A new type of catalyst based on microfiber supports with microfibers twined into looped threads (lemniscate) that in turn form a structured flexible stable and geometrically regular bulk bed permeable to a reaction flow and not requiring any additional structurial elements is described. Deep toluene oxidation experiments show that the proposed platinum lemniscate glass-fiber catalyst (LGFC) considerably surpasses (by 8–10 times and more) familiar geometric types of catalysts, microfiber and otherwise, in both the specific observed activity per unit active component mass and the ratio between the observed activity and the specific hydraulic resistance. The reason for its superiority is a uniquely high efficiency of mass transfer in the external diffusion region of reactions. Among the promising fields of application for the proposed systems are fast gasphase catalytic reactions, liquid-phase catalytic reactions, and complicated reaction processes, in which the selectivity and the yield of target products are sensitive to diffusion inhibition.