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Three years later, Augustin Cauchy proved the list complete by stellating the Platonic solids, and almost half a century after that, in 1858, Bertrand provided a more elegant proof by faceting them. The following year, Arthur Cayley gave the Kepler–Poinsot polyhedra the names by which they are generally known today.
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.
1.4 Kepler-Poinsot solids. 1.5 Achiral nonconvex uniform polyhedra. 2 Chiral Archimedean and Catalan solids. ... Printable version; In other projects Wikidata item;
Print/export Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide ... 5 Platonic solids: 4 Kepler–Poinsot solids: 3 ...
Políedre de Kepler-Poinsot; Usage on cs.wikipedia.org Wikipedista diskuse:Glivi/Archiv do 5.3. 2007; Usage on fi.wikipedia.org Keplerin–Poinsot’n kappale; Usage on fr.wikipedia.org Polyèdre; Usage on gl.wikipedia.org Poliedro regular; Usage on ko.wikipedia.org 케플러-푸앵소 다면체; Usage on oc.wikipedia.org Solids de Kepler-Poinsot
Print/export Download as PDF; Printable version; ... Pages in category "Kepler–Poinsot polyhedra" The following 5 pages are in this category, out of 5 total.
Johnson solids (92, convex, non-uniform) Bipyramids Pyramids Stellations: Stellations: Polyhedral compounds Deltahedra (Deltahedra, equilateral triangle faces) Snub polyhedra (12 uniform, not mirror image) Zonohedron (Zonohedra, faces have 180°symmetry) Dual polyhedron: Self-dual polyhedron Catalan solid
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 ...