  This work deals with two types of Feynman integrals in perturbative quantum
field theory: the 2-loop 2-point kite, with 5 arbitrary internal masses, and
its completion by a sixth propagator, to give a 3-loop tetrahedral tadpole,
with 6 arbitrary masses. These general-mass cases cover broken and unbroken
gauge theories, based on the Lie algebras U(1), SU(2) and SU(3), for the
electromagnetic, weak and strong interactions. The elliptic substructure of
these integrals should not be regarded as an obstruction. Rather, it is a
bonus, thanks to the arithmetic-geometric mean of Gauss. Compact formulae are
given, to handle all cases. Zero-mass limits are carefully considered.
Anomalous thresholds of triangles in the kite pose no problem. The number
theory of tadpoles is investigated, with intriguing results.
