The C-320 Fullerene Polyhedron

Posted on 7 October 2017 by RobertLovesPi

The duals of the geodesic domes are polyhedra with hexagonal and pentagonal faces. This particular one has 320 vertices, with those vertices representing carbon atoms in the molecular version of this solid. Here is C₃₂₀ as a polyhedron.

The next image shows this molecule as a ball-and-stick model.

Finally, here it is as a space-filling molecular model.

All three images were created with Stella 4d: Polyhedron Navigator. This is the page to visit if you want to try Stella for yourself: http://www.software3d.com/Stella.php.

The Construction of a Zome Model of a 240-Atom Fullerene Molecule, In Seven Pictures

Posted on 5 October 2017 by RobertLovesPi

You can buy your own Zome at http://www.zometool.com.

A Faceting of the Rhombcuboctahedron

Posted on 30 September 2017 by RobertLovesPi

Faceted Rhombicubocta

This particular faceting of the rhombcuboctahedron can also be viewed as a cluster of stella octangulae. I made it using Stella 4d, polyhedron-manipulating software you can try, for yourself, at http://www.software3d.com/Stella.php.

The Truncated Stella Octangula

Posted on 25 September 2017 by RobertLovesPi

This can also be called the compound of two truncated tetrahedra.

Compound of Two truncated tetrahedra

This image was created using Stella 4d, which you can try at this website.

A Pinwheel of Rhombi #2

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rhombic pinwheel

A Pinwheel of Rhombi

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pinwheel of rhombi

Two Times Seven Is Fourteen

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twice7is14

Twice Nine Is Eighteen

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Creating a New Polyhedron from the Snub Dodecahedron

Posted on 13 September 2017 by RobertLovesPi

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.

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The Cubic Rhombicosidodecahedroid

Posted on 10 September 2017 by RobertLovesPi

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.