A fundamental result of toric geometry is that there is a bijection between toric varieties and fans. More generally, it is known that some class of manifolds having well-behaved torus actions can be classified in terms of combinatorial data containing simplicial complexes. In this study, we investigate the relationship between the toric objects over a simplicial complex and the complex obtained by polytopal wedge operation from the one. As an immediate corollary, we classify all real toric varieties with a few generators. Furthermore, we give simpler and complete proofs of classification and projectiveness of complex toric varieties with a few generators. This work is jointly with Hanchul Park.