2 citations · 3 across the 5 of their papers we have counts for
4 papers · 1 filter
Regular polytopes, sphere packings and Apollonian sections
Iván Rasskin
In this paper, we explore the geometry and the arithmetic of a family of polytopal sphere packings induced by regular polytopes in any dimension. We prove that every integral polyt…
A polytopal generalization of Apollonian packings and Descartes' theorem
Jorge L. Ramírez Alfonsín, Iván Rasskin
We present a generalization of Descartes' theorem for the family of polytopal sphere packings arising from uniform polytopes. The corresponding quadratic equation is expressed in t…
Ball packings for links
Jorge Luis Ramírez Alfonsín, Ivan Rasskin
The ball number of a link , denoted by , is the minimum number of solid balls (not necessarily of the same size) needed to realize a necklace representing . In this…
Self-dual Maps I : antipodality
Luis Montejano, Jorge L. Ramírez Alfonsín, Ivan Rasskin
A self-dual map is said to be \emph{antipodally self-dual} if the dual map is antipodal embedded in with respect to . In this paper, we investigate nece…