On Fri, Sep 11, 2009 at 3:34 PM, <rcs@xmission.com> wrote:
Quoting Dan Asimov <dasimov@earthlink.net>: <snip>
But (as is well-known) a perfectly regular dodecahedron can be inscribed in a perfect cube with 3 pairs of opposite edge passing through the face centers of the 3 pairs of opposite faces, resp., of the cube.
Is there something similar connecting the regular icosahedron and the regular octahedron? It will have to be a little different, since 6|12 but 8~|20.
Rich
You can realize an icosahedron as the convex hull of six line segments that sit inside an octahedron -- the segments lie under its six vertices and their endpoints are on the icosahedron's edges, cutting them up in some golden-ratio-ish sort of way. --Michael -- Forewarned is worth an octopus in the bush.