Heptagonal tiling

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Heptagonal tiling
Heptagonal tiling.svg
Rank3
TypeRegular
SpaceHyperbolic
Notation
Bowers style acronymHeat
Coxeter diagramx7o3o (CDel node 1.pngCDel 7.pngCDel node.pngCDel 3.pngCDel node.png)
Schläfli symbol{7,3}
Elements
Faces6N Heptagons
Edges21N
Vertices14N
Vertex figureTriangle, edge length 2cos(π/7)
Measures (edge length 1)
Circumradius
Related polytopes
ArmyHeat
RegimentHeat
DualOrder-7 triangular tiling
Topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[7,3]
ConvexYes

The order-3 heptagonal tiling, or just heptagonal tiling or heat, is a regular tiling of the hyperbolic plane. 3 heptagons join at each vertex.

This tiling is the simplest tiling with three regular polygons at each vertex that neither fits in Euclidean space like the hexagonal tiling does, nor folds into spherical space like the dodecahedron (pentagons), cube (squares), or tetrahedron (triangles).

Related polytopes[edit | edit source]

o7o3o truncations
Name OBSA Schläfli symbol CD diagram Picture
Heptagonal tiling heat {7,3} x7o3o
Uniform tiling 73-t0.png
Truncated heptagonal tiling theat t{7,3} x7x3o
Uniform tiling 73-t01.png
Triheptagonal tiling thet r{7,3} o7x3o
Uniform tiling 73-t1.png
Truncated order-7 triangular tiling thetrat t{3,7} o7x3x
Uniform tiling 73-t12.png
Order-7 triangular tiling hetrat {3,7} o7o3x
Uniform tiling 73-t2.png
Small rhombitriheptagonal tiling srothet rr{7,3} x7o3x
Uniform tiling 73-t02.png
Great rhombitriheptagonal tiling grothet tr{7,3} x7x3x
Uniform tiling 73-t012.png
Snub triheptagonal tiling snathet sr{7,3} s7s3s
Uniform tiling 73-snub.png

External links[edit | edit source]