Scott Kim - Motley Dissections - G4G13 April 2018

This talk discusses motley dissections — polygons cut into polygons and polyhedra cut into polyhedra such that no two pieces every completely share an edge or a face. The most famous motley dissection is the squared square. My contribution extends this to triangled triangles, pentagoned pentagons, boxed boxes, tetrahedraed tetrahedra, and octahedraed octahedra. I show many motley dissections in 2 and 3 dimensions, show how motley dissections are related to polyhedra in a manner similar to polyhedral duality, and in particular, show how the boxed box (a motley dissection of a rectangular solid into rectangular solids) is isomorphic to the 24-cell, one of the regular polyhedra in 4-space.