This paper presents the properties of the discrete analytical hyperpla
nes. They are defined analytically in the discrete domain by Diophanti
ne equations. We show that the discrete hyperplane is a generalization
of the classical digital hyperplanes. We present original properties
such as exact point localization and space thing. The main result is t
he links made between the arithmetical thickness of a hyperplane and i
ts topology. (C) 1997 Academic Press.