The　face　of　the　mortise-tenon　line　graphs　provide　important　information　for　reconstructing　its　3D　structure.　In　this　paper,　an　algorithm　is　used　to　identify　the　face　of　line　graphs.　The　geometric　properties　are　added　to　the　depth　first　algorithm　to　generate　the　loop　set,　using　backtrack　algorithm　to　find　the　optimal　solution　according　to　the　principle　that　the　edges　are　shared　by　two　faces,　which　contains　solution　of　special　mortise-tenon　structure.　©　2018,　Springer　International　Publishing　AG.