Zonotope

A zonotope is a Minkowski sum of finitely many line segments, equivalently an affine map image of a cube. For vectors ${\xi }_j$, the set ${\sum }_j[0,1]{\xi }_j$ is the support of the associated box spline. A centred version uses $[-1/2,1/2]{\xi }_j$ instead. In two dimensions, sums of differently directed segments give centrally symmetric polygons; repeated directions lengthen their corresponding edges without adding new edge directions.