A novel 3D ultramicroporous triptycene-based polyimide framework with high surface area (1050 m2 g-1) and thermal stability was synthesized. It exhibits relatively high CO₂ (3.4 mmol g^-1 at 273 K and 1 bar), H₂ (7 mmol g^-1 at 77 K and 1 bar), and olefin sorption capacity, good CO₂/N₂ (45) and CO2/CH4 (9.6) selectivity at 273 K and 1 bar, as well as promising C₂H₄/CH₄ and C₃H₆/CH₄ selectivities at 298 K, making it a potential candidate for CO₂ capture, H₂ storage, and hydrocarbon gas separation applications. © The Royal Society of Chemistry 2016.