Ehrhart's polynomial for equilateral triangles in Z³

الأصل · EN

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 polytope and it depends heavily on the value d and its divisors, where d=√a²+b²+c²/3 and (a,b,c) ((a,b,c)=1) is a vector with integer coordinates normal to the plane containing the triangle.