Truncated pentagonal tiling

Truncated pentagonal tiling
Rank	3
Type	Uniform
Space	Hyperbolic
Notation
Bowers style acronym	Topeat
Coxeter diagram	x5x4o ()
Elements
Faces	5N squares, 4N decagons
Edges	10N+20N
Vertices	20N
Vertex figure	Isosceles triangle, edge lengths √2, √(5+√5)/2, √(5+√5)/2
Measures (edge length 1)
Circumradius	${\frac {\sqrt {-9-5{\sqrt {5}}}}{2}}\approx 2.24613i$
Related polytopes
Army	Topeat
Regiment	Topeat
Dual	Tetrakis order-5 square tiling
Abstract & topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[5,4]
Convex	Yes

The truncated pentagonal tiling or topeat is a uniform tiling of the hyperbolic plane. 2 decagons and 1 square join at each vertex. As the name suggests, it can be formed from the truncation of the pentagonal tiling.

Representations

A truncated pentagonal tiling has the following Coxeter diagrams:

• x5x4o () (main symmetry)
• x5x5x () (omnitruncated order-5 pentagonal tiling)
• x5x4s () (as alternated faceting)

External links

• Klitzing, Richard. "topeat".
• Wikipedia contributors. "Truncated order-4 pentagonal tiling".