Fat Shellable Spheres

Abstract

The fatness of a 4-polytope or 3-sphere is defined as $(f_1+f_2-20)/(f_0+f_3-10)$. We construct arbitrarily fat, strongly regular CW 3-spheres that are both shellable and dual shellable. These spheres have $f$-vectors $(\hat{I}˜(n),\hat{I}˜(n\hat{I}\pm (n)),\hat{I}˜(n\hat{I}\pm (n)),\hat{I}˜(n))$, where $\hat{I}\pm$ is the inverse Ackermann function.

30 pages, 6 figures