I am very sorry for my question. Probably it was appreciated as naive and therefore as an off-topic. It is a fact that my domain - modal logics - is far of geometry and topology. The polyhedra are of interest for me as beautiful constructions and I am very thankful to Alex Degtyarev and David Speyer for their kind replies and competent answers.

I do not insist that it consisted of "normal" plane hexagons. The hexagons might be decomposed in triangles and respectively, the “general” form would be a sphere. In fact, I am interested if there exists a Buckminster-style construction avoiding pentagonal points. In such a construction more than 3 “curbed” hexagons would be joined at some points (eventually, 6k triangles). Which is your topological example? Vladimir