Division of \(n\)-dimensional Euclidean space into circumscribed \(n\)-cuboids (Q2214287)

A theorem in the plane and an unproved statement in three-space by \textit{W. Böhm} [Arch. Math. 21, 326--330 (1970; Zbl 0201.53402)] are quoted here in the following way. Theorem 1.1. A division of the plane by lines into circumscribed quadrilaterals necessarily consists of tangent lines to a given conic. Theorem 1.2. A division of three-space by planes into circumscribed cuboids necessarily consists of three families of planes such that all planes in each family intersect along a line and the three lines obtained as the intersections of planes of these families are coplanar. The purpose of this paper is to give a proof of Theorem 1.2 and to extend it to higher dimensions. \{In the reviewer's opinion, a few more explicit definitions and explanations might have supported the understanding of the true content of the theorems and the proof.\}