Periodic Triangulations of Zn

Dutour Sikirić, Mathieu; Garber, Alexey (2020) Periodic Triangulations of Zn. Electronic journal of combinatorics, 27 . pp. 1-19. ISSN 1077-8926

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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. Other important property is the regularity and central-symmetry property of triangulations. Full enumeration for dimension at most 4 is obtained. 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 an infinity of possible adjacent simplices. We found 950 periodic triangulations in dimension 5 but finiteness is unknown.

Item Type:	Article
Uncontrolled Keywords:	Polytope ; Triangulations ; Periodic ; Enumeration
Subjects:	NATURAL SCIENCES > Mathematics
Divisions:	Division for Marine and Enviromental Research
Depositing User:	Mathieu Dutour
Date Deposited:	08 Dec 2020 14:24
URI:	http://fulir.irb.hr/id/eprint/6105
DOI:	10.37236/8298

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