Parallelotope

1983 [North Holland/Elsevier], Robert S. Borden, A Course in Advanced Calculus, 1998, Dover, page 83, Suppose now that P is a k-dimensional parallelotope, 1<k<n, in Eⁿ.

1997, Daniel A. Klain, Gian-Carlo Rota, Introduction to Geometric Probability, Cambridge University Press, Accademia Nazionale dei Lincei, page 30, We develop next a theory of invariant valuations for the lattice of finite unions of orthogonal parallelotopes, having edgers parallel to a fixed frame. […] This follows from the basic fact that the intersection of two parallelotopes is a parallelotope.

It has 2ᵏ gyrovertices, k#43;1 of which are the gyropoints of S, and k 2#123;k-1#125; gyroedges, in full analogy with parallelotopes.