  In this paper we calculate the Ehrhart's polynomial associated with a
2-dimensional regular polytope (i.e. equilateral triangles) in $\mathbb Z^3$.
The polynomial takes a relatively simple form in terms of the coordinates of
the vertices of the polytope and it depends heavily on the value $d$ and its
divisors, where $d=\sqrt{\frac{a^2+b^2+c^2}{3}}$ and $(a,b,c)$
($\gcd(a,b,c)=1$) is a vector with integer coordinates normal to the plane
containing the triangle.

Number Theory;Combinatorics