About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my own little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with those of my employer, nor any other organization, nor institution, of any kind.

One of Many Faceted Truncated Icosahedra

Posted on 18 September 2022 by RobertLovesPi

I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

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

Posted on 17 September 2022 by RobertLovesPi

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 Tessellation Featuring Regular Hexagons, Rhombi, and Six-Pointed Stars

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These Are My People

Posted on 10 September 2022 by RobertLovesPi

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

Posted on 5 September 2022 by RobertLovesPi

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

Posted on 31 August 2022 by RobertLovesPi

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.