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Deformations of associahedra and visibility graphs. (English) Zbl 1317.52018
Summary: Given an arbitrary polygon \(P\) with holes, we construct a polytopal complex analogous to the associahedron based on its convex diagonalizations of \(P\). This polytopal complex is shown to be contractible, and a geometric realization is provided based on the theory of secondary polytopes. We then reformulate a combinatorial deformation theory and present an open problem based on visibility which is a close cousin to the Carpenter’s rule theorem of compitational geometry.

MSC:
52B11 \(n\)-dimensional polytopes
57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
68R05 Combinatorics in computer science
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