11 Aug
2017
11 Aug
'17
6:17 p.m.
On Friday, August 11, 2017, 5:04:38 PM PDT, Dan Asimov <dasimov@earthlink.net> wrote: Here is a one way to attack the n-dimensional case of regular polygons whose vertices lie in Z^n. Suppose there's a regular p-gon P, p in {3,4,5,...} with vertices in Z^n. If n >= p then R^p \sub R^n, so the standard basis vectors of R^p show that such a p-gon always exists. ----------------------------------------------------------------- But these standard basis vectors form a (p-1)-simplex, and for p>3, do not lie in a common 2-plane. For example, in Z^4, the basis vectors (1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1) form a tetrahedron. -- Gene