A Generalized Formulation of the Concept of the “Cube” – A Hidden Relationship of a Topological Nature between the Cube and Truncated Octahedron
Journal: International Journal of Scientific Engineering and Science (Vol.2, No. 1)Publication Date: 2018-02-15
Authors : Nikos Kourniatis;
Page : 1-4
Keywords : Cube; polyhedra topology; truncated octahedron;
Abstract
This first objective of this paper is to search for higher-dimensional cube structures and explore their relationship with certain Archimedean polyhedra. In particular, the research focuses on the relationship between the six-dimensional cube and the truncated octahedron. The problem is approached through the study of higher-dimensional hypercube projections in three-dimensional space and, subsequently, on a plane, and the finding that each n-hypercube can result from a composition of lower-dimensional cubes. This procedure basically leads to the generalization of the concept of the cube through its successive projections in different dimensions, and finally reveals a relationship of a topological nature between the cube and Archimedean solids, such as the truncated octahedron.
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