Kepler-Poinsot Solid -- from Wolfram MathWorld

The Kepler-Poinsot solids are the four regular concave polyhedra with intersecting facial planes. They are composed of regular concave polygons and were unknown to the ancients. A list of the Kepler-Poinsot solids as implemented in the Wolfram Language can be given by PolyhedronData["KeplerPoinsot"]. The small stellated dodecahedron appeared ca. 1430 as a mosaic by Paolo Uccello on the floor ...…

The Kepler-Poinsot Polyhedra - George W. Hart

The Kepler-Poinsot Polyhedra. If we do not require polyhedra to be convex, we can find four more regular solids.As in the Platonic solids, these solids have identical regular polygons for all their faces, and the same number of faces meet at each vertex.What is new is that we allow for a notion of "going around twice" which results in faces which intersect each other.…

Kepler-Poinsot Solids, the non-convex regular polyhedra

The Kepler-Poinsot solids are the four non-convex regular polyhedra. Each one has identical regular faces, and identical regular vertex figures. These models were made using nets generated by Great Stella, but could also be made using Stella4D or Small Stella. Click on the images below to see a bigger picture and get more information about how ...…

Kepler-Poinsot solids - The Worlds of David Darling

The Kepler-Poinsot solids are four regular non-convex polyhedra that exist in addition to the five regular convex polyhedra known as the Platonic solids.As with the Platonic solids, the Kepler-Poinsot solids have identical regular polygons for all their faces, and the same number of faces meet at each vertex. What is new is that we allow for a notion of "going around twice," which results in ...…

Regular Polyhedra Brilliant Math & Science Wiki

A regular polyhedron has the following properties: faces are made up of congruent regular polygons; the same number of faces meet at each vertex. There are nine regular polyhedra all together: five convex polyhedra or Platonic solids four "star" polyhedra or Kepler-Poinsot polyhedra. Regular polyhedra (particularly the Platonic ...…

On infinite Kepler Poinsot polyhedra

Kepler-Poinsot solids, and it is infinite, like the 3 regular Petrie-Coxeter polyhedra (see Fig. 1). Thus, it is an example of a polyhedron that merges the Kepler-Poinsot and the Petrie-Coxeter ideas and perhaps that is why it remained undiscovered ever since (see [1]). One could discuss that really is a new…

Category:Kepler-Poinsot solids - Wikimedia Commons

Category:Kepler-Poinsot solids. From Wikimedia Commons, the free media repository. Jump to navigation Jump to search. Great dodecahedron. Small stellated dodecahedron. Great icosahedron. Great stellated dodecahedron. Sets of all four solids, like this one, are in Sets of all Kepler-Poinsot solids.Named after: Johannes Kepler, Louis Poinsot…