Tag Archives: rhombic triacontahedron

The Eighteenth Stellation of the Rhombicosidodecahedron Is an Interesting Polyhedral Compound

The 18th stellation of the icosidodecahedron, shown above, is also an interesting compound. The yellow component of this compound is the rhombic triacontahedron, and the blue-and-red component is a “stretched” form of the truncated icosahedron.  This was made using Stella … Continue reading

Posted in Mathematics | Tagged , , , , , , , | Leave a comment

Using Rhombic Triacontahedra to Build an Icosidodecahedron

These two polyhedra are the icosidodecahedron (left), and its dual, the rhombic triacontahedron (right). One nice thing about these two polyhedra is that one of them, the rhombic triacontahedron, can be used repeatedly, as a building-block, to build the other … Continue reading

Posted in Mathematics | Tagged , , , , , , | 1 Comment

A Transparent Rhombic Triacontahedron

I made this using Stella 4d: Polyhedron Navigator. You may try this software, for free, at http://www.software3d.com/Stella.php.

Posted in Mathematics | Tagged , , , , | Leave a comment

A Polyhedral Journey, Beginning With an Expansion of the Rhombic Triacontahedron

The blue figure below is the rhombic triacontahedron. It has thirty identical faces, and is one of the Catalan solids, also known as Archimedean duals. This particular Catalan solid’s dual is the icosidodecahedron. I use a program called Stella 4d … Continue reading

Posted in Mathematics | Tagged , , , , , , , , , , , | Leave a comment

One of Many Possible Facetings of the Rhombic Triacontahedron

The simplest way I can explain faceting is that it takes a familiar polyhedron’s vertices, and then connects them in unusual ways, so that you obtain different edges and faces. If you take the convex hull of a faceted polyhedron, … Continue reading

Posted in Mathematics | Tagged , , , , , , , | Leave a comment

92 Dodecahedra, Arranged as a Single Rhombic Triacontahedron

With 92 dodecahedra, if you arrange them just right, you can make a model of a rhombic triacontahedron: For purposes of comparison, here is what the rhombic triacontahedron normally looks like: Also, referring back to the first model shown, here … Continue reading

Posted in Mathematics | Tagged , , , , , | 3 Comments

The Final Stellation of the Rhombic Triacontahedron, Together with Its Dual, a Faceting of the Icosidodecahedron

Sharp-eyed, regular readers of this blog will notice that this is the same polyhedron shown in the previous post, which was described as the “final stellation of the compound of five cubes,” due to the coloring scheme used in the … Continue reading

Posted in Mathematics | Tagged , , , , , , , , , , , , | Leave a comment