The Twelve Five-Valent Vertices of a Rhombic Triacontahedron, Peeking Through Each Face of a Dodecahedron

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The Five-Valent Vertices of a Rhombic Triacontahedron, Peeking Through Each Face of a Dodecahedron

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

Cluster of 120 Dodecahedra

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Cluster of 120 Dodecahedra

Software credit: see http://www.software3d.com/Stella.php — free trial download available.

Cluster of Sixty Icosidodecahedra

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Cluster of Sixty Icosidodecahedra

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

Cluster of Sixty Rhombicosadodecahedra

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

The 43rd Stellation of the Snub Dodecahedron

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The 43rd Stellation of the Snub Dodecahedron

It can sometimes be difficult to distinguish between kites and rhombi. In this case, the edges between rhombi which meet five at a vertex are slightly shorter than the other types of edges here, making the yellow faces here, of which there are sixty, kites. The blue equilateral triangles are twenty in number.

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.

Zonohedron Featuring 870 Rhombic Faces of 15 Types

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Zonohedron Featuring 870 Rhombic Faces of 15 Types

 

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.

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 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.

The Convex Hull of the Polyhedral Cluster Found in the Previous Post

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The Convex Hull of the Polyhedral Cluster Found in the Previous Post

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.

Rhombic Triacontahedron Featuring Octadecagonal Designs On Its Faces

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Rhombic Triacontahedron Featuring Octadecagonal Designs On Its Faces

The octagonal design on each face appears in the last post here, and was made using both Geometer’s Sketchpad and MS-Paint. After cropping this image, I projected it onto the faces of this polyhedron, the rhombic triacontahedron, using Stella 4d, a program you can try for yourself at http://www.software3d.com/php.