Supernovae Bursting Forth From a Pentagonal Icositetrahedron

Posted on 22 November 2022 by RobertLovesPi

I made this with Stella 4d, which you can try for free here.

Cuboctahedron Thirteen

Posted on 22 November 2022 by RobertLovesPi

This is for fans of House MD in general, and Olivia Wilde (Dr. Remy Hadley, better known as “Thirteen”) in particular. It’s off the air now, but still available on Amazon. I made this .gif using Stella 4d, which you can try right here.

It’s All Been Done Before — Or Has It?

Posted on 22 November 2022 by RobertLovesPi

I’m trying extremely hard to come up with a polyhedral design no one has ever seen before. I think I might have found one — possibly even two.

To make this, I drew a point with 360 rays coming from it, using Geometer’s Sketchpad. I then took a screenshot of that, and projected it onto each face of a rhombic triacontahedron. Two versions are presented here — one where the images appear to rotate, and one where they don’t. I sincerely hope you are seeing these for the first time.

I could not have made these without Stella 4d: Polyhedron Navigator, which you can try for yourself — for free — at this website. It’s simply the best program out there for making polyhedral images.

A Symmetrohedron Which Is Also a “Near Near Miss”

Posted on 22 November 2022 by RobertLovesPi

I’ve spent a lot of time over the years looking for “near misses” to the Johnson Solids, and I’ve found two of them in all that time, starting in 2003. This isn’t one, for it has an edge length deviation of about 11%, which is too much to get overly excited about. It is, however, a symmetrohedron. The hexagons, pentagons, and yellow triangles are all regular; it’s only the blue triangles which are irregular (and isosceles). It has 122 faces in all. I think I can also say, with confidence, that it is a “near near miss.” In other words, it’s nearly a near-miss to the Johnson Solids. Confused yet? I know I am.

I made this using Stella 4d, software you can try for free at http://www.software3d.com/Stella.php.

Stella Octangula, Times Nine

Posted on 14 November 2022 by RobertLovesPi

I made this with a program called Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

Tessellation Featuring Regular Octagons, Regular Pentagons, Concave Octagons, and Concave Hexadecagons

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Tessellation Featuring Isosceles Trapezoids, Convex Pentagons, Regular Hexagons, Convex Heptagons, Equiangular Octagons, and Equiangular Hexadecagons

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A 32-faced Polyhedron Featuring 4 Regular Heptagons

Posted on 12 November 2022 by RobertLovesPi

In addition to the four regular heptagons, this polyhedron has four quadrilateral faces, plus 24 triangles. I made it using Stella 4d, which you can try for free here. The second image, below, shows the same polyhedron from a different angle.