The rhombic enneacontahedron has 90 faces; 30 are narrow rhombi (hidden here), and 60 are wider rhombi (decorated with the op art piece from two posts ago).
Software credit: see the polyhedral software I used at http://www.software3d.com/stella.php — free trial download available.
The images on the faces are colorized versions of my last post here. This transfer was accomplished using software you can find at http://www.software3d.com/stella.php.
One of many photographs of Saturn provided by the Cassini spacecraft, and then projected onto the faces of a rhombic triacontahedron with the software available at http://www.software3d.com/stella.php.
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.
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.
RobertLovesPi.net 