  The Penrose tiling is directly related to the atomic structure of certain
decagonal quasicrystals and, despite its aperiodicity, is highly symmetric. It
is known that the numbers 1, $-\tau $, $(-\tau)^2$, $(-\tau)^3$, ..., where
$\tau =(1+\sqrt{5})/2$, are scaling factors of the Penrose tiling. We show that
the set of scaling factors is much larger, and for most of them the number of
the corresponding inflation centers is infinite.
