I still have B M Stewart's book, Adventures among the toroids, which is conspicuous for its size (13" X 5" X .75"), it stands out, or rather up, in any book case. The subtitle is A study of ORIENTABLE POLYHEDRA with REGULAR FACES. Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Sat, May 23, 2020 at 1:08 PM Adam P. Goucher <apgoucher@gmx.com> wrote:
For n >= 6, you can take a Császár polyhedron sharing the vertex-set (and indeed edge-set) with a regular 7-vertex simplex.
The problems for n in {3, 4, 5} are certainly interesting!
-- APG.
Sent: Saturday, May 23, 2020 at 4:48 PM From: "Dan Asimov" <dasimov@earthlink.net> To: "math-fun" <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Can an equilateral toroidal polyhedron
----- have fewer than 32 faces? —rwg -----
If it's not embedded anywhere, it can have just two faces.
If it's embedded in n-space for fixed n, this is a terrific question!
(Likewise for other surfaces, like the Klein bottle.)
—Dan
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