Point-ellipse configurations and related topics

In this paper we introduce point-ellipse configurations and point-conic configurations . We study some of their basic properties, illustrated by properly chosen examples, and describe two interesting infinite families of balanced point-ellipse, respectively point-conic 6-configurations. The construc...

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Bibliographic Details
Published in:Beiträge zur Algebra und Geometrie 2022-09, Vol.63 (3), p.459-475
Main Authors: Gévay, Gábor, Bašić, Nino, Kovič, Jurij, Pisanski, Tomaž
Format: Article
Language:English
Subjects:
Algebra
Algebraic Geometry
Cartesian coordinates
Configurations
Convex and Discrete Geometry
Geometry
Mathematics
Mathematics and Statistics
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Summary:In this paper we introduce point-ellipse configurations and point-conic configurations . We study some of their basic properties, illustrated by properly chosen examples, and describe two interesting infinite families of balanced point-ellipse, respectively point-conic 6-configurations. The construction of the first family is based on Carnot’s theorem, whilst the construction of the second family is based on the Cartesian product of two regular polygons. Finally, we describe a point-conic configuration based on the regular 24-cell.
ISSN:0138-4821
2191-0383
DOI:10.1007/s13366-021-00587-y