  In the present paper we investigate geometric characteristics of compact
metric spaces, which can be described in terms of Gromov-Hausdorff distances to
simplexes, i.e., to finite metric spaces such that all their nonzero distances
are equal to each other. It turns out that these Gromov-Hausdorff distances
depend on some geometrical characteristics of finite partitions of the compact
metric spaces; some of the characteristics can be considered as a natural
analogue of the lengths of edges of minimum spanning trees. As a consequence,
we constructed an unexpected example of a continuum family of pairwise
non-isometric finite metric spaces with the same distances to all simplexes.
