U-tiling: UQC4080
h-net
1 record listed.
| Image |
h-net name |
Orbifold symbol |
Transitivity (Vert,Edge,Face) |
Vertex Degree |
2D Vertex Symbol |
 |
hqc1185 |
*2244 |
(3,4,2) |
{4,12,8} |
{6.3.3.6}{6.3.3.6.3.3.6.3.3.6.3.... |
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
|
False
|
|
sqc8608
|
|
P42/mmc |
131 |
tetragonal |
{4,12,8} |
12 |
(3,4) |
|
G
|
False
|
|
sqc8494
|
|
I-42d |
122 |
tetragonal |
{4,12,8} |
12 |
(3,5) |
|
D
|
False
|
|
sqc2565
|
|
P-42m |
111 |
tetragonal |
{4,8,12} |
6 |
(3,4) |
Topological data
| Vertex degrees | {4,12,8} |
| 2D vertex symbol | {6.3.3.6}{6.3.3.6.3.3.6.3.3.6.3.3}{3.3.3.3.3.3.3.3} |
| Dual tiling |  |
D-symbol
Genus-3 version with t-tau cuts labelled
<5.1:144:73 3 5 7 9 82 12 14 16 18 91 21 23 25 27 100 30 32 34 36 109 39 41 43 45 118 48 50 52 54 127 57 59 61 63 136 66 68 70 72 75 77 79 81 84 86 88 90 93 95 97 99 102 104 106 108 111 113 115 117 120 122 124 126 129 131 133 135 138 140 142 144,2 57 6 9 8 11 66 15 18 17 20 30 24 27 26 29 33 36 35 38 48 42 45 44 47 51 54 53 56 60 63 62 65 69 72 71 74 129 78 81 80 83 138 87 90 89 92 102 96 99 98 101 105 108 107 110 120 114 117 116 119 123 126 125 128 132 135 134 137 141 144 143,10 4 5 15 16 26 27 13 14 35 36 37 22 23 42 43 46 31 32 51 52 40 41 62 63 49 50 71 72 64 58 59 69 70 67 68 82 76 77 87 88 98 99 85 86 107 108 109 94 95 114 115 118 103 104 123 124 112 113 134 135 121 122 143 144 136 130 131 141 142 139 140:6 3 6 3 6 3 3 6 3 3 3 3 3 3 3 3 3 3 3 3,4 12 8 4 4 4 4 12 8 4 4 4> {(2, 61): 't3^-1', (2, 62): 't3^-1', (2, 52): 't3*tau2*t3', (2, 53): 't3*tau2*t3', (2, 50): 't3*tau2*t1^-1', (2, 51): 't3*tau2*t1^-1', (2, 45): 't3*tau2*t1^-1', (2, 34): 't1', (2, 35): 't1', (1, 83): 't1^-1*tau2*t3', (2, 142): 'tau1^-1*t2^-1*tau3*t1*tau2^-1*t3^-1', (2, 143): 'tau1^-1*t2^-1*tau3*t1*tau2^-1*t3^-1', (1, 65): 't3^-1*tau2^-1*t1', (2, 133): 'tau1^-1', (2, 134): 'tau1^-1', (2, 122): 't3*tau2*t1^-1', (2, 123): 't3*tau2*t1^-1', (2, 117): 't3*tau2*t1^-1', (2, 106): 'tau3^-1', (2, 107): 'tau3^-1', (2, 97): 't2^-1', (2, 98): 't2^-1'}