--- res: bibo_abstract: - Every collection of t≥2 n2 triangles with a total of n vertices in ℝ3 has Ω(t4/n6) crossing pairs. This implies that one of their edges meets Ω(t3/n6) of the triangles. From this it follows that n points in ℝ3 have only O(n8/3) halving planes.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Tamal foaf_name: Dey, Tamal foaf_surname: Dey - 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 bibo_doi: 10.1007/BF02574381 bibo_issue: '1' bibo_volume: 12 dct_date: 1994^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/0179-5376 dct_language: eng dct_publisher: Springer@ dct_title: Counting triangle crossings and halving planes@ ...