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The hexabasic book is the cone of the 1-dimensional skeleton of the union oftwo tetrahedra glued along a common face. The universal 3-dimensionalpolyhedron UP is the product of a segment and the hexabasic book. We show thatany 2-dimensional link in 4-space is isotopic to a surface in UP. The proof isbased on a representation of surfaces in 4-space by marked graphs, links withdouble intersections in 3-space. We construct a finitely presented semigroupwhose central elements uniquely encode all isotopy classes of 2-dimensionallinks.

All 2-dimensional links in 4-space live inside a universal 3-dimensional polyhedron