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His research in geometry, statics and dynamics is important. He was the inventor of geometrical mechanics, investigating how a system of forces acting on a rigid body could be resolved into a single force and a couple. He wrote an important work on polyhedra in 1809, discovering four new regular polyhedra, two of which appear in Kepler's work of 1619 but Poinsot was unaware of this. In 1810 Cauchy proved that, with this definition of regular, the enumeration of regular polyhedra is complete. A mistake was discovered in Poinsot's (and hence Cauchy's) definition in 1990 when an internal inconsistency became apparent.
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