3 papers
math.MG2025
On Dense Tetrahedra in Binary Sphere Packings
Thomas Fernique, Daria Pchelina
This paper considers the density of tetrahedra arising in a specific decomposition of packings of unequal spheres in . It aims to extend a bound obtained in 2D in the…
cs.CG2022
Density of triangulated ternary disc packings
Thomas Fernique, Daria Pchelina
We consider ternary disc packings of the plane, i.e. the packings using discs of three different radii. Packings in which each ''hole'' is bounded by three pairwise tangent discs a…
math.MG2021
Compact Packings are not always the Densest
Thomas Fernique, Daria Pchelina
We provide a counterexample to a conjecture by B. Connelly about density of circle packings