## Parallelotope

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.