  Periodic instantons, also called calorons, are the BPS solutions to the pure
Yang-Mills theories on $\mathbb{R}^3\times S^1$. It is known that the calorons
interconnect with the instantons and the BPS monopoles as the ratio of their
size to the period of $S^1$ varies. We give, in this paper, the action density
configurations of the $SU(2)$ calorons of higher instanton charges with several
platonic symmetries through the numerical Nahm transform, after the
construction of the analytic Nahm data. The calorons considered are 5-caloron
with octahedral symmetry, 7-caloron with icosahedral symmetry, and 4-caloron
interconnecting tetrahedral and octahedral symmetries. We also consider the
large period, or the instanton, limits of the Nahm data, i.e., the ADHM limits,
and observe the similar spatial distributions of the action densities with the
calorons.
