Move a point
along a line from an initial point to a final point. It
traces out a line segment . When is translated from an initial
position to a final position, it traces out a parallelogram . When is translated, it traces
out a parallelepiped . The generalization of to dimensions is then called a parallelotope. has vertices and

s, where is a binomial coefficient
and ,
1, ...,
(Coxeter 1973). These are also the coefficients of .