Two Zome Compounds: Five Cubes, and Five Rhombic Dodecahedra

The blue figure in the center of this model is the compound of five cubes. If you take a cube, and build pyramids of just the right height on each of that cube’s faces, those pyramids form a rhombic dodecahedron, as seen below.

In the model at the top of this post, yellow rhombic dodecahedra have been built around each cube in the compound of five cubes. The yellow figure in the top is, therefore, the compound of five rhombic dodecahedra.

I made these models out of Zome. If you’d like to try Zome for yourself, the place to go to buy it is http://www.zometool.com.

A Zome Model of the Compound of the Icosidodecahedron and Its Dual, the Rhombic Triacontahedron

The polyhedral compound above contains an icosidodecahedron (blue) and a rhombic triacontahedron (red). In this compound, the icosidodecahedron’s edges are bisected, while the rhombic triacontahedron’s edges are split into segments with lengths in the square of the golden ratio (~2.618 to 1).

If you want Zome of your own, the place to buy it is http://www.zometool.com.

A Question About Algebra II

This happened over twenty years ago, and it still cracks me up. I’m not going to name the student, but I did provide a clue by using the appropriate school colors.

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.