Four Rhombic Polyhedra, Each Made From Zome

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.

A Tessellation Featuring Regular Hexagons and Two Types of Rhombi

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).

The Rhombic Octagonoid, a Zonohedron With Ninety Faces

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 I’ve also had students make it. It is the largest zonohedron which can be built using only red and yellow Zome (available here). I thought it needed a name, so I made one up.

A Radial Tessellation Using Three Types of Rhombi

radial tessellation using three types of rhombi

The yellow rhombi have angles of 40 and 140 degrees, while the blue rhombi have angles of 80 and 100 degrees, just like in the last post here. However, that post did not include the red rhombi, which have angles of 60 and 120 degrees.