A Rhombicosidodecahedron-Variant Which Features Octagons

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A Rhombicidodecahedron-Variant Which Features Octagons

This polyhedron contains the twenty triangles and twelve pentagons of a rhombicosidodecahedron — but they are all smaller than those found in that solid. As a result, the thirty squares of the rhombicosidodecahedron have each become, instead, irregular octagons.

To try the software I use to generate these images, simply visit http://www.software3d.com/stella.php — where a free trial download is available.

A Big Ball of Pyramids

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A Big Ball of Pyramids

To create this, a central rhombicosidodecahedron had each of its faces augmented by pyramids, each of which uses only equilateral triangles for lateral faces.

Software credit: The program used to make this image, Stella 4d, may be tried for free at http://www.software3d.com/stella.php.

A Polyhedral Snowman

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A Polyhedral Snowman

We’re out of school today because of an ice storm, and I wanted to make a snowman. However, we got very little snow — mostly freezing rain and sleet fell — so I can’t make a traditional snowman. Also, it’s really cold outside. So, instead, I stayed inside, where it’s warm, and made a polyhedral snowman out of (from top to bottom) an icosahedron, an icosidodecahedron, and a rhombicosidodecahedron.

Software credit: see http://www.software3d.com/stella.php for a free trial download of Stella 4d, the software used to make this image.

Cluster of Sixty Rhombicosadodecahedra

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Augmented IcosaSoftware credit: see http://www.software3d.com/stella.php — free trial download available.

The Thirtieth Stellation of the Great Rhombicosidodecahedron

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The Thirtieth Stellation of the Great Rhombicosidodecahedron

Software credit: visit http://www.software3d.com/stella.php for more information on the program used to make this rotating image. A free trial download is available.

A Central Icosahedron, Augmented with Rhombicosidodecahedra On Each Face

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A Central Icosahedron, Augmented with Rhombicosidodecahedra On Each Face

Software credit: visit http://www.software3d.com/stella.php for more information on the program used to make this rotating image. A free trial download is available.

A Cube of Conjoined Rhombicosidodecahedra

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A Cube of Conjoined Rhombicosidodecahedra

To make this “cube,” I started with an octahedron, and then augmented all eight of its faces with rhombicosidodecahedra. Such polyhedral manipulations are quick and easy with Stella 4d, available at http://www.software3d.com/stella.php.

The Eighteenth Stellation of a Rhombicosidodecahedron Which Had Invisible Square Faces

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The Eighteenth Stellation of a Rhombicosidodecahedron Which Had Invisible Square Faces

Created using Stella 4d, software which is available at http://www.software3d.com/stella.php.

Sol, Terra, and Luna On a Rhombicosidodecahedron

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Sol, Terra, and Luna On a Rhombicosidodecahedron

Projecting images on the sun, earth, and moon onto the faces of a rhombicosidodecahedron was accomplished with Stella 4d, software you may try for free at http://www.software3d.com/Stella.php.

The Offspring of the Rhombicosidodecahedron and the Truncated Icosahedron

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The Offspring of the Rhombicosidodecahedron and the Truncated Icosahedron

For more on the software used to make this, please see http://www.software3d.com/stella.php.