Four, Six, Nine, and Eighteen

This mathematical illustration includes two shapes of rhombi (orange and green), isosceles trapezoids (blue), regular hexagons (yellow), regular enneagons (red), and a single regular octadecagon (violet).

Expanding the Icosidodecahedron

This is the icosidodecahedron. It’s one of the thirteen Archimedean solids. To make an expanded version of it, I first augmented each of its faces with a prism.

Next, I formed the augmented icosidodecahedron’s convex hull.

This expanded icosidodecahedron has the twelve pentagonal faces (shown in red) and twenty triangular faces (shown in blue) of the original icosidodechedron. It also has sixty rectangular faces (yellow), and sixty isosceles triangles (shown in green). That’s a total of 152 faces.

To do all of this, I used a program called Stella 4d. If you’d like to try Stella for yourself, for free, just visit this website:

A Golden Tessellation of Quadrilaterals

In this tessellation, golden rectangles are shown in yellow. The orange darts are each made of two golden gnomons, joined at a leg — while the blue rhombi are each made of two golden triangles, sharing a base.

A Rhombic Triacontahedron, Decorated with Geometric Artwork

To make this rotating .gif, I navigated to the rhombic triacontahedron in Stella 4d, and then loaded images onto its thirty faces, with the image being the one I blogged in the post right before this one. This program, Stella, has a free trial download you can get right here.

Yellowstone Bison Stops Traffic

The wildlife in Yellowstone National Park live there; the people are merely visitors. I stopped our car when I saw a bison (what some call buffalo) grazing by the side of the road; I wanted a good picture.

I certainly did not expect what happened next — the bison decided to calmly strut into traffic! He stayed there a while, too. In Yellowstone, the wildlife have the right-of-way.