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Just as the associahedron corresponds to the lattice of subdivisions of a convex polygon, the cyclohedron corresponds to the lattice of centrally-symmetric subdivisions of a regular polygon with an even number of sides. This model represents a 3-dimensional shadow of the 4-dimensional cyclohedron. The 4-dimensional cyclohedron corresponds to centrally-symmetric subdivisions of a regular decagon, so one should expect some 5-fold symmetries. Indeed, this shadow has the property that it has a 2-dimensional shadow with 5-fold rotational symmetry.