Projecting images on the sun, earth, and moon onto the faces of a rhombicosidodecahedron was accomplished with Stella 4d, software you may try for free at http://www.software3d.com/Stella.php.
The larger moon shown, Saturn’s largest, is Titan, recognizable by its hazy atmosphere. The smaller one, which looks more like our own moon, is Rhea.
This image was captured by the Cassini spacecraft, which has been investigating the Saturnian system now for years.
Projecting the images onto the faces of a rhombic dodecahedron was done with Stella 4d, software you may try for free at http://www.software3d.com/stella.php.
I found this here: http://www.nasa.gov/mission_pages/cassini/multimedia/gallery-indexRhea.html
If I had a “bucket list,” things like seeing this with my own eyes would be on it.
Roger Penrose is famous for many things, including the discovery of aperiodic tilings, the most familiar of which involves two types of rhombus:
I think I have made a minor discovery about this Penrose tiling, and that is that one can add regular pentagons to it, in varying levels of pentagon-density, as shown in the first image, without it losing its aperiodicity. (I created only the first image, not the second.) I have not, however, proven this, and doubt I will.
Is this conjecture provable? I think so, but I lack the ability to write such a proof myself.
Software used: see http://www.software3d.com/stella.php.
The triakis tetrahedron is the dual of the truncated tetrahedron.
Software used: see http://www.software3d.com/stella.php.
The triakis octahedron is the dual of the truncated cube.
Software used: see http://www.software3d.com/stella.php.
RobertLovesPi.net 