--- res: bibo_abstract: - Consider a random set of points on the unit sphere in ā„d, which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polytope, whose boundary approximates the sphere. We focus on the case dā€‰=ā€‰3, for which there are elementary proofs and fascinating formulas for metric properties. In particular, we study the fraction of acute facets, the expected intrinsic volumes, the total edge length, and the distance to a fixed point. Finally we generalize the results to the ellipsoid with homeoid density.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Arseniy foaf_name: Akopyan, Arseniy foaf_surname: Akopyan foaf_workInfoHomepage: http://www.librecat.org/personId=430D2C90-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-2548-617X - foaf_Person: foaf_givenName: Herbert foaf_name: Edelsbrunner, Herbert foaf_surname: Edelsbrunner foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-9823-6833 - foaf_Person: foaf_givenName: Anton foaf_name: Nikitenko, Anton foaf_surname: Nikitenko foaf_workInfoHomepage: http://www.librecat.org/personId=3E4FF1BA-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-0659-3201 bibo_doi: 10.1080/10586458.2021.1980459 dct_date: 2021^xs_gYear dct_identifier: - UT:000710893500001 dct_isPartOf: - http://id.crossref.org/issn/1058-6458 - http://id.crossref.org/issn/1944-950X dct_language: eng dct_publisher: Taylor and Francis@ dct_title: The beauty of random polytopes inscribed in the 2-sphere@ ...