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.