A highly gas permeable polymer with exceptional size selectivity is prepared by fusing triptycene units together via a polymerization reaction involving Troger's base formation. The extreme rigidity of this polymer of intrinsic microporosity (PIM-Trip-TB) facilitates gas permeability data that lie well above the benchmark 2008 Robeson upper bounds for the important O-2/N-2 and H-2/N-2 gas pairs.