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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.
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 ...
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.
Platonic solids (5, convex, regular) Archimedean solids (13, convex, uniform) Kepler–Poinsot polyhedra (4, regular, non-convex) Uniform polyhedra (75, uniform) Prismatoid: prisms, antiprisms etc. (4 infinite uniform classes) Polyhedra tilings (11 regular, in the plane) Quasi-regular polyhedra Johnson solids (92, convex, non-uniform) Bipyramids
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.
1.4 Kepler-Poinsot solids. 1.5 Achiral nonconvex uniform polyhedra. 2 Chiral Archimedean and Catalan solids. ... Printable version; In other projects Wikidata item;
Platonic solid: Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron; Regular spherical polyhedron. Dihedron, Hosohedron; Kepler–Poinsot polyhedron (Regular star polyhedra) Small stellated dodecahedron, Great stellated dodecahedron, Great icosahedron, Great dodecahedron; Abstract regular polyhedra (Projective polyhedron)
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.