Tetrapentagonal tiling

Tetrapentagonal tiling
Rank	3
Type	Uniform
Space	Hyperbolic
Notation
Bowers style acronym	Tepet
Coxeter diagram	o5x4o ()
Elements
Faces	5N squares, 4N pentagons
Edges	20N
Vertices	10N
Vertex figure	Rectangle, edge lengths √2 and (1+√5)/2
Measures (edge length 1)
Circumradius
Related polytopes
Army	Tepet
Regiment	Tepet
Dual	5-4 rhombille tiling
Abstract & topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[5,4]
Convex	Yes

The tetrapentagonal tiling or tepet is a uniform tiling of the hyperbolic plane. 2 pentagons and 2 squares join at each vertex. It can be formed from the rectification of the pentagonal tiling or its dual order-5 square tiling.

Representations[edit | edit source]

The tetrapentagonal tiling has the following Coxeter diagrams:

v t e truncations
Name	OBSA	Schläfli symbol	CD diagram	Image
Pentagonal tiling	peat	${5,4}$
Tetrapentagonal tiling	tepet	r ${5,4}$
Order-5 square tiling	pesquat	${4,5}$
Truncated pentagonal tiling	topeat	t ${5,4}$
Small rhombitetrapentagonal tiling	srotepet	rr ${5,4}$
Truncated order-5 square tiling	topesquat	t ${4,5}$
Great rhombitetrapentagonal tiling	grotepet	tr ${5,4}$
Snub tetrapentagonal tiling	stepet	sr ${5,4}$

v t e truncations
Name	OBSA	Schläfli symbol	CD diagram	Image
Order-5 pentagonal tiling	pepat	${5,5}$
Pentapentagonal tiling = Pentagonal tiling	peat	r ${5,5}$
Order-5 pentagonal tiling	pepat	${5,5}$
Truncated order-5 pentagonal tiling	topepat	t ${5,5}$
Small rhombipentapentagonal tiling = Tetrapentagonal tiling	tepet	rr ${5,5}$
Truncated order-5 pentagonal tiling	topepat	t ${5,5}$
Great rhombipentapentagonal tiling = Truncated pentagonal tiling	topeat	tr ${5,5}$
Snub pentapentagonal tiling	spepat	sr ${5,5}$