Abstract: Fourier telescopes permit observations over a very broad band of energy. They generally include synthetic spatial filtering structures, known as multilayer grids or grid pairs consisting of alternate layers of absorbing and transparent materials depending on whether neutrons or photons are being imaged. For hard x-rays and gamma rays, high (absorbing) and low (transparent) atomic number elements, termed high-Z and low-Z materials may be used. Fabrication of these multilayer grid structures is not without its difficulties. Herein the alternate layers of the high-Z material and the low-Z material are inserted in a polyhedron, transparent to photons of interest, through an open face of the polyhedron. The inserted layers are then uniformly compressed to form a multilayer grid.