On angles in higher order Brillouin tessellations and related tilings in the plane Edelsbrunner, Herbert ; https://orcid.org/0000-0002-9823-6833 Garber, Alexey Ghafari, Mohadese Heiss, Teresa ; https://orcid.org/0000-0002-1780-2689 Saghafian, Morteza ddc:510 For a locally finite set in R2, the order-k Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in k. As an example, a stationary Poisson point process in R2 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. 6, 85–127 (1970)). Springer Nature 2024 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/14345 https://research-explorer.ista.ac.at/download/14345/17301 Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. On angles in higher order Brillouin tessellations and related tilings in the plane. <i>Discrete and Computational Geometry</i>. 2024;72:29-48. doi:<a href="https://doi.org/10.1007/s00454-023-00566-1">10.1007/s00454-023-00566-1</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00454-023-00566-1 info:eu-repo/semantics/altIdentifier/issn/0179-5376 info:eu-repo/semantics/altIdentifier/e-issn/1432-0444 info:eu-repo/semantics/altIdentifier/wos/001060727600004 info:eu-repo/semantics/altIdentifier/arxiv/2204.01076 info:eu-repo/semantics/altIdentifier/pmid/39610762 info:eu-repo/semantics/openAccess