Cleaved Abstract Polytopes

Abstract

From a given abstract n-polytope P and a given integer k we derive two abstract polytopes Clk(P) and \({\widetilde {Cl}_k}\left( P \right)\) of ranks n and n−1, respectively. These constructions generalise the truncation of convex polyhedra and the dual of a geometric construction yielding Petrie’s polyhedron {4,6|4}. We determine sufficient and necessary conditions to guarantee that Clk(P) and \({\widetilde {Cl}_k}\left( P \right)\) are regular.

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Correspondence to Daniel Pellicer.

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Pellicer, D. Cleaved Abstract Polytopes. Combinatorica 38, 709–737 (2018). https://doi.org/10.1007/s00493-016-3518-3

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Mathematics Subject Classification (2000)

  • 06A07
  • 06A11
  • 05E45
  • 52B70
  • 52B15