Putting convex d-polytopes inside frames

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We introduce a construction of large neighborly and nearly-neighborly families of d-polytopes in Ed, obtained by putting smaller such families in rods, to form suitable frames for a larger collection. We use it to exhibit, among general results, a nearly-neighborly family, consisting of 9 × 4 d - 2 combinatorially d-boxes in Ed, for every d≥ 3 (like 36 3-boxes in E3) and a neighborly family of 3 × 2 d - 1 of prisms over d-simplices (like 12 triangular prisms in E3).

Original languageEnglish
Article number32
JournalJournal of Geometry
Issue number2
StatePublished - 1 Aug 2018

Bibliographical note

Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.


  • Nearly-neighborly families
  • Neighborly families
  • Rods and frames

ASJC Scopus subject areas

  • Geometry and Topology


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