polyhedra | RobertLovesPi.net

Icosahedron of Mandalas

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Icosahedron of Mandalas

Made using software available at http://www.software3d.com/stella.php

Cluster of Great Dodecahedra

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This was created with software available at http://www.software3d.com/Stella.php.

Augmented Rhombicosidodecahedron

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Augmented Rhombicosidodecahedron

Each face of a rhombicosidodecahedron has been augmented with a pyramid, with all edges being kept the same length.

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

Faceted Rhombicosidodecahedron

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Faceted Rhombicosidodecahedron

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

Faceted Rhombic Dodecahedron

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Faceted Rhombic Dodecahedron

The faces of this polyhedron are 24 congruent isosceles triangles. It was created using software you can try at http://www.software3d.com/stella.php.

Expanded Rhombicosidodecahedron

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Expanded Rhombicosidodecahedron

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

Compound of Three Rectangular Solids

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Compound of Three Rectangular Solids

Created using software found at http://www.software3d.com/stella.php

A Pulsating Zonohedron

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A Zonohedron

This polyhedron is an example of a zonohedron — a polyhedron with faces which are all zonogons, each of which is congruent and parallel to another zonogon on the opposite side of the polyhedron.

Of course, this just raises the question, “What’s a zonogon?” It’s a special type of polygon, one with an even number of sides, and with opposite sides congruent and parallel.

The pulsating effect is just for fun — a feature which is optional in Stella 4d, the program I used to make this. I started with an icosahedron/dodecahedron compound, stellated it many times, and then zonohedrified the result. This software makes all these operations easy, and may be tried for free at http://www.software3d.com/stella.php.

Dodecahedron with Mandalas

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Dodecahedron with Mandalas

This rotating image took three different programs to create. First, I made the mandala (seen in the previous post) using Geometer’s Sketchpad. Next, I used MS-Paint to complete the colorization of it. Finally, I used Stella 4d (see http://www.software3d.com/stella.php if you’d like to try or buy it) to put this mandala on each face of a dodecahedron, and then create the rotating .gif you see here.

I find both Stella 4d and Geometer’s Sketchpad to be indispensable tools for mathematical investigations and the creation of geometrical art, and highly recommend both programs.