  Geometrization of the fundamental interactions has been extensively studied
during the century. The idea of introducing compactified spatial dimensions
originated by Kaluza and Klein. Following their approach, several model were
built representing quantum numbers (e.g. charges) as compactified space-time
dimensions. Such geometrized theoretical descriptions of the fundamental
interactions might lead us to get closer to the unification of the principle
theories.
  Here, we apply a $3+1_C+1$ dimensional theory, which contains one extra
compactified spatial dimension $1_C$ in connection with the flavour quantum
number in Quantum Chromodynamics. Within our model the size of the $1_C$
dimension is proportional to the inverse mass-difference of the first low-mass
baryon states. We used this phenomena to apply in a compact star model -- a
natural laboratory for testing the theory of strong interaction and the
gravitational theory in parallel.
  Our aim is to test the modification of the measurable macroscopical
parameters of a compact Kaluza-Klein star by varying the size of the
compactified extra dimension. Since larger the $R_C$ the smaller the mass
difference between the first spokes of the Kaluza-Klein ladder resulting
smaller-mass stars. Using the Tolman-Oppenheimer-Volkov equation, we
investigate the $M$-$R$ diagram and the dependence of the maximum mass of
compact stars. Besides testing the validity of our model we compare our results
to the existing observational data of pulsar properties for constraints.
