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math.CO2021★ 1 cited
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.CO2021
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…