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.

These Are My People

For decades, I have been told that one of my great-grandmothers was half-Cherokee, making me at least 1/16th Native American. Recently, though, I sent a DNA sample to AncestryDNA, and these are the results — no Native Americans of any kind. I was also told that I have no Irish ancestors, and that’s not supported by the data, either. Here are the numbers that go with the map above.

The results do support a less precise estimate of my ethnicity: I’m an American mutt. No surprise there.

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.