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math.MG2026
The lattice covering density of the regular octahedron
Yanlu Lian, Fei Xue
We prove that the lattice covering density of the regular octahedron is , settling a conjecture of Dougherty and Faber.
math.MG2026
Non-Separable Homothetic Triangles, Part I: Constructions and Lower Bounds
Yanlu Lian, Fei Xue, Qihui Yuan
A finite family of planar convex bodies is called a non-separable family if no line disjoint from its union has at least one member in each open half-plane. In this paper, we prove…
math.MG2026
Minimal Covering Bodies and a Minkowski-Type Criterion for Lattice Coverings
Yanlu Lian, Fei Xue
We study convex bodies whose translates by a fixed lattice cover space and for which every proper convex subbody loses this property. In three dimensions, the convex hull of indepe…