On the Metrics Induced by Icosidodecahedron and Rhombic Triacontahedron

The theory of convex sets is a vibrant and classical field of modern mathematics with rich applications.If every points of a line segment that connects any two points of the set are in the set, then it is convex.The more geometric aspects of convex sets are developed introducing some notions, but primarily polyhedra.A polyhedra, when it is convex, is an extremely important special solid in R n .Some examples of convex subsets of Euclidean 3-dimensional space are Platonic Solids, Archimedean Solids and Archimedean Duals or Catalan Solids.In this study, we give two new metrics to be their spheres an archimedean solid icosidodecahedron and its archimedean dual rhombic triacontahedron.