Classification of flexible Kokotsakis polyhedra with quadrangular base

By Ivan Izmestiev. 2014

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A Kokotsakis polyhedron with quadrangular base is a neighborhood of a quadrilateral in a quad surface. Generically, a Kokotsakis polyhedron is rigid. Up to now, several flexible classes were known, but a complete classification was missing. In the present paper, we provide such a classification. The analysis is based on the fact that the dihedral angles of a Kokotsakis polyhedron are related by an Euler-Chasles correspondence. It results in a diagram of elliptic curves covering complex projective planes. A polyhedron is flexible if and only if this diagram commutes.

Subfields: Geometry and Topology, Information Systems

View Paper: https://www.semanticscholar.org/paper/a861a84051e54d7aaa643446315731ffa02ca088