  We present the correspondence between non-interacting multi-hadron fermion
star equation of state in the many-flavor limit and the degrees of freedom of a
Kaluza\,--\,Klein compact star. Many flavors can be interpreted in this
framework as one extra compacti\-fied spatial dimension with various,
more-and-more massive hadron state excitations. The effect of increasing the
degrees of freedom was investigated on the equation of state and in connection
with the mass-radius relation, $M(R)$. The maximum mass of the star,
$M_{\mathrm{max}}$ were also calculated as a function of the maximum number of
excited states, $n$ and the size of the compactified extra dimension,
$R_{\mathrm{c}}$.
