The next image was produced by rendering all the blue faces above invisible, and then changing the color-scheme to “rainbow color mode.” For both of these stellated polyhedra, the convex hull would simply be an icosidodecahedron (not shown here).
These images were both created using Stella 4d, which you can try and/or buy at www.software3d.com/Stella.php.
I’ve had some success lately finding near-misses to the Johnson solids by making face-based zonish versions of various polyhedra. These were found during that search, and are certainly not near-misses, but I still find them interesting, primarily due to their symmetry. Like the others, they were found using Stella 4d, which you can try or buy at http://www.software3d.com/Stella.php.
The top image was formed by making this modification to the icosahedron, and the one below (which you can enlarge with a click) was created by doing the same thing to an icosidodecahedron.
Both of these were created using Stella 4d, available at http://www.software3d.com/Stella.php. To enlarge the second image, simply click on it.
The two versions differ in their coloring-scheme, and, also, the pentagons and blue almost-triangles (actually irregular hexagons) are hidden in the second version, which you can make larger with a click:
Both images were created using Stella 4d, which you can try or buy at http://www.software3d.com/Stella.php.
I thought I would try to paint a migraine headache, and a few years ago, I did so, and painted this. I then fell asleep, and woke up, with, of course, a migraine.
The dodecahedron and the icosahedron are dual to each other, and can be combined to make this well-known compound.
In hyperspace, the analog to the dodecahedron is the hyperdodecahedron, also known as the 120-cell, as well as the hecatonicosachoron. Its dual is the 600-cell, or hexacosichoron, made of 600 tetrahedral cells. The image at the top is the compound of these two polychora, rotating in hyperspace.
These images were made using Stella 4d, available at http://www.software3d.com/Stella.php.
The cube and the octahedron are dual to each other, and can be combined to make this well-known compound (below; can be enlarged with a click).
In hyperspace, the analog to the cube is the tesseract, also known the 8-cell, the octachoron, and the hypercube. Its dual is the 16-cell, or hexadecachoron, made of 16 tetrahedral cells. The image at the top is the compound of these two polychora, rotating in hyperspace.
These images were made using Stella 4d, available at http://www.software3d.com/Stella.php.
Both of these were made using Stella 4d: Polyhedron Navigator. It’s available at http://www.software3d.com/Stella.php.
If you want to enlarge this second image, simply click on it.
I created this using Stella 4d, which is available (including a free trial download) at http://www.software3d.com/Stella.php. With adjustments in edge lengths to make the bond lengths correct, this would be the shape of a C180 fullerene molecule.
If the thirty-two faces of the truncated icosahedron are hidden, and only the sixty extra hexagons are visible, this polyhedron looks like this:
In “rainbow color mode,” it has an even more interesting appearance:
RobertLovesPi.net 