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Its <jats:italic>f<\/jats:italic>-vector is identified in distribution with the <jats:italic>f<\/jats:italic>-vector of a beta\u2019 polytope generated by <jats:italic>n<\/jats:italic> random points in\u00a0<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathbb {R}^d$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow>\n                      <mml:mi>R<\/mml:mi>\n                    <\/mml:mrow>\n                    <mml:mi>d<\/mml:mi>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. Explicit formulas for the expected <jats:italic>f<\/jats:italic>-vector are provided for any <jats:italic>d<\/jats:italic> and the low-dimensional cases <jats:inline-formula><jats:alternatives><jats:tex-math>$$d\\in \\{2,3,4\\}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>d<\/mml:mi>\n                    <mml:mo>\u2208<\/mml:mo>\n                    <mml:mo>{<\/mml:mo>\n                    <mml:mn>2<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mn>3<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mn>4<\/mml:mn>\n                    <mml:mo>}<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> are studied separately. This implies an explicit formula for the total number of <jats:italic>k<\/jats:italic>-dimensional faces in the spherical Voronoi tessellation as well.<\/jats:p>","DOI":"10.1007\/s00454-021-00315-2","type":"journal-article","created":{"date-parts":[[2021,7,4]],"date-time":"2021-07-04T18:02:15Z","timestamp":1625421735000},"page":"1330-1350","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["The Typical Cell of a Voronoi Tessellation on the Sphere"],"prefix":"10.1007","volume":"66","author":[{"given":"Zakhar","family":"Kabluchko","sequence":"first","affiliation":[]},{"given":"Christoph","family":"Th\u00e4le","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,7,4]]},"reference":[{"issue":"1\u20132","key":"315_CR1","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1080\/17442509408833870","volume":"46","author":"E Arbeiter","year":"1994","unstructured":"Arbeiter, E., Z\u00e4hle, M.: Geometric measures for random mosaics in spherical spaces. 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