Periodic triangulations of Zn

Authors

Mathieu Dutour Sikiric
Alexey Garber, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

5-2020

Abstract

We consider in this work triangulations of Z n that are periodic along Z n . They generalize the triangulations obtained from Delaunay tessellations of lattices. In certain cases we impose additional restrictions on such triangulations such as regularity or invariance under central symmetry with respect to the origin; both properties hold for Delaunay tessellations of lattices. Full enumeration of such periodic triangulations is obtained for dimension at most 4 . In dimension 5 several new phenomena happen: there are centrally-symmetric triangulations that are not Delaunay, there are non-regular triangulations (it could happen in dimension 4 ) and a given simplex has a priori infinitely many possible adjacent simplices. We found 950 periodic triangulations in dimension 5 but finiteness of the whole family is unknown.

Comments

Original published version available at https://doi.org/10.37236/8298

Recommended Citation

Sikirić, Mathieu Dutour, and Alexey Garber. 2020. “Periodic Triangulations of Zn.” The Electronic Journal of Combinatorics 27 (2): P2.36. https://doi.org/10.37236/8298.

Creative Commons License

This work is licensed under a Creative Commons Attribution-No Derivative Works 4.0 International License.

Publication Title

The Electronic Journal of Combinatorics

DOI

10.37236/8298