Summary

The most common associahedron is a polyhedron with nine faces: six pentagons and three quadrilaterals. Under the requirement that all nine faces be regular polygons, it is not possible to construct this associahedron, as pointed out in Eugenia Cheng's book "How to Bake Pi". Without regularity, then there are several constructions, such as those described in Casselman's 2007 AMS Feature Column (see www.ams.org/samplings/feature-column/fcarc-associahedra). The 3D object posted here has regular quadrilaterals (e.g. squares), and non-regular pentagons with vertical lines of symmetry. It was created based on an idea from Brigitte Servatius of Worcester Polytechnic Institute.