An integrated type synthesis method for polyhedral mechanisms based on polyhedron is proposed. The properties of the polyhedron are considered and the corresponding generalized mechanism is built based on strategies that geometric components are regarded as construction members. Topological graph and configuration matrix are used to describe the generalized mechanism. The target mechanism and its descriptions are obtained from the generalized mechanism via designing the construction members appropriately. Possible types are then enumerated using set operations according to the configuration matrix. The axes of the kinematic pairs are set based on the geometric properties of the polyhedron. Degrees-of-freedom (DOFs) of those possible types are calculated using the modified G–K criterion based on screw theory, and the type synthesis results with DOF more than 0 are obtained. Tetrahedral mechanisms with revolute and sliding pairs are synthesized, and they have 135 configuration results with lower-mobility, which validates the accuracy and effectiveness of the proposed method. Some application examples of the tetrahedral mechanisms are further illustrated for potential values of synthesized mechanisms in robot field.