# ICS 269, Spring 2001: Theory Seminar

## 20 April 2001:

Triangles and Squares

David Eppstein

Slides for this talk can be found at
http://www.ics.uci.edu/~eppstein/junkyard/escher4d.pdf

Which unit-side-length convex polygons can be formed by packing together
unit squares and unit equilateral triangles? For instance you can pack
six triangles around a common vertex to form a regular hexagon. It turns
out that there is a pretty set of 11 solutions. We describe connections
from this puzzle to the combinatorics of 3- and 4-dimensional polyhedra,
using illustrations from the works of M. C. Escher.