Pick's Theorem in Two-Dimensional Subspace of ℝ(3)

In the Euclidean space ℝ(3), denote the set of all points with integer coordinate by ℤ(3). For any two-dimensional simple lattice polygon P, we establish the following analogy version of Pick's Theorem, k(I(P) + (1/2)B(P) − 1), where B(P) is the number of lattice points on the boundary of P in ℤ(3), I(P) is the number of lattice points in the interior of P in ℤ(3), and k is a constant only related to the two-dimensional subspace including P.