Here we present the solid-state thermal Huisgen cycloaddition polymerization of a tripodal triptycene-based AB3-type monomer (1), featuring one azide group at the bridgehead position and three alkyne groups at the 1,8,13-positions. Monomer 1 self-assembles into a “2D + 1D” structure and undergoes polymerization upon heating in the solid state without disrupting the self-assembled structure of the monomer. The resulting polymer is insoluble and likely composed of hyperbranched polymers with cyclic structures, which are highly entangled with one another to form a polycatetane network. The solid-state polymerization of a thin-film of 1 also proceeds successfully while preserving the original surface morphology at the nanoscale.