The paper describes five regular polyhedra - tetrahedron, hexahedron, octahedron, icosahedron and dodecahedron. Regular polyhedra are also called Platonic solids, after the Greek philosopher Plato who first described them. The basic characteristics of regular polyhedra are described, and by applying Euler's polyhedral formula, it is shown why there are only five of them. In the central part of the paper, it is shown step by step how regular polyhedra can be formed by folding paper using the Japanese origami method, traditional and modular. The steps are shown visually and described, and for the sake of understanding the presentation, the meanings of the origami symbols are also given. By applying the paper folding method in mathematics lessons, interest, creativity and analytical and critical thinking can be aroused in students. The advantages of such work are multiple, but still underutilized. Therefore, this work can serve as an incentive for application and further research.