parallelotope

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 ${\\displaystyle P}$ is a ${\\displaystyle k}$-dimensional parallelotope, ${\\displaystyle 1<k<n}$, in ${\\displaystyle E^{n}}$.

   • 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, Taylor & Francis (CRC Press), page 187,

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

Translations

generalization of parallelogram and parallelepiped

French: parallélotope m German: Parallelotop n