  The recently discovered $d^*(2380)$ hexaquark is expected to be the lightest
member of an extended SU(3) antidecuplet of hexaquark states. The experimental
search for the other heavier and strange partners of the $d^*(2380)$ in the
antidecuplet is a challenging task. Evaluating the most appropriate
methodologies necessitates some understanding of the underlying properties of
the decuplet states such as mass, width and decay branches. In this paper we
provide estimates of these key properties for all decuplet states,
extrapolating from information and insights garnered for the $d^*(2380)$. The
predictions form a basis for the design of future discovery experiments.
