In the $\delta$-realization of $\operatorname{bsd}(T,T)$, the face of $\operatorname{bsd}(T,T)$ which corresponds to $(\tau,$$\mathfrak{T}$$)$ is the Minkowski sum $\delta\tau+(1-\delta)$$\mathfrak{T}$.

The $\delta$-realization of $\operatorname{bsd}(T,T)$ yields a cellular map $\mathfrak{d}^{\delta}\colon\operatorname{bsd}(T,T)\rightarrow T$, which maps $(\tau,$ $\mathfrak{T}$$)$ to $\tau$. (I.e., the small copy of $\tau$ in itself is stretched to full size, and the space between the small copies is collapsed into the smallest face.