  In each of the 10 cases with propagators of unit or zero mass, the finite
part 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 $\omega_p:=dz/
(\lambda^{-p}-z)$, where $\lambda$ is the sixth root of unity. Three diagrams
yield only $\zeta(\Omega^3\omega_0)=1/90\pi^4$. In two cases $\pi^4$ combines
with the Euler-Zagier sum $\zeta(\Omega^2\omega_3\omega_0)=\sum_{m>
n>0}(-1)^{m+n}/m^3n$; in three cases it combines with the square of Clausen's
$Cl_2(\pi/3)=\Im \zeta(\Omega\omega_1)=\sum_{n>0}\sin(\pi n/3)/n^2$. The case
with 6 masses involves no further constant; with 5 masses a
Deligne-Euler-Zagier sum appears: $\Re \zeta(\Omega^2\omega_3\omega_1)=
\sum_{m>n>0}(-1)^m\cos(2\pi n/3)/m^3n$. The previously unidentified term in the
3-loop rho-parameter of the standard model is merely $D_3=6\zeta(3)-6
Cl_2^2(\pi/3)-{1/24}\pi^4$. The remarkable simplicity of these results stems
from two shuffle algebras: one for nested sums; the other for iterated
integrals. Each diagram evaluates to 10 000 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 is 2. Mass involves
the novel base-3 set SC$^*(3)$. All 10 diagrams reduce to SC$^*(3)\cup$SC$^*
(2)$ constants and their products. Only the 6-mass case entails both bases.
