  Let $\mathscr T$ be a $2$-Calabi--Yau triangulated category, $T$ a cluster
tilting object with endomorphism algebra $\Gamma$. Consider the functor
$\mathscr T( T,- ) : \mathscr T \rightarrow \mod \Gamma$. It induces a
bijection from the isomorphism classes of cluster tilting objects to the
isomorphism classes of support $\tau$-tilting pairs. This is due to Adachi,
Iyama, and Reiten.
  The notion of $( d+2 )$-angulated categories is a higher analogue of
triangulated categories. We show a higher analogue of the above result, based
on the notion of maximal $\tau_d$-rigid pairs.
