  The $\mathit{SU}(3)$ tensor multiplicities are piecewise polynomial of degree
$1$ in their labels. The pieces are the chambers of a complex of cones. We
describe in detail this chamber complex and determine the group of all linear
symmetries (of order $144$) for these tensor multiplicities. We represent the
cells by diagrams showing clearly the inclusions as well as the actions of the
group of symmetries and of its remarkable subgroups.
