polyhedron | RobertLovesPi.net

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.

Compound of Five Rhombic Dodecahedra

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Compound of Five Rhombic Dodecahedra

These images were created with software you can find at http://www.software3d.com/stella.php.

If you make the faces invisible, and just view a wire-frame model, this compound looks like this:

This second image will get larger if you click on it.

Twenty Interpenetrating, Rotating Equiangular Golden Hexagons

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Alternating sides of these hexagons have lengths in the Golden Ratio. I created this as a faceting of the rhombicosidodecahedron. It also has faces which are star pentagons and triangles, but those faces are hidden in this view.

(Created using software from www.software3d.com/stella.php)

Itaumiped, My Polyhedral Asteroid City

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Fanciful Polyhedral Asteroid City

I’d want to live in one of the twisting pentagonal towers. Any time I invent an imaginary planet (or planetoid, in this case), I always name it “Itaumiped.” That’s an anagram for “I made it up.”

(To learn more about the software used to create this .gif, please visit http://www.software3d.com/stella.php.)

Icosidodecahedral Nulloid

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Icosidodecahedral Nulloid

Like all nulloids, this has zero volume. It may be seen as six intersecting, regular decagons. Some consider nulloids a subset of polyhedra; others do not.

I made this using Stella 4d, which you can find at http://www.software3d.com/stella.php.

Cuboctahedral Nulloid

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Cuboctahedral Nulloid

Like all nulloids, this has zero volume. It may be seen as four intersecting, regular hexagons. Some consider nulloids a subset of polyhedra; others do not.

I made this using Stella 4d, which you can find at http://www.software3d.com/stella.php.