Arbitrarily Large Neighborly Families of Congruent Symmetric Convex 3-Polytopes

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dc.creatorErickson, Jeff
dc.date2001-06-12
dc.date.accessioned2026-07-07T04:42:07Z
dc.date.available2026-07-07T04:42:07Z
dc.descriptionWe construct, for any positive integer n, a family of n congruent convex polyhedra in R^3, such that every pair intersects in a common facet. Previously, the largest such family contained only eight polytopes. Our polyhedra are Voronoi regions of evenly distributed points on the helix (t, cos t, sin t). With a simple modification, we can ensure that each polyhedron in the family has a point, a line, and a plane of symmetry. We also generalize our construction to higher dimensions and introduce a new family of cyclic polytopes.
dc.description9 pages, 5 figures
dc.identifierhttps://arxiv.org/abs/math/0106095
dc.identifierhttp://arxiv.org/abs/math/0106095
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61638
dc.subjectCombinatorics
dc.subjectMetric Geometry
dc.subject52B05 (52B10, 52B12)
dc.titleArbitrarily Large Neighborly Families of Congruent Symmetric Convex 3-Polytopes
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