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  • $\begingroup$ In Mathematica 10.1 I believe you can just do pts = CirclePoints[8]. $\endgroup$ Commented Sep 26, 2015 at 5:31
  • $\begingroup$ The basic polytopes, up to 12 edges, are defined in Mathematica by their names. E.g. for an octagon you first execute Needs["Polytopes`"]. The Vertices[Octagon] gives the coordinates and NumberOfEdges[Octagon] the number of edges. $\endgroup$ Commented Sep 26, 2015 at 6:43