Two Different Double Cuboctahedra, and Their Duals

Posted on 11 March 2023 by RobertLovesPi

There are at least two ways to make a double cuboctahedron. One way is to join two cuboctahedra at a square face.

The dual of a single cuboctahedron is a rhombic dodecahedron. The dual of this first double cuboctahedron, however, doesn’t look like a rhombic dodecahedron at all.

Another way to make a double cuboctahedron is to join two cuboctahedra at a triangular face.

Here’s the dual of the second type of double cuboctahedron.

I created these four polyhedra using Stella 4d, a program you can download and try for free, as a trial version, at this website.

The Latest Episode (With Bandit the Kitten and The Flaming Lips)

Posted on 9 March 2023 by RobertLovesPi

So we’re watching the latest episode of Star Trek: Picard tonight, as we do every Thursday night, when Bandit the Kitten decides to tear a gash in my leg with his incredibly sharp claws.

I waited until the show was over before pouring rubbing alcohol on it, which, of course, stung quite sharply,

In that moment of stinging, I realized that there’s a song for this occasion. It’s by The Flaming Lips.

My favorite lines in this song, “The Gash,” form a question: “Will the fight for our sanity / Be the fight of our lives?” With this kitten here in our apartment, it just might be exactly that.

An Octahedron “Hugging” a Rhombic Dodecahedron

Posted on 9 March 2023 by RobertLovesPi

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

Three Different Compounds of the Octahedron and the First Stellation of the Rhombic Dodecahedron

Posted on 8 March 2023 by RobertLovesPi

These compounds differ in the relative sizes of their components. I made all three using Stella 4d, which you can try for free right here.

Three Two-Part Compounds Similar to Kepler’s “Stella Octangula”

Posted on 7 March 2023 by RobertLovesPi

I made these using Stella 4d: Polyhedron Navigator. You can give this software a try, right here, for free.

Two Six-Part Polyhedral Compounds

Posted on 5 March 2023 by RobertLovesPi

I stumbled across this compound the other day, while playing around with Stella 4d: Polyhedron Navigator (available here).

At first, I thought this was a compound of six tetrahedra, but careful examination reveals that the tetrahedra are missing parts along the middle of some of their edges. I looked up the canonical compound of six tetrahedra in Stella‘s library, and here it is. As you can see, it’s quite similar — but it does have those “missing” pieces added.

A Four-Part Polyhedral Compound

Posted on 26 February 2023 by RobertLovesPi

I stumbled across this while playing around with my favorite polyhedron-manipulation tool, Stella 4d. You can try this program for free at http://www.software3d.com/Stella.php.

The Tetrahemihexahedron, and Its Two Stellations

Posted on 26 February 2023 by RobertLovesPi

The tetrahemihexahedron is one of the uniform polyhedra. Its faces are four equilateral triangles, as well as three squares. The squares are shown in yellow in the model above, and pass through the center of the polyhedron. It has tetrahedral symmetry, and seven faces in total. I know of no other polyhedra which have seven faces and any form of polyhedral symmetry.

If you stellate this polyhedron once, you get a tetrahedron.

The tetrahemihexahedron only has two stellations, and I really like the second one, shown below.

I made these models using Stella 4d: Polyhedron Navigator, which you can try for free at this website: http://www.software3d.com/Stella.php.

On “Meeting” Lou Reed

Posted on 25 February 2023 by RobertLovesPi

So I just dreamed that Lou Reed was in our house, resting on the couch, having come to Arkansas to make preparations to play a concert in Fayetteville, the city where I was born. I went to the couch, saw Lou, and softly squealed, “Lou Reed!”

He woke up a bit, then grumbled, “I’m sleeping, man,” and so I turned down the TV, pulled down windowshades, and tiptoed out of the room.

I then woke up (in a nested dream, but I didn’t know that yet), and said, “Aw man, Lou Reed is dead!” I went and checked the couch, found the pillow and blanket Lou had been using in my dream, but the couch was otherwise empty. I then woke up for real, and wrote down what had just happpened. There was nothing left to do except listen to Lou’s music, which I’m doing now.