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arXiv · 2509.20771

Fat Shellable Spheres

Joshua Hinman
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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 $(Θ(n),Θ(nα(n)),Θ(nα(n)),Θ(n))$, where $α$ is the inverse Ackermann function.

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Joshua Hinman. 2025-09-25. Fat Shellable Spheres. https://arxiv.org/abs/2509.20771

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