The yellow figure is a rhombic dodecahedron, and the red pieces form six rhombi which intersect the faces of the yellow figure. There are also hypershort red struts connecting the red rhombi to each other. It’s not exactly a polyhedron, but I had fun making it. I built it using Zome, which you can buy for yourself at http://www.zometool.com.
The polyhedron above is called the rhombic triacontahedron, one of the Catalan solids. Its thirty faces are each golden rhombi — rhombi with diagonals in the golden ratio.
This yellow polyhedron is called the rhombic enneacontahedron. It has ninety faces — sixty wide rhombi, and thirty narrow rhombi.
This third polyhedron is called the rhombic hexecontahedron, and its faces are sixty golden rhombi. It is the 26th stellation of the rhombic triacontahedron. It can also be viewed as an assemblage of twenty golden parallelopipeds, each meeting at the exact center of the polyhedron. A single golden parallelopiped is shown below, and it resembles a cube that has had too much to drink, causing it to lean over.
These four rhombic polyhedra were all constructed from Zome. If you’d like to have some Zome of your own, the website to visit is http://www.zometool.com.
This tessellation is made of blue regular hexagons, as well as rhombi containing 40 and 140 degree angles (red), and rhombi containing 80 and 100 degree angles (yellow).
Is there anything more relaxing than constructing a tessellation?
To make this zonohedron with Stella 4d (available as a free trial download here), start with a dodecahedron, and then perform a zonohedrification based on both faces and vertices. It is similar to the rhombic enneacontahedron, with thirty equilateral octagons replacing the thirty narrow rhombic faces of that polyhedron.
I’ve run into this polyhedron from time to time, and have also had students make it. It is the largest zonohedron which can be built using only red and yellow Zome (available here) of a single strut-length (short, medium, or long). I thought it needed a name, so I made one up.