3
votes
0answers
120 views

n-dimensional Delaunay Triangulation of Lattices

I have several questions concerning the Delaunay triangulation of a high dimensional lattice. Given an $n$-dimensional lattice $L$ and its Delaunay triangulation (partition of $R^n$ into simplices ...
9
votes
0answers
288 views

How small parallelograms are we guaranteed to get, when we select the two sides from different plane lattices?

Title question description: Select two lattices $\Lambda_1$ and $\Lambda_2$ (here a lattice=additive free abelian group without accumulation points) of maximal rank two in the real plane. We normalize ...
20
votes
1answer
469 views

Voronoi cell of lattices with the same profile

Definition 1. Given a body $V$ in $\mathbb R^n$, the function $p_V\colon \mathbb R_+\to \mathbb R_+$ $$p_V(r)=\mathop{\rm vol} [V\cap B_r(0)]$$ will be called profile of $V$. Definition 2. Define ...