About RobertLovesPi

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

The Google Calendar (updated for 21 AG)

This is the Google calendar, which I invented in 14 AG. I was born in 30 BG, and it is now 21 AG. The calendar used most often in the West has several serious flaws — the lack of a year zero is but one of them. On this calendar, Google Year Zero is the year Google first went on-line (1998 CE, on the Western calendar). Each new year on the Google calendar begins on January 1st, as billions of people are already used to. This calendar is offered to all, as a secular replacement for the multiple, culture-specific calendars we are using now.

The Golden Rhombus, the Rhombic Triacontahedron, and the Rhombic Hexecontahedron

There’s a special rhombus which is called the “golden rhombus,” because its diagonals are in the golden ratio. To construct it with compass and straight edge, you first construct a golden rectangle (shown with blue edges and a yellow interior), and then connect the midpoints of its sides to form a rhombus (with edges shown in red).

Several polyhedra can be made which use golden rhombi as their faces. The most well-known of these polyhedra is the rhombic triacontahedron, which has 30 such faces. It is the dual of the icosidodecahedron.

If the rhombic triacontahedron is stellated 26 times, the result is the (non-convex) rhombic hexecontahedron. It has 60 golden rhombi as faces.

Both of these polyhedra can be constructed with Zometools (available at http://www.zometool.com). With white Zomeballs and red Zomestruts, these polyhedra look a lot like this:

The flat image at the top of this post was created using Geometer’s Sketchpad and MS-Paint. The four rotating polyhedral images were created using Stella 4d: Polyhedron Navigator, which you can purchase, or try for free, at http://www.software3d.com/Stella.php.

The Third Stellation of the Pentagonal Icositetrahedron Is a Compound of Two Irregular Dodecahedra

Here’s the pentagonal icositetrahedron. It is the dual of the snub cube.

And here is its third stellation. As you can see, it’s a compound of two irregular dodecahedra.

I made these images using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.

A Rhombic Triacontahedron, Constructed From Other Polyhedra

The components of this toroidal polyhedron are 32 rhombicosidodecahedra, 120 pentagonal prisms, and 60 dodecahedra. I assembled it using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php. Three different coloring-schemes are shown here.