Ümit Ziya SAVCI

Truncated Truncated Dodecahedron ve Truncated Truncated Icosahedron Uzayları

Konveks kümeler teorisi, zengin uygulamalara sahip modern matematiğin canlı ve klasik bir alanıdır. Konveks kümelerin geometrik yönleri, bazı kavramlar, fakat öncelikle çokyüzlülerin tanıtılmasıyla geliştirilmiştir. Konveks olduğunda bir çokyüzlü, ℝ? de çok önemli bir özel cisimdir. Öklid 3 boyutlu uzayın konveks alt kümelerinin bazı örnekleri Platonik cisimler, Arşimet cisimleri ve Arşimet dualleri veya Katalan cisimleridir. Metriklerle çokyüzlüler arasında bazı ilişkiler vardır. Örneğin, küp, sekizyüzlü, deltoidal icositetrahedron'un sırasıyla, maksimum, Taksi, Çin dama uzaylarının birim küresi olduğu görülmektedir. Bu çalışmada, kürelerinin truncated truncated dodecahedron ve truncated truncated icosahedron olan iki yeni metrik tanıtıldı.

Truncated Truncated Dodecahedron and Truncated Truncated Icosahedron Spaces

The theory of convex sets is a vibrant and classical field of modern mathematics with richapplications. The more geometric aspects of convex sets are developed introducing some notions, but primarilypolyhedra. A polyhedra, when it is convex, is an extremely important special solid in ℝ?. Some examples ofconvex subsets of Euclidean 3-dimensional space are Platonic Solids, Archimedean Solids and ArchimedeanDuals or Catalan Solids. There are some relations between metrics and polyhedra. For example, it has beenshown 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 truncated truncated dodecahedron andtruncated truncated icosahedron.

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