h-net: hqc2026


Topological data

Orbifold symbol*22222
Transitivity (vertex, edge, ring)(5,6,2)
Vertex degrees{4,3,3,4,4}
2D vertex symbol {5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}{7.7.7.7}
Delaney-Dress Symbol <2026.2:12:1 3 5 7 9 11 12,2 4 5 6 8 10 12,1 2 3 6 7 8 9 10 11 12:5 7,4 3 3 4 4>
Dual net hqc1925

Derived s-nets

s-nets with faithful topology

20 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 sqc5253 Fmmm 69 orthorhombic {4,3,3,4,4} 14 (5,6)
Full image sqc5505 Fmmm 69 orthorhombic {4,4,3,3,4} 14 (5,6)
Full image sqc11207 P4/mmm 123 tetragonal {4,3,3,4,4} 28 (5,6)
Full image sqc10829 I4122 98 tetragonal {4,3,3,4,4} 28 (5,7)
Full image sqc10830 Fddd 70 orthorhombic {4,3,3,4,4} 28 (5,7)
Full image sqc10849 I4122 98 tetragonal {4,3,3,4,4} 28 (5,7)
Full image sqc10854 Fddd 70 orthorhombic {4,3,3,4,4} 28 (5,7)
Full image sqc10855 Fddd 70 orthorhombic {4,3,3,4,4} 28 (5,7)
Full image sqc10862 I4122 98 tetragonal {4,3,3,4,4} 28 (5,7)
Full image sqc11124 I4122 98 tetragonal {4,3,3,4,4} 28 (5,7)
Full image sqc11172 Fddd 70 orthorhombic {4,3,3,4,4} 28 (5,7)
Full image sqc11173 Fddd 70 orthorhombic {4,3,3,4,4} 28 (5,7)
Full image sqc11203 I4122 98 tetragonal {4,3,3,4,4} 28 (5,7)
Full image sqc827 Pmmm 47 orthorhombic {3,4,4,3,4} 7 (5,6)
Full image sqc4823 P4222 93 tetragonal {4,3,4,3,4} 14 (5,6)
Full image sqc4893 Cmma 67 orthorhombic {4,4,4,3,3} 14 (5,6)
Full image sqc4894 P4222 93 tetragonal {4,3,3,4,4} 14 (5,6)
Full image sqc5060 P4222 93 tetragonal {3,3,4,4,4} 14 (5,6)
Full image sqc5506 Cmma 67 orthorhombic {4,4,3,3,4} 14 (5,6)

s-nets with edge collapse


Derived U-tilings

10 records listed.
Image U-tiling name PGD Subgroup Transitivity (Vert,Edge,Face) Vertex Degree Vertex Symbol P net G net D net
Tiling details UQC5348 *22222a (5,6,2) {4,3,3,4,4} {5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}... No s‑net Snet sqc11124 No s‑net
Tiling details UQC5349 *22222a (5,6,2) {4,3,3,4,4} {5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}... Snet sqc10692 Snet sqc10829 Snet sqc4823
Tiling details UQC5350 *22222b (5,6,2) {4,3,3,4,4} {5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}... Snet sqc4733 Snet sqc10854 Snet sqc4893
Tiling details UQC5351 *22222b (5,6,2) {4,3,3,4,4} {5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}... Snet sqc5505 Snet sqc11173 Snet sqc827
Tiling details UQC5352 *22222b (5,6,2) {4,3,3,4,4} {5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}... Snet sqc5253 Snet sqc10855 Snet sqc827
Tiling details UQC5353 *22222a (5,6,2) {4,3,3,4,4} {5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}... No s‑net Snet sqc10849 No s‑net
Tiling details UQC5354 *22222b (5,6,2) {4,3,3,4,4} {5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}... Snet sqc827 Snet sqc11172 Snet sqc5506
Tiling details UQC5355 *22222b (5,6,2) {4,3,3,4,4} {5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}... No s‑net Snet sqc10830 No s‑net
Tiling details UQC5356 *22222a (5,6,2) {4,3,3,4,4} {5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}... Snet sqc11207 Snet sqc11203 Snet sqc5060
Tiling details UQC5357 *22222a (5,6,2) {4,3,3,4,4} {5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}... Snet sqc10693 Snet sqc10862 Snet sqc4894

Symmetry-lowered hyperbolic tilings