# Mathematical Papercraft

Here are some interesting objects made from paper. Something like this is a good project for a winter break. They're fun to work on, and satisfying to complete.

## The Stellated Icosahedron

This is a stellated icosahedron made with 30 Sonobe modules in 6 colors. The colors are arranged in 6 interlocking bands, with 5 distinct colors meeting at each of 12 star-shaped faces. There are 20 triangular points in 10 antipodal pairs. These each have 3 colors, and the 10 pairs represent all possible choices of 3 colors.

You can find instructions online, but see my version for instructions about arranging the colors.

## The Stellated Dodecahedron

This is a stellated dodecahedron made with 30 of M. Mukhopadhyay's super simple isosceles triangle module. It has the same coloring arangement as the stellated icosahedron above.

## The Compound of Five Tetrahedra

This shows 5 interlocking tetrahedra arranged with their vertices forming a dodecahedron. Read more on the Wikipedia article. Click through for my construction notes.

## The Klein Quartic

A Klein quartic made with 24 heptagons (7-sided shapes). In a 4-dimensional space (CP^2), this can be done with regular heptagons, and the shape has 168 symmetries. This is the largest possible for a 3-holed donught! To push the shape down to 3 dimensions destroys most of this symmetry, and distorts the regular heptagons severely. But by doing so we can construct it out of paper!

tags: papercraft | mathart