A k-transversal to a family of sets in $$\mathbb {R}^d$$ is k-dimensional affine subspace that intersects each set the family. In 1957 Hadwiger provided necessary and sufficient condition for pairwise disjoint, planar convex have 1-transversal. After series three papers among authors Goodman, Pollack, Wenger from 1988 1990, Hadwiger’s Theorem was extended conditions $$(d-1)$$ -transversals fini...