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If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in\u00a0<jats:italic>k<\/jats:italic>. As an example, a stationary Poisson point process in <jats:inline-formula><jats:alternatives><jats:tex-math>$${{{\\mathbb {R}}}}^2$$<\/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:mn>2<\/mml:mn>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is locally finite, coarsely dense, and generic with probability one. For such a set, the distributions of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in order-1 Delaunay mosaics given by Miles (Math. Biosci. <jats:bold>6<\/jats:bold>, 85\u2013127 (1970)).<\/jats:p>","DOI":"10.1007\/s00454-023-00566-1","type":"journal-article","created":{"date-parts":[[2023,9,7]],"date-time":"2023-09-07T19:01:48Z","timestamp":1694113308000},"page":"29-48","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane"],"prefix":"10.1007","volume":"72","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9823-6833","authenticated-orcid":false,"given":"Herbert","family":"Edelsbrunner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9474-2077","authenticated-orcid":false,"given":"Alexey","family":"Garber","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohadese","family":"Ghafari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1780-2689","authenticated-orcid":false,"given":"Teresa","family":"Heiss","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4201-5775","authenticated-orcid":false,"given":"Morteza","family":"Saghafian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,9,7]]},"reference":[{"issue":"3","key":"566_CR1","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/BF02187788","volume":"5","author":"F Aurenhammer","year":"1990","unstructured":"Aurenhammer, F.: A new duality result concerning Vorono\u012d diagrams. 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