  When Daan Krammer and Stephen Bigelow independently proved that braid groups
are linear, they used the Lawrence-Krammer-Bigelow representation for generic
values of its variables q and t. The t variable is closely connected to the
traditional Garside structure of the braid group and plays a major role in
Krammer's algebraic proof. The q variable, associated with the dual Garside
structure of the braid group, has received less attention.
  In this article we give a geometric interpretation of the q portion of the
LKB representation in terms of an action of the braid group on the space of
non-degenerate euclidean simplices. In our interpretation, braid group elements
act by systematically reshaping (and relabeling) euclidean simplices. The
reshapings associated to the simple elements in the dual Garside structure of
the braid group are of an especially elementary type that we call relabeling
and rescaling.
