On symmetric realizations of the simplicial complex of 3-crossing-free sets of diagonals of the octagon

Motivated by the question of the polytopal realizability of the simplicial complex n,k of (k + 1)-crossing-free sets of diagonals of the convex n-gon, we study the first open case, namely when n = 8 and k = 2. We give a complete description of the space of symmetric realizations of 8,2, that is, of the polytopes P whose boundary complex is isomorphic to 8,2, and such that the natural action of the dihedral group on 8,2 defines an action on P by isometry.

• Type: Journal
• Year: 2009
• Where: CCCG
• Authors: Jürgen Bokowski, Vincent Pilaud
• Keywords: CCCG 2009, Computational Geometry, Polytopal Realizability, Simplicial Complex, Symmetric Realizations