Two Half-Visible Catalan Solids

The Catalan Solids shown here are the dysdyakis dodecahedron (dual of the great rhombicuboctahedron) and the dysdyakis triacontahedron (dual of the great rhombicosidodecahedron). In each one, all the faces are scalene triangles, and half of them have been rendered invisible, so that you can see the inside view of faces on the far side of each polyhedron. The remaining faces are shown in “rainbow color mode.”

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

Two Different Double Cuboctahedra, and Their Duals

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.

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

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.

Two Six-Part Polyhedral Compounds

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.

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.