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Workshop

Flexible pentagonal bipyramids and their Galois groups

  • Jan Legerský (Czech Technical University in Prague, Czech Republic)
E1 05 (Leibniz-Saal)

Abstract

When a bipyramid flexes, the distance between the two opposite vertices of the two pyramids changes. Therefore, there is a map that associates each realization of the bipyramid to the distance between the two opposite vertices. From an algebraic point of view, this determines a field extension between the field of univariate rational functions and the field of rational functions on the configuration curve of the bipyramid. In this talk, we present a classification of flexible pentagonal bipyramids with respect to the Galois group of this field extension.

As a consequence of the result, we construct an embedded flexible polyhedron with 8 vertices. This answers negatively a long-standing question whether the flexible embedded polyhedron by Steffen, which has 9 vertices, is an embedded flexible polyhedron with the least number of vertices.

conference
29.07.24 02.08.24

MEGA 2024

MPI für Mathematik in den Naturwissenschaften Leipzig (Leipzig) E1 05 (Leibniz-Saal)
Universität Leipzig (Leipzig) Felix-Klein-Hörsaal

Mirke Olschewski

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Saskia Gutzschebauch

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Christian Lehn

Ruhr-Universität Bochum

Irem Portakal

Max Planck Institute for Mathematics in the Sciences

Rainer Sinn

Universität Leipzig

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences

Simon Telen

Max Planck Institute for Mathematics in the Sciences

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