Move a point along a Line for 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 -D is then called a
parallelotope. has vertices and

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

**References**

Coxeter, H. S. M. *Regular Polytopes, 3rd ed.* New York: Dover, pp. 122-123, 1973.

Klee, V. and Wagon, S. *Old and New Unsolved Problems in Plane Geometry and Number Theory.*
Washington, DC: Math. Assoc. Amer., 1991.

Zaks, J. ``Neighborly Families of Congruent Convex Polytopes.'' *Amer. Math. Monthly* **94**, 151-155, 1987.

© 1996-9

1999-05-26