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 \(P\), \((f_1+f_2)/(f_0+f_3)\). 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 \(\mathbb{R}^3\). We show that fatness is not bounded for the more general class of strongly regular CW decompositions of the 3-sphere.