Original scientific paper

On the Metrics Induced by Icosidodecahedron and Rhombic Triacontahedron

Zeynep Can ; Faculty of Arts and Sciences, Aksaray University, Aksaray,Turkey
Özcan Gelişgen orcid.org/0000-0001-7071-6758 ; Faculty of Arts and Sciences, Eskişehir Osmangazi University, Eskişehir, Turkey
Rüstem Kaya ; Faculty of Arts and Sciences, Eskişehir Osmangazi University, Eskişehir, Turkey

Abstract

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.

Keywords

Archimedean solids; Catalan solids; metric; Chinese Checkers metric; Icosidodecahedron; Rhombic triacontahedron

Hrčak ID:

151329

URI

https://hrcak.srce.hr/151329

Publication date:

19.1.2016.

Article data in other languages: croatian

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