The angles in this tessellation are all either 60^{o} or 120^{o}. Each chevron is a concave hexagon which can be broken down into four equilateral triangles.

# Tag Archives: geometry

## Tessellation of Regular Hexagons, Rhombi, and Six-Pointed Stars

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## Spectral Tessellation of Equilateral Triangles and Concave Hexagons

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## Mandala 18

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# The Compound of Ten Octahedra and Its Dual, the Compound of Ten Cubes

I stumbled upon the compound above while playing with facetings, starting with the rhombic triacontahedron. Here’s the compound’s dual.

I made these rotating models using* Stella 4d*, a program you can try for free at this website.

# The Thirty Squares of a Rhombicosidodecahedron

I made this by hiding the pentagons and triangles of a rhombicosidodecahedron, then putting the remaining faces, all squares, into “rainbow color mode.” I did this using *Stella 4d: Polyhedron Navigator*, which you can try for free right here.

# A Symmetrohedron With 182 Faces

This symmetrohedron’s regular faces are twelve pentagons, thirty octagons, and twenty triangles. Its irregular faces include sixty yellow isosceles trapezoids, as well as sixty blue isosceles trapezoids. That makes 182 faces in all.

I used *Stella 4d: Polyhedron Navigator* to make this, and you can try this program yourself, as a free trial download, at http://www.software3d.com/Stella.php.