Talk:List of uniform polyhedra
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This is a first pass article, including the complete list of 75 uniform polyhedra, 11 uniform tessellations, and sampling of infinite sets of prism and antiprism.
Tom Ruen 00:01, 7 October 2005 (UTC)
- I think it would make sense to include Skilling's great disnub dirhombidodecahedron [1] (Phil. Trans. A 278 (1975), pp 111-135). In view of the inclusion of tilings in this page and of uniform tilings with hollow tiles in Table 8 of Uniform Polyhedra (Phil. Trans. A 246 (1954), pp 401-450), there is a logical case for covering all the uniform tilings with hollow tiles, apeirogons and zigzags listed by Grünbaum, Miller and Shephard (in The Geometric Vein: The Coxeter Festschrift, pp 17-64), but that's a large collection, without proof of completeness, and if you include them then there's the question of infinite uniform polyhedra in three dimensions where I don't know of a good comprehensive list of the known polyhedra for any definition you might choose. Joseph Myers 19:42, 8 October 2005 (UTC)
- Tom Ruen 04:24, 15 October 2005 (UTC)
- P.S. On "great disnub dirhombidodecahedron", very interesting. Going beyond 2 faces/edge is fun to consider, but I don't think you can call that a polyhedron. Maybe a "Polyhedron network" or something else since it would enclose multiple volumes. Such an ennumeration has a place in geometry, but not here, except as a link if such an article is writen.
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- ON the "great disnub dirhombidodecahedron", I've been rethinking my rejection of this "polyhedron". Initially I rejected it as a true polyhedron for having more than 2 faces per edge. On RETHINKING, technically an even number of faces per edge might be considered as a topological polyhedron with geometrically overlapping edges. Well, I'll have to think further on this! Tom Ruen 20:42, 5 December 2005 (UTC)
The "vertex figure" for W79 looks like the polyhedron itself. ?? --Anton Sherwood 06:43, 7 January 2006 (UTC)
In the image for W114, the pentagrams look farther apart than in Wenninger's picture. --Anton Sherwood 07:06, 7 January 2006 (UTC)
--> Late note - I've corrected link for VF/W79 and uploaded correct image for W114. Tom Ruen 04:01, 1 February 2006 (UTC)
