Journal for Geometry and Graphics 30 (2026), No. 1, 075--088
Copyright by the authors licensed under CC BY SA 4.0
Constructing Flexible Polyhedra by Twinning
Elvar W. Atlason
University College London, London, United Kingdom
elvar.atlason.23@ucl.ac.uk
Simon D. Guest
University of Cambridge, Cambridge, United Kingdom
sdg@eng.cam.ac.uk
Polyhedra are generically rigid, but can be made to flex under certain symmetry conditions. We generalise Raoul Bricard’s flexible octahedra from 1897 to construct an infinite family of combinatorially distinct flexible polyhedra with self-intersections, forming the only known infinite family of flexible polyhedra. By removing edges from these models, we can make new crinkles of infinitely many different topologies. These crinkles can be used to construct flexible triangulated surfaces. We show this in a particular example to make a flexible embedded polyhedron with a large range of motion.
Keywords: Flexible polyhedra, self-intersecting polyhedra, symmetric constructions, Bricard octahedra, crinkles.
MSC: 52C25; 52B10, 51M20, 70B10, 70B15
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