Watched an interesting documentary on various phenomena that can be observed in the sky... And finally understood what exactly I photographed one summer morning in 2011 (see attached image).
That appeared to be a phenomenon caused by presence of certain hexagonal crystals of ice in the air. As the documentary stated, the column of light could be even more pronounced, with better-defined edges.
As House MD put it, "Trust me it's way cooler to know"...