An Enneagonal Mandala

enneagonal mandala

I made this years ago — in 2010 — and just found it today, on Facebook. That was two years before this blog started. I like finding such “lost works,” but it doesn’t happen often these days. 

Four Polyhedra Featuring Enneagons

enneagons and octagons

enneagons and kites

octagons enneagons bowtie trapezoids

Dual of Convex hull

Enneagons are also called nonagons; they are polygons with nine sides. I used Stella 4d to make these four rotating polyhedra, and you may try this program for yourself at

A Polyhedron Made of Enneagons and Pentagons


This polyhedron has 20 enneagons and 12+60=72 pentagons (of two types) as faces. I made it using Stella 4d, which is available at

Three Convex Polyhedra with Tetrahedral Symmetry, Each Featuring Four Regular Enneagons


In addition to the four regular enneagons, the polyhedron above also has rhombi and isosceles triangles as faces. The next one, however, adds equilateral triangles, instead, to the four regular enneagons, along with trapezoids and rectangles.


Only the last of these three truly deserves to be called a symmetrohedron, in my opinion, for both its hexagons and enneagons are regular. Only the “bowtie trapezoid” pairs are irregular.

four reg enneagons and four reg hexagons and six pairs of bowtie hexagons

All three of these polyhedra were created using software called Stella 4d: Polyhedron Navigator, which I use frequently for the blog-posts here. You can try it for free at this website.

Nine (2015) / Nine (2013)

First, the newer version I just made:

nine 2015

Next, the 2013 version, which I recently found, along with a bunch of other previously-lost stuff from around then. The two are simply color-inversions of each other, according to the rules for color-inversion used by MS-Paint.

nine 2013