A Cluster of Twenty Great Icosahedra, Excavated from the Faces of a Central Icosahedron, Along with Its Dual

Posted on 28 May 2015 by RobertLovesPi

These twenty great icosahedra were excavated from the faces of a central icosahedron, which is concealed in the figure’s center. These excavations exceed the limits of the central icosahedron, resulting in each great icosahedron protruding in a direction opposite that of the face from which it is excavated. In a certain sense, then, the figure above has negative volume.

To make this, I used software called Stella 4d: Polyhedron Navigator. It can be researched, bought, or tried for free here.

Also, here is the dual of the polyhedral cluster above, made with the same program.

Four Hollow Polyhedron-Variants Related to the Rhombic Triacontahedron and the Icosahedron

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Four Hollow Polyhedron-Variants Related to the Rhombic Triacontahedron and the Icosahedron

To make any of these smaller images as large as the first one, simply click on the smaller image of your choice.

These are all members of the same stellation-sequence, just like the two octahedron-variants in the last post.

I made these in just a few minutes with software, written by a friend of mine, called Stella 4d: Polyhedron Navigator. You can check it out for yourself at http://www.software3d.com/Stella.php. A free trial download is available.

The Augmented Great Dodecahedron II

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The Augmented Great Dodecahedron II

To make this, I used the polyhedron found in the last post, using software I bought at http://www.software3d.com/stella.php, to alter the coloring scheme to make each face a different color unless it is parallel to another, in which case it has the same color as all parallel faces.

Which coloring-scheme do you like best?