  We introduce and investigate the class of skeletally Dugundji spaces as a
skeletal analogue of Dugundji space. The main result states that the following
conditions are equivalent for a given space $X$: (i) $X$ is skeletally
Dugundji; (ii) Every compactification of $X$ is co-absolute to a Dugundji
space; (iii) Every $C^*$-embedding of the absolute $p(X)$ in another space is
strongly $\pi$-regular; (iv) $X$ has a multiplicative lattice in the sense of
Shchepin \cite{s76} consisting of skeletal maps.
