polyhedra | RobertLovesPi.net

Kryptonite

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Kryptonite

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

A Polyhedron with 182 Faces

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A Polyhedron with 182 Faces

The faces of this polyhedron include:

12 decagons
30 octagons
60 light-colored hexagons
20 dark-colored hexagons
60 isosceles trapezoids

It was made with Stella 4d, software you can try and/or buy at http://www.software3d.com/stella.php.

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.

A Bowtie Symmetrohedron Featuring Twelve Decagons and Twenty Equilateral Triangles

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A Bowtie Symmetrahedron Featuring Twelve Decagons and Twenty Equilateral Triangles

Created using software you can try at http://www.software3d.com/stella.php.

Later edit: I found this same polyhedron on another website, one that has been online longer than my blog, so I now for, for certain, that this was not an original discovery of my own. At http://www.cgl.uwaterloo.ca/~csk/projects/symmetrohedra/, it is named the “alternate bowtie dodecahedron” by Craig Kaplan and George W. Hart.

122-Faced Zonohedron with Equal Edge Lengths

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122-Faced, Equal-Edge-Length Zonohedron

The 122 Faces are:

12 regular decagons
20 regular hexagons
60 squares
30 equilateral (but not equiangular) octagons

Created with Stella 4d, avaialable at http://www.software3d.com/stella.php.

Lightning Bolts and Triskelions

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Lightning Bolts and Triskelions

The yellow “triskelions” here are twenty in number, and are made of three irregular pentagons each. The red “lightning bolts” between them are thirty in number, and are made with two irregular quadrilaterals each.

I stumbled across this polyhedron by accident, while playing with different polyhedral transformations possible using Stella 4d: Polyhedron Navigator. You may try this software yourself at http://www.software3d.com/Stella.php as a free trial download, before deciding whether to purchase the fully-functioning version.

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.

A Variant of Kepler’s Stella Octangula

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A Variant of Kepler's Stella Octangula

Johannes Kepler named the compound of two tetrahedra the “stella octangula,” thus helping make it one of the best-known polyhedral compounds today. This variant uses triakis tetrahedra in place of the Platonic tetrahedra in that compound. The triakis tetrahedron is a Catalan solid, and is dual to the truncated tetrahedron.

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

The Compound of Six Dodecahedra

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The Compound of Six Dodecahedra

Some polyhedral compounds are well-known, such as the compound of five cubes, while others are less famous. I had never heard of this compound before building one today (virtually, not as a physical model). However, a quick Google-search told me that I was not the first person to discover it.

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