caa a22 4500 445884290 CHVBK 20180317145554.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10711-010-9533-4 doi (NATIONALLICENCE)springer-10.1007/s10711-010-9533-4 The element number of the convex regular polytopes [Elektronische Daten] [Jin Akiyama, Ikuro Sato] 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. Springer Science+Business Media B.V., 2010 Regular polytopes nationallicence Element number nationallicence Element set nationallicence Dehn invariant nationallicence Akiyama Jin Research Institute of Educational Development, Tokai University, 2-28-4 Tomigaya, Shibuya, 151-8677, Tokyo, Japan aut Sato Ikuro Department of Pathology, Research Institute, Miyagi Cancer Center, 47-1 Medeshima-shiote (Azanodayama), 981-1293, Natori-city, Miyagi, Japan aut Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 269-278 0046-5755 151:1<269 2011 151 10711 https://doi.org/10.1007/s10711-010-9533-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9533-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Akiyama Jin Research Institute of Educational Development, Tokai University, 2-28-4 Tomigaya, Shibuya, 151-8677, Tokyo, Japan aut NATIONALLICENCE 700 1- Sato Ikuro Department of Pathology, Research Institute, Miyagi Cancer Center, 47-1 Medeshima-shiote (Azanodayama), 981-1293, Natori-city, Miyagi, Japan aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 269-278 0046-5755 151:1<269 2011 151 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer