Iron Associahedron

Created when the three pentagons on the top and the three pentagons on the bottom of the dodecahedron are joined so as to form the figure called an associahedron. Instead of thinking of it as a solid, one can consider just the vertices and edges as a graph drawn in space. This three dimensional graph occurs in several parts of mathematics, including the theory of cluster algebras, where it is the exchange graph for the triangulations of a hexagon.https://orb.binghamton.edu/mathematical_sculptures/1059/thumbnail.jp