Closed string field theory from polyhedra

A fully nonpolynomial framework for closed string field theory is studied. All interactions are geometrical, the pattern of string overlaps gives polyhedra with equal perimeter faces and three edges at each vertex. All interactions are cubic in the sense that at most three strings can coincide at a point. The three point vertex used is that of Witten which is seen to be quite natural in the framework of quadratic differentials and to induce a very symmetric decomposition of moduli space. copyright 1989 Academic Press, Inc