h-net: hqc27


Topological data

Orbifold symbol*24(12)
Transitivity (vertex, edge, ring)(2,1,1)
Vertex degrees{4,12}
2D vertex symbol {4.4.4.4}{4.4.4.4.4.4.4.4.4.4.4.4}
Vertex coordination sequence [(4, 40, 76, 720, 1364, 12920, 24476, 231840), (12, 24, 228, 432, 4092, 7752, 73428)]
Delaney-Dress Symbol <27.1:2:2,1 2,1 2:4,4 12>
Dual net hqc24

Derived s-nets

s-nets with faithful topology

7 records listed.
Image s-net name Other names Space group Space group number Symmetry class Vertex degree(s) Vertices per primitive unit cell Transitivity (Vertex, Edge)
Full image sqc867 ftw Pm-3m 221 cubic {4,12} 4 (2,1)
Full image sqc908 R-3m 166 rhombohedral {4,12} 4 (2,2)
Full image sqc4938 I41/a 88 tetragonal {4,12,4} 8 (3,3)
Full image sqc4939 I-42d 122 tetragonal {4,12,4} 8 (3,3)
Full image sqc875 P-42m 111 tetragonal {4,4,12} 4 (3,2)
Full image sqc5081 scp I41/amd 141 tetragonal {4,12,4} 8 (3,2)

s-nets with edge collapse


Derived U-tilings

3 records listed.
Image U-tiling name PGD Subgroup Transitivity (Vert,Edge,Face) Vertex Degree Vertex Symbol P net G net D net
Tiling details UQC87 *2626 (4,4,1) {4,12,12,4} {4.4.4.4}{4.4.4.4.4.4.4.4.4.4.4.... Snet sqc867 Snet sqc908 Snet sqc867
Tiling details UQC3293 *2244b (3,2,2) {4,12,4} {4.4.4.4}{4.4.4.4.4.4.4.4.4.4.4.... Snet sqc246 Snet sqc4938 Snet sqc5081
Tiling details UQC3294 *2244a (3,2,2) {4,12,4} {4.4.4.4}{4.4.4.4.4.4.4.4.4.4.4.... No s‑net Snet sqc4939 Snet sqc875

Symmetry-lowered hyperbolic tilings