About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.

Two Mandalas (from 2013)

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

“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.

I made all of these using Stella 4d, which you can try free at http://www.software3d.com/Stella.php.

A Polyhedron With Sixty Isosceles Trapezoids and Twelve Regular Pentagons as Faces

The polyhedron above is the convex hull of the pyramid-augmented snub dodecahedron seen in the last post. The one below is its dual, and its faces are sixty kites, and twenty equilateral triangles.

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

This Just In . . . Phidippus Audax Is Officially Earth’s Cutest Spider

I found this playful little guy in Hope, Arkansas, today. Spiders are my favorite animal, and jumping spiders are my favorite group of spider species . . . but phidippus audax is my favorite jumping spider! They act a lot like miniature cats, stalking and pouncing on prey. If you ever see a black and white jumping spider, look for green iridescent chelicerae. If you see this distinctive reflective, metallic green, you’ve found yourself a p. audax. Treat them well, and they’ll eat lots of insects that would otherwise cause problems for us.

This particular spider waved at me, and remained very expressive during our entire encounter. He’d study his surroundings, utterly still, until springing into action so fast that my eyes got left behind, in a cloud of confusion. Fortunately, my wife is skilled with a camera, and was able to catch this shot.

I Went and Got My DNA Examined

Here’s one of the things I found from my recent subscription to AncestryDNA. I’m surprised, because I was told (as a child) that I was at least 1/16th Cherokee, and had a lot of French as well. I was also told I had Scotch-Irish, but no Irish proper.

“Lots of English” is about the only thing where what I was told when young, and what the DNA says, actually match.