The　paper　presents　a　kirigami　tessellation　based　on　two-fold　symmetric　Bricard　6R　linkage　and　spherical　4R　linkage.　The　mobility　and　kinematics　are　analysed　by　the　screw　theory.　The　tessellation　can　be　folded　to　cylindrical-like　structure　and　to　a　dense　polyhedral-like　tubular　structure　via　the　interference　between　the　sheets.　The　folding　property　of　the　tessellation　is　only　related　with　two　kinds　of　dihedral　angles　in　the　structures.　Hence,　it　is　potential　to　form　variable　sandwich　layers　which　work　with　one　DOF.　©　2022,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Switzerland　AG.