# Poinsot, Louis (1777–1859)

Louis Poinsot was a French mathematician who invented **geometrical mechanics**,
investigating how a system of forces acting on a rigid body can be resolved
into a single force and a couple. Together with Gaspard Monge,
he help geometry regain its leading role in mathematical research in France
in the eighteenth century. He wrote an important work on polyhedra in 1809, discovering four new regular polyhedra, which are now known as
the Kepler-Poinsot solids.
Two of these had been found by Johannes Kepler in 1619 but Poinsot was unaware of this; the two additional ones that Poinsot
discovered were the **great dodecahedron** and the **great
icosahedron**. In 1810 Augustin Cauchy proved that, with this definition of regular, the enumeration of regular
polyhedra is complete (although a mistake was discovered in Poinsot's, and
hence Cauchy's, definition in 1990 when an internal inconsistency became
apparent.) Poinsot also worked in number
theory, studying Diophantine
equations with a view to expressing numbers as the difference of two
squares and primitive roots.