In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra. They may be obtained by stellating the regular convex dodecahedron and...

polyhedrons as in 5 Platonic solids and 13 Archimedean solids—2 quasiregular and 11 semiregular— the non-convex star polyhedra as in 4 Kepler–Poinsot...

discovered the four Kepler-Poinsot polyhedra in 1809. Two of these had already appeared in Kepler's work of 1619, although Poinsot was unaware of this...

faces) and four Kepler–Poinsot polyhedrons. Nevertheless, some polyhedrons may not possess one or two of those symmetries: A polyhedron with vertex-transitive...

Goldberg polyhedron Kepler-Poinsot polyhedron List of regular polytopes Prince Rupert's cube Regular polytope Regular skew polyhedron Toroidal polyhedron Gardner...

In geometry, the small stellated dodecahedron is a Kepler–Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {⁠5/2⁠,5}. It is one of...

on a vertex of this polyhedron or inside of it. It was studied by Max Brückner after the discovery of Kepler–Poinsot polyhedron. It can be viewed as...

polyhedra (the Platonic solids), and four regular star polyhedra (the Kepler–Poinsot polyhedra), making nine regular polyhedra in all. In addition, there...

In geometry, the great dodecahedron is one of four Kepler–Poinsot polyhedra. It is composed of 12 pentagonal faces (six pairs of parallel pentagons), intersecting...

as Kepler–Poinsot polyhedra. Kepler may have also found another solid known as elongated square gyrobicupola or pseudorhombicuboctahedron. Kepler once...

of regular icosahedron, which consists of 59 polyhedrons. The great dodecahedron, one of the Kepler–Poinsot polyhedra, is constructed by either stellation...

solids and (star) Kepler–Poinsot polyhedra – form dual pairs, where the regular tetrahedron is self-dual. The dual of an isogonal polyhedron (one in which...

In geometry, the great stellated dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol {⁠5/2⁠,3}. It is one of four nonconvex regular polyhedra...

polyhedral compounds, four Kepler-Poinsot polyhedra, and thirteen Archimedean solids, constructing or collecting polyhedron models has become a common...

dodecahedron, geometric solids; see Kepler–Poinsot polyhedron This disambiguation page lists articles associated with the title Kepler star. If an internal link...

Kepler defined stellation for polygons and polyhedra as the process of extending edges or faces until they meet to form a new polygon or polyhedron....

4-polytope Rub el Hizb Star (glyph) Star polyhedron, Kepler–Poinsot polyhedron, and uniform star polyhedron Starfish Grünbaum & Shephard (1987). Tilings...

nonprismatic uniform star polyhedra includes the 4 regular ones, called the Kepler–Poinsot polyhedra, 14 quasiregular ones, and 39 semiregular ones. There are...

Kepler (1571 – 1630). Kepler conjecture Kepler triangle Kepler–Bouwkamp constant Kepler–Poinsot polyhedron Kepler's laws of planetary motion Kepler's...

meaning its dual is the regular tetrahedron itself. 4 regular star Kepler–Poinsot solids: great dodecahedron, small stellated dodecahedron, great icosahedron...

triangular tiling Regular polyhedron Platonic solid Tetrahedron Cube Octahedron Dodecahedron Icosahedron Kepler–Poinsot polyhedron (regular star polyhedra)...

forms the outer shell of the great stellated dodecahedron, a Kepler–Poinsot polyhedron with twelve pentagram faces. Each edge of the triakis icosahedron...

In geometry, the great icosahedron is one of four Kepler–Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol {3,5⁄2} and Coxeter-Dynkin...

vertex figures. There are four regular star polyhedra, known as the Kepler–Poinsot polyhedra. The Schläfli symbol {p,q} implies faces with p sides, and...

edges. The regular dodecahedron can be faceted into one regular Kepler–Poinsot polyhedron, three uniform star polyhedra, and three regular polyhedral compound...

polyhedra: Regular polyhedra, that is, the five Platonic solids and the four Kepler–Poinsot polyhedra. Disphenoid tetrahedra. Crown polyhedra, also known as stephanoid...

each vertex. The great icosahedron is one of the four regular star Kepler–Poinsot polyhedra. Its Schläfli symbol is {3, ⁠5/2⁠}. Like the convex form,...

convex polyhedra (where the densities are all 1) and the non-convex Kepler–Poinsot polyhedra. Projective polyhedra all have Euler characteristic 1, like...

14-metre (46 ft) statue named the Kepler Star. It consists of two internally illuminated Kepler–Poinsot polyhedrons, appearing like a giant star in the...

characteristics, as being quasiregular. Two are based on dual pairs of regular Kepler–Poinsot solids, in the same way as for the convex examples: the great icosidodecahedron...