Mathematics | RobertLovesPi.net

Faceted Rhombicosidodecahedron II

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Faceted Rhombicosidodecahedron

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

This polyhedron has sixty faces which are kites, and twelve which are regular pentagons. It was created, by stellating a snub dodecahedron, using software you can find at http://www.software3d.com/stella.php.

Compound of the Tesseract and Its Dual, the 16-Cell

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Compound of the Tesseract and Its Dual, the 16-Cell

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

The Tetrated Dodecahedron

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The tetrated dodecahedron is a near-miss Johnson solid. It was first discovered in 2002 by Alex Doskey. I then independently rediscovered it in 2003, and named it, not learning of Doskey’s original discovery for several years after that.

It has 28 faces: twelve regular pentagons, arranged in four panels of three pentagons each; four equilateral triangles (shown in blue); and six pairs of isosceles triangles (shown in yellow). All edges of the tetrated dodecahedron have the same length, except for the shared bases of these isosceles triangles, which are approximately 1.07 times as long as the other edges. This polyhedron has tetrahedral symmetry.

(All images here were produced using Stella 4d, which you may try for free, after downloading the trial version from this website: www.software3d.com/Stella.php.)

So Close! Ring of Sixteen Rhombic Enneacontahedra . . . Nearly.

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So Close! Ring of Sixteen Rhombic Enneacontahedra . . . Nearly.

One always hopes the ring closes, but sometimes it doesn’t. Perhaps if the rhombic enneacontahedra were oriented differently? I may have to examine this further.

Software used: see http://www.software3d.com/stella.php to try it.

Another View of the 600-Cell

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Not long ago, I posted one rotating projection of the regular polytope known as the 600-cell. Here is another.

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

A Three-Part Polyhedral Compound

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A Three-Part Polyhedral Compound

A random discovery with the program at http://www.software3d/stella.php.

Rhombicosidodecahedral Cluster

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Rhombicosidodecahedral Cluster

It’s made of rhombicosidodecahedra, and has the overall shape of a rhombicosidodecahedron as well. To make it, I started with the polyhedron in the last post, and then augmented each green pentagonal face with a rhombicosidodecahedron. I used software available here: http://www.software3d.com/stella.php.

Dodecahedral Cluster of Icosidodecahedra

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Dodecahedral Cluster of Icosidodecahedra

To obtain this polyhedron, I took the one from the last post, and then augmented the twenty outermost triangles with icosidodecahedra. The fact that this new cluster has the overall shape of a dodecahedron caught be by surprise.

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