This dissertation discusses the development of new polymeric membranes for use in gas separation applications. Polymer membranes offer a more energy-efficient method for separations compared to many typical industrial techniques, such as distillation. However, membrane performance is typically limited by a natural tradeoff between the gas permeability, a measure of the gas throughput across the membrane, and the selectivity, the sieving capability of the material. Therefore, highly permeable membranes generally suffer from low selectivities and vice versa. This challenge can be combatted at the macromolecular level by strategically designing the polymer backbone to have bulky moieties and/or rigid, tortuous elements to disrupt polymer chain packing and increase the fractional free volume of the material. The unique molecule, triptycene, is a rigid, three-dimensional, pinwheel-shaped molecule that fits these design criteria and is investigated at length in this dissertation through a series of triptycene-based polyimides. Composed of three bulky benzene "blades", triptycene is found to be effective at disrupting polymer chain packing, which increases free volume and provides more possible pathways for diffusion, thereby increasing permeability. Additionally, small internal free volume cavities, similar in size to many common gas penetrants, are trapped in the clefts of the benzene blades. These small voids, which are intrinsic to the triptycene molecule, create configuration-based free volume that boosts the membrane's selectivity. This bimodal free volume size distribution proved to be favorable architecture for gas transport, as evidenced by simultaneously enhanced gas permeabilities and selectivities compared to those of conventional glassy polymers. Additionally, fundamental structure/property relationships of the triptycene-polyimides were studied through minute variations to the polymer backbone design. It was determined that the performance could be improved further through the introduction of trifluoromethyl groups neighboring the triptycene moiety and by incorporating very rigid polymer backbone elements. Furthermore, the promising gas transport properties of the materials studied in this work provide motivation for continued research in the field of triptycene-based polymers for gas separation membranes.