Characterization of convex polyhedra with regular polygonal faces by minimal number of parameters
Let \(C\) be the class of convex polyhedra with regular polygonal faces. The subclass of uniform convex polyhedra consists of the Platonic solids, the Archimedean solids and two infinite families of prisms and antiprisms, while the subclass of non-uniform convex polyhedra consists of the Johnson solids.NEWLINENEWLINEThe purpose of this article is to find a minimal set of parameters \(p_1,\ldots,p_k\) which are describing some properties of the elements of the given class \(C\), such that there are sequences \((p_1,\ldots,p_n)\), where \(1\leq n\leq k\), of these parameters which are different from each other for every element of the given class. To obtain such a characterization, the author analyzes 16 parameters and computes their values all over the solids of uniform and non-uniform convex polyhedra. Comparing various sets of these parameters, the author finds three of them (one triplet) which are different for each solid of the class \(C\) except the two infinite families of prisms and antiprisms. Furthermore, three quadruplets are found which are different for each solid of the class \(C\). In conclusion, it is mentioned that the class \(C\) is divided into 38 equivalent classes with respect to one of these parameters.
scientific article; zbMATH DE number 6329408