The element number of the convex regular polytopes |
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Authors: | Jin Akiyama Ikuro Sato |
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Institution: | 1.Research Institute of Educational Development,Tokai University,Tokyo,Japan;2.Department of Pathology,Research Institute, Miyagi Cancer Center,Natori-city, Miyagi,Japan |
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Abstract: | Let Σ be a set of n-dimensional polytopes. A set Ω of n-dimensional polytopes is said to be an element set for Σ if each polytope in Σ is the union of a finite number of polytopes
in Ω identified along (n − 1)-dimensional faces. In this paper, we consider the n-dimensional polytopes in general, and extend the notion of element sets to higher dimensions. In particular, we will show
that in the 4-space, the element number of the six convex regular polychora is at least 2, and in the n-space (n ≥ 5), the element number is 3, unless n + 1 is a square number. |
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