Mathematics of rigidity | Nonconvex polyhedra

Flexible polyhedron

In geometry, a flexible polyhedron is a polyhedral surface without any boundary edges, whose shape can be continuously changed while keeping the shapes of all of its faces unchanged. The Cauchy rigidity theorem shows that in dimension 3 such a polyhedron cannot be convex (this is also true in higher dimensions). The first examples of flexible polyhedra, now called Bricard octahedra, were discovered by Raoul Bricard. They are self-intersecting surfaces isometric to an octahedron. The first example of a flexible non-self-intersecting surface in , the Connelly sphere, was discovered by Robert Connelly. Steffen's polyhedron is another non-self-intersecting flexible polyhedron derived from Bricard's octahedra. (Wikipedia).

Flexible polyhedron
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Related pages

Flexagon | Invariant (mathematics) | Elimination theory | Rigid origami | Volume | Dehn invariant | 4-polytope | Hyperbolic geometry | Mean curvature | Tetrahedron | David A. Klarner | Dissection puzzle | Piero della Francesca | Sphere | Isometry | Orientability | Bricard octahedron | Steffen's polyhedron | Octahedron | Geometry | Convex set | Cauchy's theorem (geometry)