  In this paper we derive from arguments of string scattering a set of eight
tetrahedron equations, with different index orderings. It is argued that this
system of equations is the proper system that represents integrable structures
in three dimensions generalising the Yang-Baxter equation. Under additional
restrictions this system reduces to the usual tetrahedron equation in the
vertex form. Most known solutions fall under this class, but it is by no means
necessary. Comparison is made with the work on braided monoidal 2-categories
also leading to eight tetrahedron equations.
