  Perturbative quantum field theory for the Ising model at the three-loop level
yields a tetrahedral Feynman diagram C(a,b) with masses a and b and four other
lines with unit mass. The completely symmetric tetrahedron C^Tet \equiv C(1,1)
has been of interest from many points of view, with several representations and
conjectures having been given in the literature. We prove a conjectured
exponentially fast convergent sum for C(1,1), as well as a previously empirical
relation for C(1,1) as a remarkable difference of Clausen function values. Our
presentation includes Propositions extending the theory of the dilogarithm Li_2
and Clausen Cl_2 functions, as well as their relation to other special
functions of mathematical physics. The results strengthen connections between
Feynman diagram integrals, volumes in hyperbolic space, number theory, and
special functions and numbers, specifically including dilogarithms, Clausen
function values, and harmonic numbers.
