It only takes a minute to sign up. This includes the 92 Johnson solids, 13 Archimedean solids, 5 Platonic solids and two infinite familes - prisms and antiprisms. However, I see two ways of extending this definition to 4D:. The list I gave above is known to be complete. But is there at least partial progress on the 4D case?
The second definition is much more restrictive, so maybe a complete classification of polychora, which satisfy 2 exists. Can you point me to some reference, please? There is some information on your first extension to 4D in Anton Sherwood's Johnson solids webpages. He calls the class CRF s: convex and regular-faced. A subset of your second extension to 4D was apparently studied by Roswitha Blind in : convex, with facets regular polyhedra, but not necessarily uniform.
Although there is a wealth of information in these webpages, I am not finding it easy to extract a clear status summary. A "segmentochoron. Blind, Roswitha. The set of convex polytopes, where their facets are bound to be regular, indeed are the polytopes already investigated by Gerd and esp. The set of convex polytopes, where only its polygonal faces are bound to be regular, are known as CRF convex, regular faced polytopes.
This set is much vaster and by no means fully classified. The Archimedean polyhedra consist of all vertex-transitive convex polyhedra whose faces are all regular polygons , excluding:. The Johnson polyhedra are all the other convex polyhedra whose faces are all regular polygons. Categories : Proven Results Convex Polyhedra. Navigation menu Personal tools Log in Request account. There are also infinite families of Prisms and Antiprisms. There exist exactly 92 Convex Polyhedra with Regular Polygonal faces and not necessary equivalent vertices.
They are known as the Johnson Solids. Polyhedra with identical Vertices related by a symmetry operation are known as Uniform Polyhedra. There are 75 such polyhedra in which only two faces may meet at an Edge , and 76 in which any Even number of faces may meet.
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