  We consider products of two Cantor sets, and obtain the optimal estimates in
terms of their thickness that guarantee that their product is an interval. This
problem is motivated by the fact that the spectrum of the Labyrinth model,
which is a two dimensional quasicrystal model, is given by a product of two
Cantor sets. We also discuss the connection with the question on the structure
of intersections of two Cantor sets, which was considered by many authors
previously.
