Small rhombitrihexagonal tiling

Small rhombitrihexagonal tiling
Rank	3
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Srothat
Coxeter diagram	x6o3x ()
Elements
Faces	2N triangles, 3N squares, N hexagons
Edges	6N+6n
Vertices	6N
Vertex figure	Isosceles trapezoid, edge lengths 1, √2, √3, √2
Measures (edge length 1)
Vertex density	$2(2\sqrt3-3) \approx 0.92820$
Related polytopes
Army	Srothat
Regiment	Srothat
Dual	Deltoidal trihexagonal tiling
Conjugate	Quasirhombitrihexagonal tiling
Abstract & topological properties
Flag count	48N
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	V3
Convex	Yes
Nature	Tame

The small rhombitrihexagonal tiling, or srothat, also called simply the rhombitrihexagonal tiling, is one of the eleven convex uniform tilings of the Euclidean plane. 1 triangle, 1 hexagon, and 2 squares join at each vertex of this tiling. It can be formed by expanding the faces of either the triangular tiling or its dual hexagonal tiling outward..

Representations

A small rhombitrihexagonal tiling has the following Coxeter diagrams:

• x6o3x () (full symmetry)
• x6s3s () (as edge-snub triangular tiling)

Related tilings

The small rhombitrihexagonal tiling is the colonel of a three-member regiment that also includes the small hexatrihexagonal tiling and the small rhombihexagonal tiling.

o6o3o truncations

Name	OBSA	Schläfli symbol	CD diagram	Picture
Hexagonal tiling	hexat	{6,3}	x6o3o
Truncated hexagonal tiling	toxat	t{6,3}	x6x3o
Trihexagonal tiling	that	r{6,3}	o6x3o
Truncated triangular tiling = Hexagonal tiling	hexat	t{3,6}	o6x3x
Triangular tiling	trat	{3,6}	o6o3x
Small rhombitrihexagonal tiling	srothat	rr{6,3}	x6o3x
Great rhombitrihexagonal tiling	grothat	tr{6,3}	x6x3x
Snub trihexagonal tiling	snathat	sr{6,3}	s6s3s

External links

• Klitzing, Richard. "srothat".

• McNeill, Jim. "Star Tesselations Type 1".

• Wikipedia Contributors. "Rhombitrihexagonal tiling".