It’s a complete accident that this tessellation popped up a second time here — I had forgotten about the first one. At least it has different colors!

# Tag Archives: heptagon

# A Tessellation Featuring Regular Heptagons and Triangles, Together with Equilateral Four- and Six-Pointed Stars

This started with the idea of attaching a regular heptagon to each side of an equilateral triangle. From there, it took on a life of its own.

Here’s another version, with different colors:

## Mandala Featuring Regular Heptagons and a Regular Tetradecagon, with Convex Pentagons and Isosceles Trapezoids

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## Tessellation Featuring Squares, Regular Heptagons, Equilateral Hexadecagons, and Equilateral Dodecagons

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# A Symmetrohedron Featuring Regular Heptagons, Regular Hexagons, Irregular Hexagons, and Irregular Pentagon-Pairs

Symmetrohedra are symmetric polyhedra which have regular polygons for most (but not necessarily all) of their faces. I made this particular one using *Stella 4d*, which you can try for yourself at this website. Here’s the net for this polyhedron, also.

This particular symmetrohedron features twelve faces which are regular heptagons, and eight faces which are regular hexagons (shown in yellow). The irregular faces are 24 pentagons, arranged in a dozen pairs, as well as the six green hexagons. That’s 50 faces in all. This solid has pyritohedral symmetry. The most unusual thing about this polyhedron are its 12 heptagonal faces.

# A Symmetrohedron Featuring Regular Heptagons and Hexagons, Along with Irregular Quadrilaterals and Triangles

Symmetrohedra are symmetric polyhedra which have regular polygons for most (but not necessarily all) of their faces. I made this particular one using *Stella 4d*, which you can try for yourself at this website. Here’s the net for this polyhedron, also.

This particular symmetrohedron features 12 faces which are regular heptagons, and 8 faces which are regular hexagons. The irregular faces are 12 isosceles triangles, 24 isosceles trapezoids, and 6 rectangles, for a total of 62 faces. It has pyritohedral symmetry. The most unusual thing about this polyhedron are its 12 heptagonal faces.

# A Polyhedron Featuring Sixty Heptagons, a Dozen Decagons, Thirty Octagons, and 120 Rectangles, Split Between Two Types at Sixty Each

I made this using *Stella 4d: Polyhedron Navigator*. This program is available as a free trial download at http://www.software3d.com/Stella.php.

# The Dual of a Geodesic Rhombicosidodecahedron

This polyhedron has, as faces, a dozen regular pentagons, thirty rhombi, and sixty irregular heptagons. I made this using *Stella 4d*, which is available as a free trial download at http://www.software3d.com/Stella.php.

# Sunflower Fourteen

This mathematical illustration of a sunflower is made of fourteen regular heptagons, fourteen irregular pentagons, and a single tetradecagon.