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

• Jürgen Bokowski ^[2] ; Vincent Pilaud ^[1]
  1. [1] École Normale Supérieure

     École Normale Supérieure

     Francia

     
  2. [2] Technische Universität
• Localización: XIII Encuentros de Geometría Computacional: Zaragoza, del 29 de junio al 1 de julio de 2009 / Alfredo García Olaverri (ed. lit.) , Javier Tejel Altarriba (ed. lit.) , 2009, ISBN 978-84-92774-11-1, págs. 83-90
• Idioma: inglés
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• Resumen

  • Motivated by the question of the polytopal realizability of the simplicial complex Γn,k of (k + 1)-crossing-free sets of diagonals of the convex n-gon, we study the first non-obvious case, namely the simplicial complex Γ8,2 of 3-crossing-free sets of diagonals of the convex octagon. We give a complete description of the space of symmetric realizations of Γ8,2, that is, of the polytopes P whose boundary complex is isomorphic to Γ8,2, and such that the natural action of the dihedral group on Γ8,2 defines an action on P by isometry.