The 48 faces of this faceted icosidodecahedron are:
Software called Stella 4d was used to make this, and it is available (with a free trial download available) at this website.
I made this using Stella 4d, software you can find at http://www.software3d.com/Stella.php. I also make a second version, with larger spheres and cylinders for the vertices and edges:
This polyhedron was created using Stella 4d, software which can be found here. It has pyritohedral symmetry.
Software credit: I made this using Stella 4d, available here.
The polyhedron above also appeared in the post immediately before this one, as the second of three images. However, here it is presented in “rainbow color mode.”
This is its final stellation:
Both virtual models were created with Stella 4d, software you may try for yourself at this website.
Thinking about the post immediately before this one led me to see if I could connect opposite triangular faces of a rhombicosidodecahedron to form a ten-part compound — and it worked with Stella 4d just as it had when I “previewed” it in my head.
The interesting dual of the above polyhedral compound, also a ten-part compound, I was not able to preview in my head (although that would be a nice ability to have), but creating it was easy with Stella:
It is difficult, in the dual, to tell what the ten components are. To help with this, in the next image, all but one component has been removed. This reveals the components of the dual to be rhombus-faced parallelopipeds which are quite flattened, compared to most parallelopipeds I have seen before. This polyhedron is isomorphic to the cube, just as the elongated octahedra in the first compound were each isomorphic to the Platonic octahedron. Given that the cube and octahedron are duals, this is no surprise.
Stella 4d may be tried for free, as a trial download, at this website: http://www.software3d.com/Stella.php.
The creator of Stella 4d, the program I used to make these rotating polyhedral images, is Robert Webb (and the software itself may be tried for free here). Recently, on Facebook, he displayed a paper model of this compound of fifteen cuboids, pointed out that it is a faceting of the icosidodecahedron, and I (being me) took that as a challenge to make it myself. Here is my first result, in which all fifteen cuboids have different colors.
I then realized that RW had rendered his in only five colors, so I studied his post more carefully, and made the appropriate adjustments to do the same:
If you’d like to find the Stella page on Facebook, here is a link to it.
I made this by faceting a truncated tetrahedron, giving it faces which are interpenetrating, red, equilateral triangles, as well as yellow crossed-edged hexagons. It can also be viewed as a central tetrahedron, with six more tetrahedra attached to its edges. This was made with Stella 4d, available at this website.
There is one truncated icosahedron at the center of this cluster, and each of its 32 faces is augmented with another truncated icosahedron, for a total of 33. I built this cluster using Stella 4d, software available here.
It is hard to find polyhedra which contain regular heptagons, but that simply makes the search more challenging, and therefore more fun. This polyhedron features six regular heptagons, and was created with Stella 4d, software available here.
RobertLovesPi.net 