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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 ...
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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 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.
It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes. It contains the 75 nonprismatic uniform polyhedra , as well as 44 stellated forms of the convex regular and quasiregular polyhedra.
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
Net Stellation facets × 20 A net of a great stellated dodecahedron (surface geometry); twenty isosceles triangular pyramids, arranged like the faces of an icosahedron. It can be constructed as the third of three stellations of the dodecahedron, and referenced as Wenninger model [W22]. Complete net of a great stellated dodecahedron.
Screenshot from Great Stella software, showing the stellation diagram and net for the compound of five tetrahedra Screenshot from Stella4D, looking at the truncated tesseract in perspective and its net, truncated cube cells hidden. Stella is a computer program available in three versions (Great Stella, Small Stella and Stella4D).