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.