The　Bennett　linkage　has　been　proposed　as　a　building　block　of　deployable　structures　as　it　can　generate　desirable　spatial　motions　with　the　least　number　of　links.　However,　these　deployable　structures　are　based　on　the　tiling　of　Bennett　linkages.　No　spatial　assembly　of　Bennett　linkages　has　been　developed　to　form　any　transformation　between　regular　and　semi-regular　polyhedrons.　In　this　paper,　we　propose　a　new　type　of　mobile　assembly　consisting　of　a　pair　of　Bennett　linkages　connected　by　four　spherical　joints.　We　show　that　this　particular　assembly　can　be　used　to　construct　transformable　polyhedrons.　Using　an　alternative　form　of　such　assembly,　a　polyhedral　transformation　between　cuboctahedron　and　octahedron　with　one　degree　of　freedom　is　realised.　The　axes　of　the　revolute　joints　within　the　Bennett　linkages　are　determined　by　the　geometrical　relationship　between　the　deployed　geometry　and　the　folded　one.　The　transformation　between　two　polyhedral　shapes　has　no　bifurcation　which　is　proven　through　kinematic　analysis　and　demonstrated　by　a　physical　model.　This　transformable　polyhedron　has　great　potential　for　the　aerospace　applications　where　transportability　and　protection　of　payload　are　critical　design　features.　(C)　2019　Elsevier　Ltd.　All　rights　reserved.