Deployable　structures　based　on　rigid　mechanisms　are　unconventional　structures　that　can　achieve　transformations　from　compact　folded　states　to　fully　deployed　surfaces.　The　mechanisms　are　of　very　low　or　even　single　mobility,　making　the　deployment　process　simpler.　Such　structures　have　found　significant　applications　across　various　fields　such　as　architecture,　aerospace　engineering,　and　robotics.　Currently,　the　constituent　mechanisms　of　these　structures　often　come　with　symmetric　geometric　conditions,　thereby　yielding　symmetric　contours.　However,　this　symmetry　requirement　makes　it　less　desirable　for　specific　scenarios　where　more　generalised　shapes　are　required.　To　fill　the　gap,　this　paper　introduces　two　novel　asymmetric　deployable　structures　whose　outlines　can　be　arbitrary　triangles　based　on　the　Wohlhart　6R　linkage.　The　first　structure　is　made　from　rod　links,　capable　of　transforming　between　two　plane-like　states.　The　second　one　is　a　modified　version　that　incorporates　rigid　panels　of　uniform　thickness　as　links,　which　can　be　folded　from　a　long　triangular　prism　to　a　shorter　one.　Their　kinematic　behaviours　are　analyzed　in　detail　and　validated　by　physical　prototypes.　We　have　also　identified　viable　approaches　to　tessellating　both　structures　into　networks　for　large-scale　applications.　This　work　lays　a　crucial　step　towards　the　construction　of　asymmetric　deployable　structures　with　generalised　contours.　©　2025　Elsevier　Ltd