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math.CO2023
Borsuk and Vázsonyi problems through Reuleaux polyhedra
Gyivan Lopez-Campos, Deborah Oliveros, Jorge L. Ramírez Alfonsín
The Borsuk conjecture and the Vázsonyi problem are two attractive and famous questions in discrete and combinatorial geometry, both based on the notion of diameter of a bounded set…
math.GT2023
Links in orthoplicial Apollonian packings
Jorge L. Ramírez Alfonsín, 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…