Rhombic embeddings of planar graphs with faces of degree 4

Details Rhombic embeddings of planar graphs with faces of degree 4 Rhombic embeddings of planar graphs with faces of degree 4

2003-05-27

arxiv.org/abs/math-ph/0305057v1

Trans. Amer. Math. Soc., 357 (2005), 3443-3458.

Physics

Mathematical Physics

11 pages, 3 figures

Scientific paper

Given a finite or infinite planar graph all of whose faces have degree 4, we
study embeddings in the plane in which all edges have length 1, that is, in
which every face is a rhombus. We give a necessary and sufficient condition for
the existence of such an embedding, as well as a description of the set of all
such embeddings.

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