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More configurations on elliptic curves

Marco Bramato, Lorenz Halbeisen and Norbert Hungerbühler

Vol. 21 (2024), No. 1, 45–56
DOI: 10.2140/iig.2024.21.45
Abstract

We construct elliptic (3rs,sr3) configurations for all integers r s 1. This solves an open problem of Branko Grünbaum. The configurations which we build have mirror symmetry and even D3 symmetry if r is a multiple of 3. The configurations are dynamic in the sense that the points can be moved along the elliptic curve in such a way that all line incidences are preserved.

Keywords
configurations, elliptic curves
Mathematical Subject Classification
Primary: 51A05, 51A20
Milestones
Received: 26 January 2023
Accepted: 12 March 2024
Published: 31 May 2024
Authors
Marco Bramato
Department of Mathematics
ETH Zürich
Zürich
Switzerland
Lorenz Halbeisen
Department of Mathematics
ETH Zürich
Zürich
Switzerland
Norbert Hungerbühler
Department of Mathematics
ETH Zürich
Zürich
Switzerland