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

s-nets with edge collapse

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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
	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	sqc11124	No s‑net
	UQC5349	*22222a	(5,6,2)	{4,3,3,4,4}	{5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}...	sqc10692	sqc10829	sqc4823
	UQC5350	*22222b	(5,6,2)	{4,3,3,4,4}	{5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}...	sqc4733	sqc10854	sqc4893
	UQC5351	*22222b	(5,6,2)	{4,3,3,4,4}	{5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}...	sqc5505	sqc11173	sqc827
	UQC5352	*22222b	(5,6,2)	{4,3,3,4,4}	{5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}...	sqc5253	sqc10855	sqc827
	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	sqc10849	No s‑net
	UQC5354	*22222b	(5,6,2)	{4,3,3,4,4}	{5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}...	sqc827	sqc11172	sqc5506
	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	sqc10830	No s‑net
	UQC5356	*22222a	(5,6,2)	{4,3,3,4,4}	{5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}...	sqc11207	sqc11203	sqc5060
	UQC5357	*22222a	(5,6,2)	{4,3,3,4,4}	{5.5.5.5}{5.7.5}{5.7.7}{7.7.7.7}...	sqc10693	sqc10862	sqc4894

Symmetry-lowered hyperbolic tilings

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