After using Google to find the image of this galaxy, I used software called Stella 4d (available at http://www.software3d.com/Stella.php) to project it onto the twelve pentagonal faces of an icosidodecahedron, and then hid the triangular faces, as well as the vertices and edges — and then set the galaxies to rotate on the faces, as well as around the axis of the polyhedron.
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.
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’ve done quite a bit on this blog involving modifiying polyhedra via augmentation, in which polyhedra are attached to faces of another polyhedra. This was made using the opposite process, excavation, where parts of a given polyhedron are removed. First, a pentagonal pyramid was excavated from each pentagonal face of the icosidodecahedron. Next, octahedra were excavated from each triangular face. Finally, the bottom face of each of these octahedra was hidden, making it possible to see all the way through this solid. I constructed this with Stella 4d, software you can try or buy at www.software3d.com/Stella.php.
Here’s the same polyhedron again, but with a different color-scheme.
This “quilt pattern” is based on the icosidodecahedron. I made it using Stella 4d, software you may try or buy at http://www.software3d.com/Stella.php.
I made this, using Stella 4d, by augmenting the thirty square faces of a great rhombicosidodecahedron with additional great rhombicosidodecahedra. The result has one of these polyhedra located in each position which corresponds to a vertex of an icosidodecahedron.
You can give this program a try yourself, for free, at http://www.software3d.com/stella.php.
We’re out of school today because of an ice storm, and I wanted to make a snowman. However, we got very little snow — mostly freezing rain and sleet fell — so I can’t make a traditional snowman. Also, it’s really cold outside. So, instead, I stayed inside, where it’s warm, and made a polyhedral snowman out of (from top to bottom) an icosahedron, an icosidodecahedron, and a rhombicosidodecahedron.
Software credit: see http://www.software3d.com/stella.php for a free trial download of Stella 4d, the software used to make this image.
Software credit: see http://www.software3d.com/stella.php — free trial download available.
Software credit: visit http://www.software3d.com/stella.php for more information on the program used to make this rotating image. A free trial download is available.
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