  In this paper, the main focus is on the Sierpinski carpet Julia sets of the
rational maps with non-recurrent critical points. We study the uniform
quasicircle property of the peripheral circles, the relatively separated
property of the peripheral circles and the locally porous property of these
carpets. We also establish some quasisymmetric rigidities of these carpets,
which generalizes the main results of Bonk-Lyubich-Merenkov to the
postcritically infinite case. In the end we give a strategy to construct a
class of postcritically infinite rational maps whose Julia sets are
quasisymetrically equivalent to some round carpets.
