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.
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).
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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?
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.
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.
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.
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.
To make this rotating .gif, I navigated to the rhombic triacontahedron in Stella 4d, and then loaded images onto its thirty faces, with the image being the one I blogged in the post right before this one. This program, Stella, has a free trial download you can get right here.
The components of this toroidal polyhedron are 32 rhombicosidodecahedra, 120 pentagonal prisms, and 60 dodecahedra. I assembled it using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php. Three different coloring-schemes are shown here.
Created with Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
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