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Perturbative quantum field theory for the Ising model at the three-loop levelyields a tetrahedral Feynman diagram C(a,b) with masses a and b and four otherlines 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 andconjectures having been given in the literature. We prove a conjecturedexponentially fast convergent sum for C(1,1), as well as a previously empiricalrelation for C(1,1) as a remarkable difference of Clausen function values. Ourpresentation includes Propositions extending the theory of the dilogarithm Li_2and Clausen Cl_2 functions, as well as their relation to other specialfunctions of mathematical physics. The results strengthen connections betweenFeynman diagram integrals, volumes in hyperbolic space, number theory, andspecial functions and numbers, specifically including dilogarithms, Clausenfunction values, and harmonic numbers.

On a three-dimensional symmetric Ising tetrahedron, and contributions to the theory of the dilogarithm and Clausen functions