From: Jan Kristian Haugland Subject: Re: 4D regular solids Date: Fri, 20 Oct 2000 22:14:43 +0200 Newsgroups: sci.math Summary: [missing] Alan Wetherby wrote: > Can someone point me to a list of 4D regular hypersolids, with numbers > of faces, edges and vertices? > > Thanks --Alan > > Sent via Deja.com http://www.deja.com/ > Before you buy. (Disclaimer: My use of "faces" and "solids" may be non-standard.) The simplex has 5 vertices, 10 edges, 10 faces and 5 solids. The hyper-cube has 16 vertices, 32 edges, 24 faces and 8 solids. The generalized octahedron is the dual of the hyper-cube and thus has 8 vertices, 24 edges, 32 faces and 16 solids. The 24-cell, made up of 24 octahedra, has 24 vertices, 96 edges, 96 faces and 24 solids. The 120-cell, made up of 120 dodecahedra, has 600 vertices, 1200 edges, 720 faces and 120 solids. The 600-cell, made up of 600 tetrahedra, and the dual of the 120-cell, has 120 vertices, 720 edges, 1200 faces and 600 solids. All in all, there are 6 regular hypersolids. In each higher dimension, there are only three: The simplex, the generalized cube and the generalized octahedron. -- Jan Kristian Haugland http://home.hia.no/~jkhaug00