3 papers
math.CO2025
A polytopal generalization of Apollonian packings and Descartes' theorem
Jorge L. RamÃrez AlfonsÃn, 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…
math.CO2024
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…
math.GT2024
Links in orthoplicial Apollonian packings
Jorge L. RamÃrez AlfonsÃn, Iván Rasskin
In this paper, we establish a connection between Apollonian packings and knot theory. We introduce new representations of links realized in the tangency graph of the regular crysta…