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 
.
