Talk:E8 polytope

The article says that the E8 polytope is the highest (dimensional?) finite nonprismatic semi-regular figure. However, the demihypercube series consist of nonprismatic semiregular_polytopes (or regular, in low dimensions), one in every dimension. So the 9-dimensional demienneract should be an obvious counter-example to this statement.
It is true, however, that the E8 polytope is the highest dimensional finite Semiregular_E-polytope.

If the statement was supposed to mean that the E8 polytope is the nonprismatic semiregular 8-polytope with the most number of vertices (unlikely), then it should be checked (in references) against the other 254 semiregular polytopes having E₈ as its Coxeter_group (not to mention the 190 polytopes of D₈ type, other than the demiocteract etc...), and if true, the statement should be changed to clearly mean this. 85.224.18.87 00:36, 20 September 2007 (UTC)

It has to do with the definition of semiregular which Gossett defined to mean a polytope which is vertex-uniform, nonprismatic, and has two or more types of regular facets. This is the last one, by that accounting. Your accounting allows for uniform facets. Tom Ruen 02:28, 20 September 2007 (UTC)

Edge path lengths?

I'm curious, does anyone know how many (vertex-edge-vertex) steps it takes to cross this polytope? For instance, the n-hypercube takes n steps, and the number of nodes a given distance away follows Pascal's triangle, so an 8-cube, with 256 vertices counts like this: 1 8 28 56 70 56 28 8 1. [1] An 8-cube has 1024 edges, while the e8 polytope has 6720 edges, so perhaps the path lengths are much smaller. The E5 polytope Demipenteract is an alternated penteract, which deletes have the vertices, so the path lengths also get cut in half, so perhaps the E8 is similar? Tom Ruen (talk) 01:51, 7 December 2007 (UTC)