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).
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- Nearly-neighborly families
- Neighborly families
- Rods and frames
ASJC Scopus subject areas
- Geometry and Topology