A transcatheter, percutaneously implantable, prosthetic heart valve is provided that comprises a lattice frame and two or more integrated cusp and leaflet folded structures attached to the lattice frame. The two or more integrated cusp and leaflet folded structures each comprise a flat sheet of biocompatible membrane that is folded to include a substantially conical shape according to a flat folding pattern. The substantially conical shape is further formed by joining apposing sides of the substantially conical shape along a seam. The two or more integrated cusp and leaflet folded structures are each attached along their respective seams to the lattice frame in a direction substantially parallel to an axis of the lattice frame. Embodiments of valves described herein have application within the entire vascular system.
