 This becomes apparent early on in the dialogue, when the Popperian Gamma protests at the Teacher’s insouciance with respect to refutation, a counterexample to Euler’s thesis (and therefore to Cauchy’s proof) that, for all regular polyhedra, the number of vertices, minus the number of edges, plus the number of faces equals two. The counterexample is a solid bounded by a pair of nested cubes, one of which is inside, but does not touch the other: