The Compound of the Cuboctahedron and Its Dual, the Rhombic Dodecahedron

Posted on 24 October 2024 by RobertLovesPi

Created with Stella 4d, which you can try for free here.

A Cluster of Fifteen Cuboctahedra

Posted on 14 September 2023 by RobertLovesPi

There’s one cuboctahedron in the center of this cluster, with each of its fourteen faces augmented by another cuboctahedron. The image below uses coloring of each face by its number of sides, while the next one is in “rainbow color mode.”

I made these images using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

Two Different Double Cuboctahedra, and Their Duals

Posted on 11 March 2023 by RobertLovesPi

There are at least two ways to make a double cuboctahedron. One way is to join two cuboctahedra at a square face.

The dual of a single cuboctahedron is a rhombic dodecahedron. The dual of this first double cuboctahedron, however, doesn’t look like a rhombic dodecahedron at all.

Another way to make a double cuboctahedron is to join two cuboctahedra at a triangular face.

Here’s the dual of the second type of double cuboctahedron.

I created these four polyhedra using Stella 4d, a program you can download and try for free, as a trial version, at this website.

Cuboctahedron Thirteen

Posted on 22 November 2022 by RobertLovesPi

This is for fans of House MD in general, and Olivia Wilde (Dr. Remy Hadley, better known as “Thirteen”) in particular. It’s off the air now, but still available on Amazon. I made this .gif using Stella 4d, which you can try right here.

A Cuboctahedron Made of Lux Blox

Posted on 16 May 2020 by RobertLovesPi

This cuboctahedron has an edge length of two. If you’d like to compare it to a Lux model with a edge length of one, just check the post right before this one. Lux Blox are fun to build with, and are sold online at http://www.luxblox.com.

Filling Space with Cuboctahedra and Octahedra

Posted on 18 March 2020 by RobertLovesPi

To get started packing space with cuboctahedra and octahedra, I started with a single octahedron, then augmented its square faces with additional cuboctahedra.

Next, I augmented each triangular face with a blue octahedron.

Next, I augmented each square face with a cuboctahedron.

Next, I added still more cuboctahedra.

The next step was to augment the yellow triangular faces with blue octahedra.

I next added more cuboctahedra.

This process may be continued without limit. I used a program called Stella 4d to make these models, and you can try this software yourself, for free, at this website.

Octahedra and Cuboctahedra Can Fill Space Without Leaving Any Gaps

Posted on 18 October 2018 by RobertLovesPi

Augmented Cubocta

I created this image using Stella 4d, which you can try for free right here. It’s much like a tessellation, but in three dimensions instead of two.

Honeycomb Made of Cuboctahedra and Octahedra

Posted on 6 June 2017 by RobertLovesPi

Augmented Cubocta.gif

This is the three-dimensional version of what is called a tessellation in two dimensions. It fills space, and can be continued in all directions.

Software used: Stella 4d, available here.

Spectral Circles on a Cuboctahedron

Posted on 3 June 2017 by RobertLovesPi

Cubocta

I used three programs to make this: Geometer’s Sketchpad, MS-Paint, and Stella 4d. The third of these may be tried for free at http://www.software3d.com/Stella.php.

A Central Icosidodecahedron, Augmented with Twenty Cuboctahedra, and Twelve More Icosidodecahedra

Posted on 10 October 2015 by RobertLovesPi

Above and below, you will find two different coloring-schemes for this particular cluster of polyhedra. I made both of these rotating images using Stella 4d, software you can buy, or try for free, right here.