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Kepler's final step was to recognize that these polyhedra fit the definition of regularity, even though they were not convex, as the traditional Platonic solids were. In 1809, Louis Poinsot rediscovered Kepler's figures, by assembling star pentagons around each vertex. He also assembled convex polygons around star vertices to discover two more ...
In the second chapter is the earliest mathematical understanding of two types of regular star polyhedra, the small and great stellated dodecahedron; they would later be called Kepler's solids or Kepler Polyhedra and, together with two regular polyhedra discovered by Louis Poinsot, as the Kepler–Poinsot polyhedra. [8]
The Kepler–Poinsot polyhedra may be constructed from the Platonic solids by a process called stellation. The reciprocal process to stellation is called facetting (or faceting). Every stellation of one polyhedron is dual, or reciprocal, to some facetting of the dual polyhedron. The regular star polyhedra can also be obtained by facetting the ...
Historically, the great dodecahedron is one of two solids discovered by Louis Poinsot in 1810, with some people named it after him, Poinsot solid.As for the background, Poinsot rediscovered two other solids that were already discovered by Johannes Kepler—the small stellated dodecahedron and the great stellated dodecahedron. [3]
Kepler (1619) discovered two of the regular Kepler–Poinsot polyhedra, the small stellated dodecahedron and great stellated dodecahedron. Louis Poinsot (1809) discovered the other two, the great dodecahedron and great icosahedron. The set of four was proven complete by Augustin-Louis Cauchy in 1813 and named by Arthur Cayley in 1859.
In geometry, the great stellated dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol {5 ⁄ 2,3}. It is one of four nonconvex regular polyhedra . It is composed of 12 intersecting pentagrammic faces, with three pentagrams meeting at each vertex.
1.4 Kepler-Poinsot solids. 1.5 Achiral nonconvex uniform polyhedra. 2 Chiral Archimedean and Catalan solids. 3 Chiral nonconvex uniform polyhedra. 4 See also.
It is one of five compounds constructed from a Platonic solid or Kepler-Poinsot solid, and its dual. It is a stellation of the great icosidodecahedron . It has icosahedral symmetry ( I h ) and it has the same vertex arrangement as a great rhombic triacontahedron .