Generalizing results from [MM1] referring to the intersection body $IK$ and the cross-section body $CK$ of a convex body $K \subset \sR^d, \, d \ge 2$, we prove theorems about maximal $k$-sections of convex bodies, $k \in \{1, \dots, d-1\}$, and, simultaneously, statements about common maximal $(d-1)$- and $1$-transversals of families of convex bodies.

MSC Classifications:

52A20, 55Mxx show english descriptions Convex sets in $n$ dimensions (including convex hypersurfaces) [See also 53A07, 53C45]
Classical topics {For the topology of Euclidean spaces and manifolds, see 57Nxx} 52A20 - Convex sets in $n$ dimensions (including convex hypersurfaces) [See also 53A07, 53C45]
55Mxx - Classical topics {For the topology of Euclidean spaces and manifolds, see 57Nxx}

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