Associahedron Shadows

This represents a 3-dimensional shadow of a 4-dimensional associahedron, also known as the Stasheff polytope.  The face lattice of this polytope coincides with the lattice of subdivisions of a convex heptagon without adjoining new vertices.  This particular realization of the associahedron has a 2-dimensional shadow whose symmetry group is the dihedral group of order 14.  This was achieved by realizing the polytope as a fiber polytope of projecting a regular 6-dimensional simplex to a regular heptagon and then subsequently projecting to 3-dimensional space.