Triskelion Based on the Golden Ratio

Incongruous Mandala

Posted on 8 February 2013 by RobertLovesPi

There’s no relationship (of which I am aware) between the Golden Ratio and regular hexagons — so of course I had to try to combine them. The results are yours to judge.

The Hyperspace Analogue of the Stella Octangula

Posted on 7 February 2013 by RobertLovesPi

The simplest polyhedron is the tetrahedron, and it is self-dual. The compound of two tetrahedra puts these duals together, and is most often called the Stella Octangula, a name Johannes Kepler gave it in the early 17th Century.

In hyperspace, or 4-space, the simplest polychoron is the pentachoron, or 5-cell. Like the tetrahedron in 3-space, it is also self-dual. Here is the compound of two of them: hyperspace’s version of the Stella Octangula.

Website to find the software used to make these images: www.software3d.com/stella.php

Rhombicosidodecahedron with Invisible Squares

Posted on 7 February 2013 by RobertLovesPi

The essential facts about this Archimedean solid: it has 62 faces total (12 pentagons, 20 triangles, and 30 squares, with the squares hidden here), 120 edges, and 60 vertices.