  We demonstrate that in the framework of standard general relativity
polytropic spheres with properly fixed polytropic index $n$ and relativistic
parameter $\sigma$, giving ratio of the central pressure $p_\mathrm{c}$ to the
central energy density $\rho_\mathrm{c}$, can contain region of trapped null
geodesics. Such trapping polytropes can exist for $n > 2.138$ and they are
generally much more extended and massive than the observed neutron stars. We
show that in the $n$--$\sigma$ parameter space the region of allowed trapping
increase with polytropic index for interval of physical interest $2.138 < n <
4$. Space extension of the region of trapped null geodesics increases with both
increasing $n$ and $\sigma > 0.677$ from the allowed region. In order to relate
the trapping phenomenon to astrophysically relevant situations, we restrict
validity of the polytropic configurations to their extension $r_\mathrm{extr}$
corresponding to the gravitational mass $M \sim 2M_{\odot}$ of the most massive
observed neutron stars. Then for the central density $\rho_\mathrm{c} \sim
10^{15}$~g\,cm$^{-3}$ the trapped regions are outside $r_\mathrm{extr}$ for all
values of $2.138 < n < 4$, for the central density $\rho_\mathrm{c} \sim 5
\times 10^{15}$~g\,cm$^{-3}$ the whole trapped regions are located inside of
$r_\mathrm{extr}$ for $2.138 < n < 3.1$, while for $\rho_\mathrm{c} \sim
10^{16}$~g\,cm$^{-3}$ the whole trapped regions are inside of $r_\mathrm{extr}$
for all values of $2.138 < n < 4$, guaranteeing astrophysically plausible
trapping for all considered polytropes. The region of trapped null geodesics is
located closely to the polytrope centre and could have relevant influence on
cooling of such polytropes or for binding of gravitational waves in their
interior.
