7 citations · 17 across the 9 of their papers we have counts for
10 papers · 1 filter
A new family of constant width bodies obtained from Reuleaux polyhedra
Marcela G. Mercado-Flores, Edgardo Roldán-Pensado
We give a construction of a body of constant width from a unit Reuleaux polyhedron that preserves all its symmetries. As opposed to the Meissner surgery, our construction modifies…
A four-dimensional body of constant width
Marcela G. Mercado-Flores, Miguel Raggi, Edgardo Roldán-Pensado
The study of bodies of constant width is a classical subject in convex geometry, with the 3-dimensional Meissner bodies being canonical examples. This paper presents a novel geomet…
On a Helly-type question for central symmetry
Alexey Garber, Edgardo Roldán-Pensado
We study a certain Helly-type question by Konrad Swanepoel. Assume that is a set of points such that every -subset of is in centrally symmetric convex position, is it tr…
Meissner Polyhedra
Luis Montejano, Edgardo Roldán-Pensado
In this paper we develop a concrete way to construct bodies of constant width in dimension three. They are constructed from special embeddings of self-dual graphs.
Helly numbers of Algebraic Subsets of
J. A. De Loera, R. N. La Haye, D. Oliveros +1
We study -convex sets, which are the geometric objects obtained as the intersection of the usual convex sets in with a proper subset . We con…
Measure Partitions Using Hyperplanes with Fixed Directions
Roman Karasev, Edgardo Roldán-Pensado, Pablo Soberón
We study nested partitions of obtained by successive cuts using hyperplanes with fixed directions. We establish the number of measures that can be split evenly simultaneously…