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

Make a band of four equilateral triangles in the plane, forming a parallelogram. 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. For all n, there is no topological embedding h: K -> R^n such that h is affine on simplices. (Exercise: prove this.) That settles one question. --Dan