Monthly Archives: November 2013

The Thirty All-Seeing Eyes of the RhombicTriacontahedron

Software used: Geometer’s Sketchpad MS-Paint Stella 4d (see http://www.software3d.com/stella.php for free trial download)

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A “Bowtie” Polyhedron Featuring Regular Enneagons and Octagons

So far as I know, no one knows how many otherwise-regular convex “bowtie” polyhedra exist — that is, convex polyhedra whose only faces are regular polygons, and pairs of isosceles trapezoids in “bowtie” formation. With the aid of software called … Continue reading

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A “Bowtie” Expansion of the Truncated Dodecahedron

This polyhedron has the twelve regular decagons and twenty regular triangles of the truncated dodecahedron, but they are moved outwards from the center, and rotated slightly, creating gaps. These gaps are then filled with thirty pairs of isosceles trapezoids in … Continue reading

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An Expansion of the Truncated Icosahedron — and, Perhaps, a New Near-Miss

To create this using Stella 4d (see http://www.software3d.com/stella.php), I started with a truncated icosahedron, augmented each of its faces with a prism that was 1.5 times as tall as the base edge length, and took the convex hull of the … Continue reading

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A Variant of the Rhombic Enneacontahedron

In the rhombic enneacontahedron, which is shown below, there are thirty narrow rhombi (shown in red) which separate twelve panels of five rhombi each (shown in yellow). This polyhedron is familiar to many people: As you can see, the rhombic … Continue reading

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Decorated Rhombic Triacontahedron

This rhombic triacontahedron is decorated with the image found in the last post, which I made using Geometer’s Sketchpad and MS-Paint. Projecting it on the faces, colorizing them, and making this rotating .gif were all done using another program, Stella … Continue reading

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Op 8

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