Associahedron

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The most prevalent associahedron is a polyhedron boasting nine faces: six pentagons and three quadrilaterals. Under the stipulation that all nine faces be regular polygons, it proves impossible to construct this associahedron, as Eugenia Cheng's book "How to Bake Pi" aptly highlights. Without demanding regularity, multiple constructions arise, such as those outlined in Casselman's 2007 AMS Feature Column (visit www.ams.org/samplings/feature-column/fcarc-associahedra). The three-dimensional object displayed here features regular quadrilaterals (e.g., squares) and non-regular pentagons with vertical lines of symmetry. It was designed based on an idea from Brigitte Servatius at Worcester Polytechnic Institute.