Spinning Dipyramids

Posted on 19 June 2022 by RobertLovesPi

I made these videos using my cell phone and a magnetic ball-and-stick polyhedron building system which my wife bought for me. It’s the sticks that have magnets in them, not the steel balls. First, a triangular dipyramid (n = 3). This is the simplest of the dipyramids.

Next, a square dipyramid, also known as an octahedron (n = 4).

Next, for n = 5, the pentagonal dipyramid.

If you limit yourself to dipyramids that have equilateral triangles for faces, that’s the complete set. Here’s what happens when you try n = 6 — the dipyramid has zero height, and collapses into a pair of isosceles trapezoids when lifted.

To get this to work, you’d need to use isosceles triangles, not equilateral ones. The same is true for n = 7 and greater numbers.

The Compound of the Platonic Tetrahedron and the Triakis Tetrahedron

Posted on 17 June 2022 by RobertLovesPi

I made this compound using Stella 4d, which you can try for free at this website.

A Faceting of the Great Rhombicosidodecahedron

Posted on 16 June 2022 by RobertLovesPi

I made this from the Archimedean Great Rhombicosidodecahedron, using a program called Stella 4d. If you’d like to try Stella for yourself, you can do so, for free, at this website: http://www.software3.com/Stella.php.

A Polyhedron Featuring Twelve Triacontagonal Faces

Posted on 15 June 2022 by RobertLovesPi

This polyhedron has 272 faces in all. I made it using Stella 4d, a program you can try for free at this website.

A 362-Faced Polyhedron

Posted on 13 June 2022 by RobertLovesPi

This solid has, as faces, 12 regular pentagons, 20 regular hexagons, and 60 isosceles triangles, along with a bunch of quadrilaterals of various types. I made it using Stella 4d, which you can try for free at this website.

Truncated Icosahedron Variant

Posted on 12 June 2022 by RobertLovesPi

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

Two Mandalas (from 2013)

Posted on 9 June 2022 by RobertLovesPi

I found these on Facebook, and could find no evidence that I’d ever blogged them here — so here they are. The first one is based on the number nine, while the second is based on fifteen.

Playing with One of Stella’s “Morph Duals” Functions

Posted on 8 June 2022 by RobertLovesPi

“Morph Duals By Tilting To Duals” is a Stella 4d feature that I haven’t used much. Here’s what happens if you apply it to an icosahedron, at the 50% morphing level: you get the compound of the icosahedron and its dual, the dodecahedron,

If you apply this same operation a second time, here’s what you get.

This appears to be a three-part compound, with two familiar components: the icosahedron (red) and the dodecahedron (orange). Remove those two components, and you get this:

Since this reminds me of an icosidodecahedron, I colored its faces to better suit that identity.

Little peeks at the edges of the solid above made me suspicious, so I hid these purple and green faces, to see the inner structure. Here’s the result.