h-net: hqc542

Topological data

Orbifold symbol	*22222
Transitivity (vertex, edge, ring)	(3,3,2)
Vertex degrees	{4,6,4}
2D vertex symbol	{5.5.5.5}{5.4.5.5.4.5}{5.4.5.4}
Delaney-Dress Symbol	<542.2:7:1 3 5 7,2 4 5 6 7,1 2 3 6 7:5 4,4 6 4>
Dual net	hqc363

Derived s-nets

s-nets with faithful topology

23 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)
	sqc1310		Fmmm	69	orthorhombic	{6,4,4}	6	(3,3)
	sqc1335		Fmmm	69	orthorhombic	{4,6,4}	6	(3,3)
	sqc6800		P4/mmm	123	tetragonal	{4,6,4}	12	(3,3)
	sqc6483		I4122	98	tetragonal	{4,6,4}	12	(3,4)
	sqc6491		I4122	98	tetragonal	{4,6,4}	12	(3,4)
	sqc6492		I4122	98	tetragonal	{4,6,4}	12	(3,4)
	sqc6607		Fddd	70	orthorhombic	{4,6,4}	12	(3,4)
	sqc6629		I4122	98	tetragonal	{4,6,4}	12	(3,4)
	sqc6643		Fddd	70	orthorhombic	{4,6,4}	12	(3,4)
	sqc6648		Fddd	70	orthorhombic	{4,6,4}	12	(3,4)
	sqc6793		Fddd	70	orthorhombic	{4,6,4}	12	(3,4)
	sqc6794		Fddd	70	orthorhombic	{4,6,4}	12	(3,4)
	sqc6799		I4122	98	tetragonal	{4,6,4}	12	(3,4)
	sqc72		Pmmm	47	orthorhombic	{4,4,6}	3	(3,3)
	sqc1256		Cmma	67	orthorhombic	{6,4,4}	6	(3,3)
	sqc1305		P42/mcm	132	tetragonal	{6,4,4}	6	(3,3)
	sqc1319		P4222	93	tetragonal	{6,4,4}	6	(3,3)
	sqc1320		P4222	93	tetragonal	{4,6,4}	6	(3,3)
	sqc1324		P42/mmc	131	tetragonal	{4,6,4}	6	(3,3)
	sqc1336		Cmma	67	orthorhombic	{4,6,4}	6	(3,3)
	sqc1357		Cmma	67	orthorhombic	{4,6,4}	6	(3,3)
	sqc1398		P4222	93	tetragonal	{4,6,4}	6	(3,3)

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
	UQC3447	*22222a	(3,3,2)	{4,6,4}	{5.5.5.5}{5.4.5.5.4.5}{5.4.5.4}	No s‑net	sqc6491	sqc1305
	UQC3448	*22222a	(3,3,2)	{4,6,4}	{5.5.5.5}{5.4.5.5.4.5}{5.4.5.4}	sqc5793	sqc6483	sqc1319
	UQC3449	*22222a	(3,3,2)	{4,6,4}	{5.5.5.5}{5.4.5.5.4.5}{5.4.5.4}	sqc6800	sqc6799	sqc1324
	UQC3450	*22222a	(3,3,2)	{4,6,4}	{5.5.5.5}{5.4.5.5.4.5}{5.4.5.4}	No s‑net	sqc6629	sqc1320
	UQC3451	*22222b	(3,3,2)	{4,6,4}	{5.5.5.5}{5.4.5.5.4.5}{5.4.5.4}	sqc1115	sqc6643	sqc1256
	UQC3452	*22222a	(3,3,2)	{4,6,4}	{5.5.5.5}{5.4.5.5.4.5}{5.4.5.4}	sqc5794	sqc6492	sqc1398
	UQC3453	*22222b	(3,3,2)	{4,6,4}	{5.5.5.5}{5.4.5.5.4.5}{5.4.5.4}	sqc1310	sqc6794	sqc72
	UQC3454	*22222b	(3,3,2)	{4,6,4}	{5.5.5.5}{5.4.5.5.4.5}{5.4.5.4}	sqc1335	sqc6648	sqc72
	UQC3455	*22222b	(3,3,2)	{4,6,4}	{5.5.5.5}{5.4.5.5.4.5}{5.4.5.4}	No s‑net	sqc6607	sqc1357
	UQC3456	*22222b	(3,3,2)	{4,6,4}	{5.5.5.5}{5.4.5.5.4.5}{5.4.5.4}	sqc72	sqc6793	sqc1336

Symmetry-lowered hyperbolic tilings

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