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.
I used three programs to make this: Stella 4d, Geometer’s Sketchpad, and MS-Paint. You can try Stella for free at http://www.software3d.com/Stella.php.
The 18th stellation of the rhombicosidodecahedron, 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 4d, which you can try for free right here.
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 one, the icosidodecahedron. To get this started, I first constructed one edge of the icosidodecahedron, simply by lining up four rhombic triacontahedra.
Three of these lines of rhombic triacontahedra make one of the icosidodecahedron’s triangular faces.
Next, a pentagon is attached to this triangle.
Next, the pentagonal ring is surrounded by triangles.
More triangles and pentagons bring this process to the half-way point. If we were building a pentagonal rotunda (one of the Johnson solids), this would be the finished product.
Adding the other half completes the icosidodecahedron.
All of these images were created using Stella 4d: Polyhedron Navigator. You may try this program yourself, for free, at http://www.software3d.com/Stella.php. The last thing I did with Stella, for this post, was to put the finished model into rainbow color mode.
I made this using Stella 4d: Polyhedron Navigator. You may try this software, for free, at http://www.software3d.com/Stella.php.