Deployable polyhedral grippers can approach the target when deployed, then enclose and capture the targets at the folded state. These grippers have attracted increasing attention for their priority in noncontact capturing missions, including the capture of spatial non-cooperative targets and delicate marine organisms. Enrichment of the relevant grippers can benefit the conduction of various capturing tasks, including the capture of spatial non-cooperative targets and delicate marine organisms. In this paper, novel one-DOF deployable polyhedral grippers able to conduct diverse capturing motions are presented, which adopt different polyhedrons and deployment diagrams. A design flow is proposed for the structural designs of these deployable polyhedral grippers, in which the core problem during the gripper construction is reducible to the structural designs and combination of multiple synchronously deployable modules. Type synthesis as well as the mobility and kinematic analysis of the synchronously deployable modules are conducted. As examples, the designs of four deployable polyhedral grippers based on different polyhedrons and deployment diagrams are presented, and the prototype of a one-DOF deployable polyhedral gripper based on a regular dodecahedron is fabricated to demonstrate the feasibility of the design. Based on the work presented in this paper, potential candidates can be provided for the noncontact capturing missions in space science and marine biology.