Tessellation of Squares and Equilateral Hexagons

Tessellation of Concave, Equilateral Octagons

Posted on 3 October 2021 by RobertLovesPi

Someone once told me that you can’t tile a plane with octagons. I enjoy proving them wrong.

Another Tessellation of Chevrons

Tessellation of Chevrons

Posted on 2 October 2021 by RobertLovesPi

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.

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

Spectral Tessellation of Equilateral Triangles and Concave Hexagons

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

Posted on 25 September 2021 by RobertLovesPi

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

Posted on 22 September 2021 by RobertLovesPi

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

Posted on 19 September 2021 by RobertLovesPi

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.