# Small rhombitrioctagonal tiling

Small rhombitrioctagonal tiling
Rank3
TypeUniform
SpaceHyperbolic
Notation
Bowers style acronymSrotoct
Coxeter diagramx8o3x ()
Elements
Faces8N triangles, 12N squares, 3N octagons
Edges24N+24N
Vertices24N
Vertex figureIsosceles trapezoid, edge legnths 1, 2, 2+2, 2
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt{-3-4\sqrt2-2\sqrt{2+\sqrt2}-2\sqrt{4+2\sqrt2}}}{2} ≈ 2.09634 i}$
Related polytopes
ArmySrotoct
RegimentSrotoct
DualDeltoidal trioctagonal tiling
Abstract & topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[8,3]
ConvexYes

The small rhombitrioctagonal tiling, or simply rhombitrioctagonal tiling, is a uniform tiling of the hyperbolic plane. 1 octagon, 1 triangle, and 2 squares join at each vertex. It can be formed by cantellation of either the octagonal tiling or its dual order-8 triangular tiling, or equivalently by rectification of the trioctagonal tiling.

## Related polytopes

o8o3o truncations
Name OBSA Schläfli symbol CD diagram Picture
Octagonal tiling ocat {8,3} x8o3o
Truncated octagonal tiling tocat t{8,3} x8x3o
Trioctagonal tiling toct r{8,3} o8x3o
Truncated order-8 triangular tiling totrat t{3,8} o8x3x
Order-8 triangular tiling otrat {3,8} o8o3x
Small rhombitrioctagonal tiling srotoct rr{8,3} x8o3x
Great rhombitrioctagonal tiling grotoct tr{8,3} x8x3x
Snub trioctagonal tiling snatoct sr{8,3} s8s3s