The Tetrahemihexahedron, and Its Two Stellations

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:

On “Meeting” Lou Reed

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.

Chiral Symmetrohedron #2

In the last post here, I displayed a chiral symmetrohedron derived from the snub dodecahedron, and today I am presenting its “little brother,” which is derived from the snub cube. Both models were created using the “morph duals by truncation” function of Stella 4d: Polyhedron Navigator, a program you can download and try, for free, at this website. This newer solid contains six squares, 32 equilateral triangles, and 24 irregular pentagons, for a total of 62 faces.

A Chiral Symmetrohedron

This symmetrohedron was derived from the snub dodecahedron. It contains twelve regular pentagons and sixty irregular pentagons, as well as eighty equilateral triangles, for a total of 152 faces. I made it using Stella 4d (with the “morph duals by truncation” function), a program you can download and try, for free, at this website.

A Symmetrohedron Derived From the Great Rhombicosidodecahedron

This solid has all the faces of the great rhombicosidodecahedron, plus 120 scalene triangles. I made it using Stella 4d, which you can try for free right here.

Kepler’s “Stella Octangula,” With Ten Variants

Here’s Johonnes Kepler’s Stella Octangula — also known as the compound of two tetrahedra.

What follows are ten variants of this solid, all made using Stella 4d: Polyhedron Navigator, which you can try for free at