Putting convex d-polytopes inside frames

Joseph Zaks

doi:10.1007/s00022-018-0433-3

Putting convex d-polytopes inside frames

Joseph Zaks

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce a construction of large neighborly and nearly-neighborly families of d-polytopes in E^d, 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 E^d, 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 language	English
Article number	32
Journal	Journal of Geometry
Volume	109
Issue number	2
DOIs	https://doi.org/10.1007/s00022-018-0433-3
State	Published - 1 Aug 2018

Bibliographical note

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

Keywords

Nearly-neighborly families
Neighborly families
Rods and frames

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s00022-018-0433-3

Cite this

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abstract = "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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AB - 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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Putting convex d-polytopes inside frames

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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