David Eppstein - Publications

Publications with Greg Kuperberg

• Fat 4-polytopes and fatter 3-spheres.
  D. Eppstein, G. Kuperberg, and G. Ziegler.
  arXiv:math.CO/0204007.
  Discrete Geometry: In honor of W. Kuperberg's 60th birthday, Pure and Appl. Math. 253, Marcel Dekker, pp. 239–265, 2003.

  We introduce the fatness parameter of a 4-dimensional polytope P, (f₁+f₂)/(f₀+f₃). It is open whether all 4-polytopes have bounded fatness. We describe a hyperbolic geometry construction that produces 4-polytopes with fatness > 5.048, as well as the first infinite family of 2-simple, 2-simplicial 4-polytopes and an improved lower bound on the average kissing number of finite sphere packings in R³. We show that fatness is not bounded for the more general class of strongly regular CW decompositions of the 3-sphere.