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  "body": "\n## Example\n\nA *flexible polyhedron* is a closed polyhedral surface in $\\R^3$ that admits a continuous non-rigid motion in which every face stays congruent to itself.\nIts edges act as hinges, and the shape changes while each face moves rigidly.\nIn the language of [[rigidity of frameworks|V5YS9BZX0N]], its framework of vertices and edges, with the faces triangulated, is flexible.\n\nBricard found flexible octahedra in 1897.\nTheir surfaces pass through themselves, so they are not boundaries of solids.\nConnelly constructed in 1977 the first flexible polyhedron without self-intersections.\nA simpler example is Steffen's polyhedron, with $9$ vertices, $21$ edges and $14$ triangular faces.\nIt satisfies Euler's formula $9 - 21 + 14 = 2$.\n\nThese examples are not convex, as they must be.\n[[Cauchy's rigidity theorem|CJ7KCDDF31]] shows that no convex polyhedron is flexible.\n\n## Explanations\n\n### L1 human\n\nImagine a closed surface made of rigid triangles joined by hinges along their edges.\nFor a convex shape such as a cube cut into triangles, nothing can move.\nSome cleverly built nonconvex shapes do wobble: they bend at the hinges while every triangle stays the same.\nSuch a shape is a flexible polyhedron.\n",
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