Re: [math-fun] Embedding simplicial complexes in Euclidean space

Right, now I've got the problem straight ... On 11/23/06, Daniel Asimov <dasimov@earthlink.net> wrote:

Make a band of four equilateral triangles in the plane, forming a parallelogram.

Minor quibble --- it's irrelevant that they're equilateral, since the embedding is affine [good word, that!]

Now identify the left and right edges of the parallelogram, creating a simplicial complex K, containing four 2-simplices, that's topologcially a Moebius band.

But, as AL implicitly points out, this is not a complex --- denoting vertices along the top line by A,C,B and the bottom by B',D,A', the triangles CDA and CDA' coincide, as well as edges AB' and A'B. WFL