Seven Different Facetings of the Truncated Icosahedron

Posted on 10 June 2018 by RobertLovesPi

The polyhedron above is the truncated icosahedron, widely known as the pattern for most soccer balls. In the image below, the faces and edges have been hidden, leaving only the vertices.

To make a faceted version of this polyhedron, these vertices must be connected in novel ways, creating new edges and faces. There are many faceted versions of this polyhedron, of which seven are shown below.

I used Stella 4d to make these polyhedral images, and you’re invited to try the program for yourself at http://www.software3d.com/Stella.php.

A Faceted Truncated Icosahedron

Posted on 27 November 2017 by RobertLovesPi

Faceted truncated icosahedron

This is one of many possible facetings of the truncated icosahedron. I made it using Stella 4d, which you can try for yourself at this website: http://www.software3d.com/Stella.php.

A Truncated Icosahedron, Formed By Silver Pipes, and Gold Fastenings

Posted on 2 January 2016 by RobertLovesPi

Trunc Icosa gold and silver

I made this precious-metal version of the truncated icosahedron using Stella 4d, a program which is available here: http://www.software3d.com/Stella.php.

A Cluster of 33 Truncated Icosahedra

Posted on 13 November 2015 by RobertLovesPi

There is one truncated icosahedron at the center of this cluster, and each of its 32 faces is augmented with another truncated icosahedron, for a total of 33. I built this cluster using Stella 4d, software available here.

A Pyritohedral Coloring-Scheme for the Truncated Icosahedron

Posted on 25 October 2015 by RobertLovesPi

While the polyhedron above, informally known as the “soccer ball,” has icosidodecahedral symmetry, its coloring-scheme does not. Instead, I colored the faces in such a way that the coloring-scheme has pyritohedral symmetry — the symmetry of a standard volleyball. This rotating image was made with Stella 4d, a program you can buy, or try for free, right here: http://www.software3d.com/Stella.php.

The Compound of the Truncated Icosahedron and the Rhombic Triacontahedron

Posted on 5 June 2015 by RobertLovesPi

I put these two polyhedra together using Stella 4d: Polyhedron Navigator. If you’d like to try this program yourself, for free, this website is the one to visit: http://www.software3d.com/Stella.php.

A Truncated Icosahedron, with Hexagons Augmented By Triangular Pyramids, in a Chiral Pattern

Posted on 1 June 2015 by RobertLovesPi

I made this using Stella 4d: Polyhedron Navigator, software available here.

Two of Many Possible Facetings of the Truncated Icosahedron

Posted on 31 May 2015 by RobertLovesPi

I made these faceted polyhedra, both facetings of the truncated icosahedron, using Stella 4d, software available here.

Buckminsterfullerene Molecular Models: Three Different Versions

Posted on 17 December 2014 by RobertLovesPi

Buckminsterfullerene, a molecule made of 60 carbon atoms, and having the shape of a truncated icosahedron, is easily modeled with Stella 4d: Polyhedron Navigator (see http://www.software3d.com/Stella.php to try or buy this program). The first image shows the”ball and stick” version used by chemists who want the bonds between atoms to be visible.

The second model is intermediate between the ball-and-stick version, and the space-filling version, which follows it.

Here’s the “closely packed” space-filling version, taken to an extreme.

Which version better reflects reality depends on the certainty level you want for molecular orbitals. A sphere representing 99% certainty would be larger than one for 95% certainty.

Four Stellations of the Truncated Icosahedron

Posted on 6 August 2014 by RobertLovesPi

The truncated isocahedron has an interesting (and long) stellation series. Here are some of the stellated forms of this polyhedron which I find particularly interesting and attractive, starting with its 41st stellation.