  The anticanonical complex has been introduced as a natural generalization of
the toric Fano polytope and so far has been succesfully used for the study of
varieties with a torus action of complexity one. In the present article we
enlarge the area of application of the anticanonical complex to varieties with
a torus action of higher complexity, for example, general arrangement
varieties. As an application of our techniques we classify the
three-dimensional canonical Fano intrinsic quadrics with automorphism group
having a maximal torus of dimension one.
