  The augmented Bergman complex of a matroid is a simplicial complex introduced
recently in work of Braden, Huh, Matherne, Proudfoot and Wang. It may be viewed
as a hybrid of two well-studied pure shellable simplicial complexes associated
to matroids: the independent set complex and Bergman complex.
  It is shown here that the augmented Bergman complex is also shellable, via
two different families of shelling orders. Furthermore, comparing the
description of its homotopy type induced from the two shellings re-interprets a
known convolution formula counting bases of the matroid. The representation of
the automorphism group of the matroid on the homology of the augmented Bergman
complex turns out to have a surprisingly simple description. This last fact is
generalized to closures beyond those coming from a matroid.
