  We study one and two-loop triangle integrals with massless propagators and
all external legs off shell. We show that there is a kinematic region where the
results can be expressed in terms of a basis of single-valued polylogarithms in
one complex variable. The relevant space of single-valued functions can be
determined a priori and the results take strikingly a simple and compact form
when written in terms of this basis. We study the properties of the basis
functions and illustrate how one can easily analytically continue our results
to all kinematic regions where the external masses have the same sign.
