The polyhedral linkage represents a unique multi-loop mechanism characterized by polyhedral layouts, enabling its global shape to be altered during deployment. While numerous single degree-of-freedom (DOF) deployable polyhedral linkages have been developed, only a handful have showcased reconfigurable properties. Inspired form the Wohlhart cube, we propose a family of single DOF reconfigurable polyhedrons by integrating planar link groups (PLGs) into the faces of the prisms. Kinematic analyses reveal that these polyhedral linkages can continuously bifurcate between expandable prism path, elongated prism path, and twist prism path through inherent kinematic bifurcation. Moreover, corresponding prototypes are fabricated to verify their kinematic properties. This work not only paves the way for the design of reconfigurable structures but also holds significant application potential in multifunctional scenarios such as deployable structures, morphing architectures, and tunable metamaterials.