Design Science Institute
Keywords: foldability, axis of spin, periodicity, allspace-filling
Abstract. All the unstable Archimedean polyhedral systems can be symmetrically transformed into Platonic polyhedral systems by accumulating edges and vertices of the respective same number at each of their normal edges and vertices. Furthermore, these Platonic polyhedral systems can always ultimately be transformed into at least one of the three possible case S of fundamental omnitriangulated structural systems, viz. the tetrahedron, the octahedron and the icosahedron. Finally, the periodic relations inherent in these rational transformations can be reduced to "Structural Quanta". Next, the dynamic topological frame models complex are constructed by the complementary allspace-fillers of platonic and Archimedean polyhedral systems, which demonstrate the reciprocal allspace-filling transformations of four dimensional mobility.