Abstract. In 3 dimensions, the Ising model is in the same universality class as -theory, whose massive 3- loop tetrahedral diagram, , was of an unknown analytical nature. In contrast, all single-scale 4-dimensional tetrahedra were reduced, in hep-th/9803091, to special values of exponentially convergent polylogarithms. Combining dispersion relations with the integer-relation finder PSLQ, we find that , with and . This empirical relation has been checked at 1,000-digit precision and readily yields 50,000 digits of , after transformation to an exponentially convergent sum, akin to those studied in math.CA/9803067. It appears that this 3-dimensional result entails a polylogarithmic ladder beginning with the classical formula for , in the manner that 4-dimensional results build on that for .