A Pinwheel of Rhombi #2

rhombic pinwheel

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A Pinwheel of Rhombi

pinwheel of rhombi

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Two Times Seven Is Fourteen

twice7is14

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Twice Nine Is Eighteen

9

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Creating a New Polyhedron from the Snub Dodecahedron

Shown below are the snub dodecahedron and its dual, the pentagonal hexecontahedron.

Seeking a way to make a “new” polyhedron (one never seen before), I augmented each face of the orange dual, above, with prisms. These prisms have a height equal to twice the average edge length of their bases.

Augmented Penta Hexeconta

Next, I used the software I use to manipulate polyhedra (Stella 4d, available here) to create the convex hull of this augmented pentagonal hexecontahedron.

starball before ttmfr expanded pentagonal hexacontahedron

Finally, I used Stella’s “try to make faces regular” function, and obtained this result, which I liked enough to stop here. There’s no way for me to know with certainty that this polyhedron has never been seen before, of course, but that didn’t stop me from having fun making it.

Unnamed starball.gif

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The Cubic Rhombicosidodecahedroid

cUBIC RHOMBICOSIDODECAHEDROID

I call the polyhedron above the cubic rhombicosidodecahedroid because it combines a cube’s six squares (shown in green) with the overall appearance of a rhombicosidodecahedron. For comparison, the latter two polyhedra are shown below.

I made these rotating images using Stella 4d: Polyhedron Navigator. This program may be tried for free at http://www.software3d.com/Stella.php.

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A Tessellation Featuring Rings of Pentagons

tessellation

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