DNA　catenanes　are　assemblies　made　up　of　two　or　more　DNA　rings　linked　together　through　mechanical　bonds,　and　they　are　desirable　for　engineering　unique　nanoscale　devices.　However,　current　methods　of　synthesizing　DNA　catenanes　rely　on　the　formation　of　strong　linking　duplexes　between　component　units　to　enable　interlocking　and　thus　do　not　permit　the　synthesis　of　complex　single-stranded　DNA　structures　with　freely　functioning　units.　We　have　recently　reported　DNA　sequences　that　can　thread　through　a　DNA　circle　without　the　formation　of　a　linking　duplex.　Here　we　show　that　these　unique　DNA　molecules　can　be　further　used　to　make　intricate　symmetric　or　asymmetric　DNA　[3]catenanes,　single-stranded　DNA　assemblies　made　up　of　a　central　mother　ring　interlocked　to　two　identical　or　fraternal　twin　daughter　rings,　which　have　never　been　reported　before.　These　addressable　freely　functioning　interlocked　DNA　rings　should　facilitate　the　design　of　elaborate　nanoscale　machines　based　on　DNA.