Massive 3-loop Feynman diagrams reducible to SC* primitives of algebras ofthe sixth root of unity

In each of the 10 cases with propagators of unit or zero mass, the finite p art of the scalar 3-loop tetrahedral vacuum diagram is reduced to 4-letter words in the 7-letter alphabet of the 1-forms Omega := dz/z and w(p) := dz/ (lambda(-p) - z), where lambda is the sixth root of unity. Three diagrams y ield only zeta(Omega(3)w(0)) 1/90 pi(4) In two cases pi(4) combines with th e Euler-Zagier sum zeta(Omega(2)w(3)w(0)) = Sigma(m>n>0)(-l)(m+n)/m(3)n; in three cases it combines with the square of Clausen's Cl-2(pi/3) = F zeta(O mega w(1)) = Sigma(n>0) sin(pi n/3)/n(2). The case with 6 masses involves n o further constant; with 5 masses a Deligne-Euler-Zagier sum appears: R zet a(Omega(2)w(3)w(1)) = Sigma(m>n>0)(-1)(m) cos(2 pi n/3)/m(3)n. The previous ly unidentified term in the 3-loop rho-parameter of the standard model is m erely D-3 = 6 zeta(3) - 6Cl(2)(2)( pi/3) - 1/24 pi(4). The remarkable simpl icity of these results stems from two shuffle algebras: one for nested sums ; the other for iterated integrals. Each diagram evaluates to 10000 digits in seconds, because the primitive words are transformable to exponentially convergent single sums, as recently shown for zeta(3) and zeta(5), familiar in QCD. Those are SC*(2) constants, whose base of super-fast computation i s 2. Mass involves the novel base-3 set SC*(3). All 10 diagrams reduce to S C*(3)USC*(2) constants and their products. Only the B-mass case entails bot h bases.