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Four numbering schemes for the uniform polyhedra are in common use, distinguished by letters: [C] Coxeter et al., 1954, showed the convex forms as figures 15 through 32; three prismatic forms, figures 33–35; and the nonconvex forms, figures 36–92.
Coxeter, Longuet-Higgins & Miller (1954) published the list of uniform polyhedra. Sopov (1970) proved their conjecture that the list was complete. In 1974, Magnus Wenninger published his book Polyhedron models, which lists all 75 nonprismatic uniform polyhedra, with many previously unpublished names given to them by Norman Johnson.
image of polyhedron; name of polyhedron; alternate names (in brackets) Wythoff symbol; Numbering systems: W - number used by Wenninger in polyhedra models, U - uniform indexing, K - Kaleido indexing, C - numbering used in Coxeter et al. 'Uniform Polyhedra'. Number of vertices V, edges E, Faces F and number of faces by type.
This category was created to reference the full set of 75 nonprismatic uniform polyhedra, as well as prismatic forms. It is a subset of Category:Polyhedra.. It is a union of 5 Platonic solids, 4 Kepler–Poinsot solids, 13 Archimedean solids, and the infinite prismatic sets in Prismatoid polyhedra, and adds 53 non-convex, non-regular uniform polyhedra.
Quasi-regular polyhedra Johnson solids (92, convex, non-uniform) Bipyramids Pyramids Stellations: Stellations: Polyhedral compounds Deltahedra (Deltahedra, equilateral triangle faces) Snub polyhedra (12 uniform, not mirror image) Zonohedron (Zonohedra, faces have 180°symmetry) Dual polyhedron: Self-dual polyhedron Catalan solid
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.
The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples. ... List of uniform tilings.
Polyhedron: Class Number and properties 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