This work is the first step towards proving that general planar polygonal networks can be constructed as patterns of carbon nanotubes. A subset of the planar polygonal networks, namely the trivalent planar networks, are studied. These patterns can be constructed from carbon nanotubes such that every intersection point of the networks is replaced with a carbon nanotube Y-junction. Accordingly the basic task is to show the basic connections of the carbon nanotube Y-junctions. The basic set of connected Y-junctions is defined and models of the structures are shown. Nanorings with two, three or more branches are constructed from two, three or more Y-junctions such that two tubes of every Y-junction are joined to the neighbouring tubes with the third tube being free. Because of the known, exceptional electronic behaviour of carbon nanotubes, combinations of basic elements of planar nanotube networks could motivate new experimental and theoretical works having the goal of finding the basic electronic tools for nanocircuits. © 2010 Elsevier B.V.