Can Penrose tilings generate regular polyhedra?

Question

Physicist Roger Penrose discovered several pairs of polygons that can each tile the infinite plane aperiodically (see https://en.wikipedia.org/wiki/Penrose_tiling). Is there way to fold such a tiling, or a finite strip of such tiling, or a finite regular pentagonal subset of such a tiling, so as to form a regular but aperiodic polyhedron? There would clearly be many follow-on questions if this were possible, but they are beyond my ability to imagine. This question was stimulated by the very interesting video there are 48 regular polyhedra.