Four Nested Rhombic Triacontahedra, Made of Zome

Posted on 16 June 2024 by RobertLovesPi

You can get Zome for yourself (or your kids) at http://www.zometool.com.

An Icosahedron, Built With Rhombic Triacontahedra and Elongated Prisms

Posted on 30 December 2023 by RobertLovesPi

I made these two versions of the icosahedron, using rhombic triacontahedra and elongated prisms, and a program called Stella 4d. You can try this program yourself, for free, at http://www.software3d.com/Stella.php.

Clusters of Rhombic Triacontahedra

Posted on 2 October 2023 by RobertLovesPi

Here’s a rhombic triacontahedron, possibly the most well-known of the Catalan solids. It’s thirty faces are all golden rhombi (rhombi with their diagonals in the golden ratio).

Here’s what you get if you augment each face with another rhombic triacontahedron:

Coloring this cluster-polyhedron by face type has this result:

So what happens if each face of this cluster-polyhedron is augmented by another rhombic triacontahedron? This does:

Here’s another view of that, in “rainbow color mode”:

I made these virtual models with Stella 4d: Polyhedron Navigator. If you’d like to try this software for free, the website to visit is http://www.software3d.com/Stella.php.

Truncating the Rhombic Triacontahedron

Posted on 21 October 2022 by RobertLovesPi

This is the rhombic triacontahedron, one of the Catalan solids.

Now here’s the same polyhedron, but with the three-valent vertices truncated, exposing twenty triangular faces.

Here’s what it looks like with only the twelve five-valent vertices truncated.

Finally, here’s the fully truncated rhombic triacontahedron.

I created these polyhedra using Stella 4d, a program you can try for free right here.

A Zome Model of the Compound of the Icosidodecahedron and Its Dual, the Rhombic Triacontahedron

Posted on 17 September 2022 by RobertLovesPi

The polyhedral compound above contains an icosidodecahedron (blue) and a rhombic triacontahedron (red). In this compound, the icosidodecahedron’s edges are bisected, while the rhombic triacontahedron’s edges are split into segments with lengths in the square of the golden ratio (~2.618 to 1).

If you want Zome of your own, the place to buy it is http://www.zometool.com.

Two Rhombic Triacontahedra, Each Decorated with Birthday Stars

Posted on 13 January 2022 by RobertLovesPi

In yesterday’s post, I unveiled my annual birthday star for my new age, 54. Today, I’m placing that 54-pointed star on each of the thirty faces of a rhombic triacontahedron. I use a program called Stella 4d (free trial available right here) to do this, and it allows images on polyhedron-faces to either be placed inside the face, or around the face. Here’s the “inside” version:

And here is the “around each face” version:

Which one do you like better?

An Intermediate Form Between the Icosidodecahedron and the Rhombic Triacontahedron

Posted on 30 January 2021 by RobertLovesPi

This polyhedron combines the faces of an icosidodecahedron (red and blue) with the those of a rhombic triacontahedron (green). The gaps between those two sets of polygons are the yellow rectangles. I made this using the “morph duals by expansion” function of Stella 4d: Polyhedron Navigator. You can try this program for yourself, free of charge, at http://www.software3d.com/Stella.php.

A Compound of the Rhombic Triacontahedron and a Truncation of the Icosahedron

Posted on 11 July 2020 by RobertLovesPi

Stellated Dual Morph 50.0%

In the compound above, the yellow hexagons are not quite regular, which is why I’m calling the yellow-and-orange polyhedron a truncation of the icosahedron, rather than simply the truncated icosahedron. I stumbled upon it while playing with Stella 4d, which you may try for free at http://www.software3d.com/Stella.php.

A Toroidal Truncated Icosahedron

Posted on 24 April 2020 by RobertLovesPi

Augmented Rhombic Triaconta

The components of this toroid are sixty rhombic triacontahedra, as well as ninety rhombic prisms with lateral edges three times as long as their base edges. I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

Augmented Rhombic Triaconta rb

A Rhombic Triacontahedron, Covered with Tessellations

Posted on 28 March 2020 by RobertLovesPi

The tessellations of the faces of this rhombic triacontahedron first appeared in my last post here. For putting the whole thing together and creating this rotating .gif, I used a program called Stella 4d. If you want to, you can try Stella for free at this website.