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Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Following is a list of shapes ... 4 Kepler–Poinsot solids:
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 ...
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This is an indexed list of the uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger. The book was written as a guide book to building polyhedra as physical models. It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes.
The regular star polyhedra are called the Kepler–Poinsot polyhedra and there are four of them, based on the vertex arrangements of the dodecahedron {5,3} and icosahedron {3,5}: As spherical tilings, these star forms overlap the sphere multiple times, called its density, being 3 or 7 for these forms.
A polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples.
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 ...
The Kepler–Poinsot polyhedra may be constructed from the Platonic solids by a process called stellation. Most stellations are not regular. The study of stellations of the Platonic solids was given a big push by H.S.M. Coxeter and others in 1938, with the now famous paper The 59 icosahedra. [91]