engleski

Periodic Triangulations of Zn

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.

Polytope ; Triangulations ; Periodic ; Enumeration

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