Title: Folding Cubes

 

Abstract: It is well-known that there are 11 different connected polyominoes of size 6 that can be folded so that their squares cover the faces a cube. If we allow larger polyominoes that may cover cube faces with multiple squares, the complete classification is still unknown. In this talk, we will will describe the classification of simply connected polyominoes that fold into a cube and discuss some of the difficulties with extending the results to multiply connected polyominoes. These challenges allow for the creation of some interesting and entertaining paper puzzles, copies of which will be provided during the talk. Time permitting, we may also discuss further results on folding polycubes and the natural extension to the remaining Platonic solids.