3 papers
math.CO2025
On colourings of cubic lattices
Igor A. Baburin
Given the integral lattice in -dimensional Euclidean space, partitions of the lattice nodes into orbits of finite-index subgroups of have been computed for $d \…
math.GR2025
Short presentations for crystallographic groups
Igor A. Baburin
A practical approach is proposed to construct short presentations for Euclidean crystallographic groups in terms of generators and relations. For our purposes a short presentation…
math.GT2019
Isotopy classes of 3-periodic net embeddings
Igor Baburin, Stephen Power, Davide Proserpio
Entangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type. We obtain periodi…