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In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra. [1] They may be obtained by stellating the regular convex dodecahedron and icosahedron, and differ from these in having regular pentagrammic faces or vertex figures. They can all be seen as three-dimensional analogues of the pentagram in one way or another.
Pages in category "Kepler–Poinsot polyhedra" The following 5 pages are in this category, out of 5 total. This list may not reflect recent changes. ...
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 regular polyhedron is identified by its Schläfli symbol of the form {n, m}, where n is the number of sides of each face and m the number of faces meeting at each vertex. There are 5 finite convex regular polyhedra (the Platonic solids), and four regular star polyhedra (the Kepler–Poinsot polyhedra), making nine regular polyhedra in all. In ...
They are also sometimes called nonconvex polyhedra to imply self-intersecting. Each polyhedron can contain either star polygon faces, star polygon vertex figures, or both. The complete set of 57 nonprismatic uniform star polyhedra includes the 4 regular ones, called the Kepler–Poinsot polyhedra, 14 quasiregular ones, and 39 semiregular ones.
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Kepler–Poinsot polyhedron (Regular star polyhedra) Small stellated dodecahedron, Great stellated dodecahedron, Great icosahedron, Great dodecahedron;
Archimedean Solids at Visual Polyhedra by David I. McCooey; Virtual Reality Polyhedra, The Encyclopedia of Polyhedra by George W. Hart; Penultimate Modular Origami by James S. Plank; Interactive 3D polyhedra in Java; Solid Body Viewer is an interactive 3D polyhedron viewer which allows you to save the model in svg, stl or obj format.