  In this note we gather and review some facts about existence of toric spaces
over 3-dimensional simple polytopes. First, over every combinatorial 3-polytope
there exists a quasitoric manifold. Second, there exist combinatorial
3-polytopes, that do not correspond to any smooth projective toric variety. We
restate the proof of the second claim which does not refer to complicated
algebro-geometrical technique. If follows from these results that any fullerene
supports quasitoric manifolds but does not support smooth projective toric
varieties.

Algebraic Topology;Algebraic Geometry;Combinatorics