"The dialogue takes place... The class gets interested in a Problem: Is there a relation between the number of vertices V, the number of edges E and the number of faces F of a polyhedra—particularly of regular polyhedra—analogous to the trivial relation between the number of vertices and edges of polygons, namely, that there are as many edges as vertices: V = E? ...After much tiral and error they notice that for all regular polyhedra V - E + F = 2. Somebody guesses that this may apply for any polyhedron whatever. Others try to falsify [test] this conjecture... it holds good. The results corroborate the conjecture, and suggest that it could be proved. It is at this point—after the stages problem and conjecture—that we... offer a proof."