Classification of flexible Kokotsakis polyhedra with quadrangular base
- Izmestiev, Ivan 1Institut für Mathematik, Freie Universität Berlin, Germany - Department of Mathematics, University of Fribourg, Switzerland
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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
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 288681
- DOI 10.1093/imrn/rnw055
- Persistent URL
- https://folia.unifr.ch/unifr/documents/305439
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