Title: A milestone for the solution to the lattice sphere covering problem in dimension n = 6.
Authors: Vallentin, Frank
Abstract: The complete classification of (primitive, generic) parallelohedra in a given dimension is a challenging computational task. Nearly 50 years have passed since the classification for the last dimension, n = 5, was completed. One application of such a classification is in solving the lattice sphere covering problem for the corresponding dimension. The paper by Dutour Sikirić & van Woerden [Acta Cryst. (2025), A81, https://doi.org/10.1107/S2053273324010143] marks a milestone in the classification effort for dimension n = 6. It provides a complete classification of all primitive iso‐edge domains; here primitive parallelohedra are identified based on their facet vectors.
Subjects: POLYHEDRA; CLASSIFICATION; SPHERES
Publication: Acta Crystallographica. Section A, Foundations & Advances, 2025, Vol 81, Issue 1, p5
ISSN: 2053-2733
Publication type: Academic Journal
DOI: 10.1107/S2053273324011513

A milestone for the solution to the lattice sphere covering problem in dimension n = 6.

Vallentin, Frank