Abstract: A process for producing composite bodies from a plurality of molded pieces made from quartz materials of different or identical structure, preferably fused quartz and/or fused silica. Also, composite bodies produced according to this process. A prismatic molded piece with a rectangular bottom surface and top surface and four plate-shaped molded pieces whose dimensions are tailored to the outer surfaces of the prismatic molded piece are produced in a first step, the plate-shaped molded pieces are then fixed to the outer surfaces of the prismatic molded piece, the prismatic molded piece and the plate-shaped molded pieces are heated together under protective gas to a predetermined temperature T&egr; above the softening temperature of the quartz material and then cooled, resulting in a prismatic composite body which is joined thermally in a material engagement and which can be severed to form a series of plate-shaped composite bodies.