A polyhedral tool for producing an orthodontic appliance has a main body with one upper and one lower surface that are parallel to each other and at least one other pair of nonparallel, opposite lateral surfaces. One of the two nonparallel surfaces of the body extends at an angle of 5°-45° and the other at angle of 45°-85° to the upper and lower surfaces of the body. Each of the nonparallel lateral surfaces is formed with a dovetail groove. Respective thin plates each have a dovetail tongue fittable into a respective one of the grooves.