Subject: Re: flat triangulation of torus
Date: Fri, 23 Feb 2001 11:24:49 -0800 (PST)
From: Nick Halloway <snowe@rain.org>

Joanna Ellis-Monaghan <joellis@emba.uvm.edu>
> Does anyone know of work done in this area?  We would be particularly
> interested in a proof that there exist *any* polyhedron at all
> homeomorphic to an orientable surface, regardless of the genus, that can
> not be realized in 3-space by flat faces.  What happens if the faces are
> not constrained to be triangles?

Is the realizability in 3-space correlated to the amount of symmetry the
combinatorial polyhedron has -- size of symmetry group, vertex/face
transitive symmetry?  I think more symmetry may mean the triangulation
is easier to put in 3-space, so one might want to look at very
un-symmetric triangulations.