Two Polyhedral Compounds Derived From Catalan Solids

Posted on 14 March 2023 by RobertLovesPi

The second stellation of the dysdyakis triacontahedron, seen above, is an interesting two-part polyhedral compound. The dysdyakis triacontahedron is one of the Catalan solids, and is the dual of the great rhombicosidodecahedron.

There’s also a “little brother” to this first compound — it’s the second stellation of the dysdyakis dodecahedron, which is the dual of the great rhombicuboctahedron. Like its “big brother,” it’s a two-part compound. It is shown below.

Interestingly, the components of these two compounds are “stretched” versions of two other Catalan solids: the pentagonal hexecontahedron (dual of the snub dodecahedron), and the pentagonal icositetrahedron (dual of the snub cube).

I made these virtual models using Stella 4d, which you can download and try for free at http://www.software3d.com/Stella.php.

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.