Symplectic geometry and combinatorics have a very strong connection, due to the existence of Hamiltonian torus actions. Such actions come with a map, called moment map, which ``transforms" a compact symplectic manifold into a convex polytope. Hence many combinatorial properties of (some special types of) polytopes can be studied using symplectic techniques. In this talk I will focus on (smooth) reflexive polytopes of dimension 2 and 3, and explain the so called "12" and "24" phenomenon using symplectic geometry.