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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
##### Keywords:
visibility graph; associahedron; secondary polytope
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