Amazing polyhedra.

Introduction

Think about a solid uniform polyhedron. How many faces are stable? A face is stable if it does not tip over when we place the object on a table.

An appeal to the impossibility of perpetual motion should convince you that at least one face is always stable. But, is there always more than one stable face? If there is only one stable face, then this implies that no matter how the object is placed on a table it always rolls around onto its only stable face!