A Note On The Metrics Induced By Triakis Icosahedron And Disdyakis Triacontahedron

Polyhedrons have been studied by mathematicians and geometers during many years, because of their symmetries. Geometricians who work in the field of polyhedra are aware of the origin of the Archimedean bodies. In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. The duals of the Archimedean solids are called the Catalan solids which are all convex and ýrregular polyhedra. The number of Catalan solids is only thirteen. There are some relations between metrics and polyhedra. For example, it has been shown that deltoidal icositetrahedron is Chinese Checker's unit sphere. In this study, we introduce two new metrics that their spheres are Triakis Icosahedron and Disdyakis Triacontahedron which are catalan solids.