icosahedron | RobertLovesPi.net

Icosahedron of Mandalas

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Icosahedron of Mandalas

Made using software available at http://www.software3d.com/stella.php

Zome Icosahedron Encasing a Rhombic Enneacontahedron

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Zome Icosahedron Encasing a Rhombic Enneacontahedron

Zome is a three-dimensional ball-and-stick geometrical modeling system based on the Golden Ratio. I have a large collection, and have used it for years, both as a teaching tool, and for my own investigations. Zome is available for sale at www.zometool.com.

Here is a close-up shot, so you can better see the interior of this figure:

Dodecahedral Cluster of Icosahedra

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Dodecahedral Cluster of Icosahedra

If you are interested in the history of this polyhedral cluster, please see the previous two posts. Also, here’s another color scheme for it:

These images were produced using Stella 4d, software you can find at www.software3d.com/Stella.php.

Icosahedral Cluster of Rhombic Triacontahedra

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Rhombic triacontahedra, due to their multiple symmetries, make excellent building blocks to make shapes resembling other polyhedra. This icosahedral cluster is far from being the only such possible “cluster” polyhedron made entirely of rhombic triacontahedra.

This .gif was created with Stella 4d, software you may find here: http://www.software3d.com/Stella.php.

The Golden Icosahedron

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The Golden Icosahedron

The Platonic Icosahedron has twenty faces which are equilateral triangles. In the Golden Icosahedron, twelve of those triangles (the yellow ones) have been replaced by acute, isosceles triangles with a leg:base ratio which is the Golden Ratio.

To try the software I used to make this, just visit http://www.software3d.com/stella.php.

Stellating the Icosahedron

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I worked on this painting from 2002-2004, then, several years later, I gave it to two good friends of mine, when they married, as a wedding present. It is 16″ x 20,” and is painted with acrylics, on canvas. The painting was given its title because of its origin, as a colored (and slightly modified) version of the stellation pattern of the icosahedron.