  We compute three families of two-loop six-point massless Feynman integrals in
dimensional regularization, namely the double-box, the pentagon-triangle, and
the hegaxon-bubble family. This constitutes the first analytic computation of
two-loop master integrals with eight scales. We use the method of canonical
differential equations. We describe the corresponding integral basis with
uniform transcendentality, the relevant function alphabet, and analytic
boundary values at a particular point in the Euclidean region up to the fourth
order in the regularization parameter $\epsilon$. The results are expressed as
one-fold integrals over classical polylogarithms suitable for fast and
high-precision evaluation.
