  To represent positive integers by regular patterns on a plane or in
three-dimensional space may be traced back to the Pythagoreans. The aim of the
present article is to explore the possibility of extending the representation
framework for integers to spaces with more than three dimensions. Thus, taking
up a definition of polygonal numbers given by Diophantus and by Nicomachus, and
generalizing the Pythagorean concept of gnomon, one is led through quite
elementary means to a single, unified definition of multidimensional number
formations henceforth called hypersolids.
