Ozcan Gelisgen, On the relations between truncated cuboctahedron, truncated icosidodecahedron and metrics,
Forum Geometricorum, 17 (2017) 273--285.

Abstract. The theory of convex sets is a vibrant and classical field of modern mathematics with rich applications. 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. There are some relations between metrics and polyhedra. For example, it has been shown that cube, octahedron, deltoidal icositetrahedron are maximum, taxicab, Chinese Checker's unit sphere, respectively. In this study, we give two new metrics to be their spheres an Archimedean solids truncated cuboctahedron and truncated icosidodecahedron.

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