Three kinds of nonlinearly pi-conjugated hexadiazo compounds were obtained from the corresponding hexaketones for which cyclotrimerizaton of the ethynyl ketones to form 1,3,5-triaroylbenzenes and deoxygenation of a calix[6]arene were key steps. The diazo compounds were photolyzed in MTHF solid solutions at cryogenic temperatures to give the corresponding hexacarbenes 3, 4, and 5. Their magnetization data obtained on a Faraday magnetic balance were analyzed in terms of the Brillouin function. On the basis of these analyses, all the hexacarbenes were concluded to have tridecet (S = 6) ground states. The temperature dependence of their ESR fine structures obeyed Curie law at 10-50 K. As 3, 4, and 5 have 1,3,5-benzenetriyl, partially dendritic, and macrocyclic structures, respectively, it has most dramatically been demonstrated that it is not the shape or geometrical symmetry of the molecules but the topological symmetry, i.e., connectivity of the carbenic centers on the pi-cross-conjugated frameworks, which is most important in determining the spin multiplicity of the alternant hydrocarbon molecules. Some merits of these polycarbenes over the Linear structures are discussed.