Seven Different Facetings of the Truncated Icosahedron

Trunc Icosa.gif

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.

Trunc Icosa vertices only

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.

Faceted Trunc Icosa

Faceted Trunc Icosa 8

Faceted Trunc Icosa 7

Faceted Trunc Icosa 5.gif

Faceted Trunc Icosa 4.gif

Faceted Trunc Icosa 3

Faceted Trunc Icosa 2.gif

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.

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.
This entry was posted in Mathematics and tagged , , , , , , , , . Bookmark the permalink.

2 Responses to Seven Different Facetings of the Truncated Icosahedron

  1. Anonymous says:

    Beautiful! Might want to fix the title. Thanks for sharing these.

    Liked by 1 person

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