  A perfect (Delaunay) ellipsoid is an ellipsoid in n-dimensional Euclidean
space that does not contain integral points in its interior, but is uniquely
defined by integral points that lie on its surface. A perfect Delaunay polytope
with respect to a positive quadratic form f() is a polytope with integral
vertices that is circumscribed by a perfect Delaunay ellipsoid with an equation
whose quadratic part is f(). This document has been corrected on January 15,
2005. Note that it represents the state of the area as of the end of 2002. For
recent research on perfect Delaunay polytopes see my recent preprint, with
Erdahl and Ordine, math.NT/0408122 on ArXiv.org .
