 31 88 49 106 107 37 39 112 65 98 99 45 47 104 122 123 53 55 128 81 61 63 114 115 69 71 120 89 77 79 85 87 93 95 113 101 103 121 109 111 117 119 125 127:4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4,4 6 4 6 6 6 4 6 4 6 6 6> {(0, 29): 't1', (0, 117): 'tau2*t3', (0, 48): 'tau2^-1', (0, 125): 't1^-1*tau3^-1*t2', (0, 92): 'tau3^-1', (0, 104): 'tau1', (0, 30): 't1', (2, 17): 't1^-1', (0, 118): 'tau2*t3', (0, 56): 't3^-1', (2, 40): 't2*tau3^-1', (0, 27): 't1', (0, 126): 't1^-1*tau3^-1*t2', (2, 113): 't1', (0, 123): 't1^-1*tau3^-1*t2*tau1*t3^-1*tau2^-1', (0, 61): 't3^-1*tau2^-1', (0, 28): 't1', (0, 40): 't2', (0, 51): 'tau2^-1', (0, 124): 't1^-1*tau3^-1*t2*tau1*t3^-1*tau2^-1', (0, 62): 't3^-1*tau2^-1', (0, 107): 'tau1', (2, 16): 't1^-1', (0, 88): 'tau3^-1', (0, 59): 't3^-1', (0, 52): 'tau2^-1', (2, 112): 't1*tau3*t2^-1', (0, 108): 'tau1', (0, 93): 'tau3^-1*t2', (0, 60): 't3^-1', (0, 31): 't1', (2, 120): 'tau2^-1*t3^-1', (0, 43): 't2', (2, 18): 't1^-1', (0, 24): 't1', (2, 23): 't1^-1', (0, 127): 't1^-1', (0, 94): 'tau3^-1*t2', (2, 114): 't1', (2, 48): 'tau2^-1*t3^-1', (0, 44): 't2', (0, 120): 't1^-1*tau3^-1*t2*tau1*t3^-1*tau2^-1', (0, 91): 'tau3^-1', (2, 119): 't1', }