#### Document Type

Article

#### Publication Date

2013

#### Publication Title

Centre for Discrete Mathematics and Computing

#### Abstract

In this paper we calculate the Ehrhart’s polynomial associated with a 2-dimensional regular polytope (i.e. equilateral triangles) in Z3. The polynomial takes a relatively simple form in terms of the coordinates of the vertices of the triangle. We give some equivalent formula in terms of a parametrization of these objects which allows one to construct equilateral triangles with given properties. In particular, we show that given a prime number p which is equal to 1 or −5 (mod 8), there exists an equilateral triangle with integer coordinates whose Ehrhart polynomial is L(t) = (pt + 2)(t + 1)/2, t ∈ N.

#### Recommended Citation

Ionascu, Eugen J., "Ehrhart's Polynomial for Equilateral Triangles in Z3" (2013). *Faculty Bibliography*. 388.

https://csuepress.columbusstate.edu/bibliography_faculty/388