Journal article

Classification of flexible Kokotsakis polyhedra with quadrangular base

  • Izmestiev, Ivan 1Institut für Mathematik, Freie Universität Berlin, Germany - Department of Mathematics, University of Fribourg, Switzerland
    01.02.2017
Published in:
  • International Mathematics Research Notices. - 2017, vol. 2017, no. 3, p. 715–808
English A Kokotsakis polyhedron with quadrangular base is a neighborhood of a quadrilateral in a quad surface. Generically, a Kokotsakis polyhedron is rigid. In this article we classify flexible Kokotsakis polyhedra with quadrangular bases. The analysis is based on the fact that any pair of adjacent dihedral angles of a Kokotsakis polyhedron is related by a biquadratic equation. This results in a diagram of branched covers of complex projective lines by elliptic curves. A polyhedron is flexible if and only if all repeated fiber products of coverings meet in the same Riemann surface, which is then the configuration space of the polyhedron.
Faculty
Faculté des sciences et de médecine
Department
Département de Mathématiques
Language
  • English
Classification
Mathematics
License
License undefined
Identifiers
Persistent URL
https://folia.unifr.ch/unifr/documents/305439
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