  We consider a four-dimensional space-time supplemented by two discrete points
assigned to a $Z_2$ algebraic structure and develop the formalism of
noncommutative geometry. By setting up a generalised vielbein, we study the
metric structure. Metric compatible torsion free connection defines a unique
finite field content in the model and leads to a discretized version of
Kaluza-Klein theory. We study some special cases of this model that illustrate
the rich and complex structure with massive modes and the possible presence of
a cosmological constant.
