parallelotope

English

Etymology

Blend of parallelogram +‎ polytope. Popularized by Canadian geometer H.S.M. Coxeter.

Noun

parallelotope (plural parallelotopes)

1. (geometry) A generalization of parallelogram and parallelepiped into a figure of arbitrary dimensionality.
   • 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 $E^{n}$.

   • 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.

   • 2015, Abraham Albert Ungar, Analytic Hyperbolic Geometry in N Dimensions‎^[1], Taylor & Francis (CRC Press), page 187:

     It has $2^{k}$ gyrovertices, $k+1$ of which are the gyropoints of $S$, and $k2^{k-1}$ gyroedges, in full analogy with parallelotopes.

Translations

generalization of parallelogram and parallelepiped

• French: parallélotope m
• German: Parallelotop n