I suggest "quad." Yes, the term is traditionally associated with university campuses, but "campus" has expanded to non-academic settings, such as Googleplex and Apple Campus.

Kids are playing in the quad.

 

Where did you park the car? In the quad.

"Communal" sounds odd as a noun. "Common" (or Commons) could work. Think "Boston Common." But like plaza and square, "common" has a more public meaning, but that may be appropriate for a Russian/Soviet application.

noun

 

Often, commons. Chiefly New England. a tract of land owned or used jointly by the residents of a community, usually a central square or park in a city or town.

 

www.dictionary.com

I suggest "quad." Yes, the term is traditionally associated with university campuses, but "campus" has expanded to non-academic settings, such as Googleplex and Apple Campus.

Kids are playing in the quad.

Where did you park the car? In the quad.

"Communal" sounds odd as a noun. "Common" (or Commons) could work. Think "Boston Common." But like plaza and square, "common" has a more public meaning, but that may be appropriate for a Russian/Soviet application.

noun

16. Often, commons. Chiefly New England. a tract of land owned or used jointly by the residents of a community, usually a central square or park in a city or town.

www.dictionary.com