Steffen's polyhedron, the simplest possible non-self-crossing 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 (1897). 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 (1977). Steffen's polyhedron is another non-self-intersecting flexible polyhedron derived from Bricard's octahedra.[1]
^Alexandrov (2010).
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In geometry, a flexiblepolyhedron is a polyhedral surface without any boundary edges, whose shape can be continuously changed while keeping the shapes...
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a member of a family of flexible polyhedra constructed by Raoul Bricard in 1897. The overall shape of one of these polyhedron may change in a continuous...
invariant is zero. The Dehn invariant of a self-intersection-free flexiblepolyhedron is invariant as it flexes. Dehn invariants are also an invariant...
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Kh (1995-04-30). "On the problem of invariance of the volume of a flexiblepolyhedron". Russian Mathematical Surveys. 50 (2): 451–452. Bibcode:1995RuMaS...
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of the (non-flexible) heptagonal faces, rather than in the (flexible) vertices. Alternatively, the quartic can be modeled by a polyhedron with octahedral...
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