About f-Vectors of Inscribed Simplicial Polytopes

2016 ◽  
Vol 55 (3) ◽  
pp. 497-521
Author(s):  
Bernd Gonska
Keyword(s):  
Simplicial Polytopes

Polytopic Prismahedrons

2018 ◽  
pp. 105-140
Keyword(s):  
Chemical Interaction ◽  
Independent Interest ◽  
Simplicial Polytopes

The structure of polytopes—polytopic prismahedrons, which are products of polytopes of lower dimensionality—is investigated. The products of polytopes do not belong to the well-studied class of simplicial polytopes, and therefore their investigations are of independent interest. Analytical dependencies characterizing the structure of the product of polytopes are obtained as a function of the structures of polytope factors. Images of a number of specific polytopic prismahedrons are obtained, tables of structures of polytopic prismahedrons are compiled, depending on the types of polytopes of the factors. Polytopic prismahedrons can be considered as a result of the chemical interaction of molecules, which, from among which there is a polytope of a certain dimension.

scholarly journals Unique Minimal Liftings for Simplicial Polytopes

2012 ◽  
Vol 37 (2) ◽  
pp. 346-355 ◽  
Author(s):  
Amitabh Basu ◽  
Gérard Cornuéjols ◽  
Matthias Köppe
Keyword(s):  
Simplicial Polytopes

scholarly journals On polytopes with small faces

1977 ◽  
Vol 18 (1) ◽  
pp. 39-49 ◽  
Author(s):  
J. N. Lillington
Keyword(s):  
Euclidean Space ◽  
Unit Sphere ◽  
Edge Length ◽  
Research Student ◽  
Simplicial Polytopes ◽  
Surface Areas ◽  
Compact Subsets

In this paper all sets considered are assumed to be compact subsets of Euclidean Space En. A number of results concerning the total edge-lengths of polyhedra have been given by various authors, many of which are mentioned in references in [1]. In [1], it was conjectured that all polytopes inscribed in the unit sphere and containing its centre have total edge-length greater than 2n. This was proved true for simplicial polytopes and shown to be best possible in the sense that there exist simplices with the stated property and with total edge-length arbitrarily close to 2n. In this paper we shall show that the bound is not always best possible if the magnitudes of the faces of such polytopes are restricted and we shall also give some related results on surface areas. This work was carried out while the author was a research student at Royal Holloway College, London and is a revised version of part of the author's thesis approved for the Ph.D. degree.

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