A Wire-Frame Zonohedron Based On the Faces, Edges, and Vertices of an Icosahedron

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A Wire-Frame Zonohedron Based On the Faces, Edges, and Vertices of an Icosahedron

This is the shape of the largest zonohedron one can make with red, yellow and blue Zome (see http://www.zometool.com for more on that product for 3-d real-world polyhedron modeling). This image was made using Stella 4d, which you can find at http://www.software3d.com/stella.php.

An Icosahedron Variant Featuring Kite-Stars

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An Icosahedron Variant Featuring Kite-Stars

This variant of the icosahedron has five kites meeting at each of its twelve vertices, forming what I call the twelve “kite-stars” of this polyhedron. Also, two kites meet at the midpoint of each of the icosahedron’s thirty edges. The emplacement of the kites changes the triangular faces of the icosahedron into equilateral, but non-equiangular, hexagons.

Software credit: see http://www.software3d.com/stella.php to try or buy Stella 4d, the software I used to create this image.

An Icosahedron, Augmented, and Then Reaugmented, with Octahedra

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An Icosahedron, Augmented, and Then Reaugmented, with Octahedra

Software credit: you can try the software I used to make this 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.

Thirty-Two Truncated Icosahedra, Clustered Around a Much Larger Icosidodecahedron

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Thirty-Two Truncated Icosahedra, Clustered Around a Much Larger Icosidodecahedron

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 Rhombic Triacontahedron, Peeking Through the Faces of an Icosahedron

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A Rhombic Triacontahedron, Peeking Through the Faces of an Icosahedron

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 Concentric Dodecahedron, Icosahedron, and Rhombic Triacontahedron

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A Concentric Dodecahedron, Icosahedron, and Rhombic Triacontahedron

Created using Stella 4d, software you can find at www.software3d.com/Stella.php.

Icosahedral Cluster of Truncated Icosahedra

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Icosahedral Cluster of Truncated Icosahedra

Software credit: see http://www.software3d.com/stella.php.

Decorated Icosahedron

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Decorated Icosahedron

The image on the faces appears in the last post here, and was made using Geometer’s Sketchpad and MS-Paint. Putting this image on the faces of an icosahedron, and then creating this rotating .gif file, was accomplished using another program, Stella 4d, which you may try for free at http://www.software3d.com/stella.php.