J. Hinman

collaborators

3 papers

math.CO2025

Fat Shellable Spheres

Joshua Hinman

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 shel…

math.CO2025

Reconstructing Polytopes and Pseudomanifolds

Joshua Hinman

We prove that every 4-polytope is determined by its edge-polygon incidences, solving an open problem of GrÃ¼nbaum. For each $d \geq 3$ , we show that not every $d$ -polytope is deter…

math.CO2024

Face Numbers of Shellable CW Balls and Spheres

Joshua Hinman

Let $X$ be the boundary complex of a $(d + 1)$ -polytope, and let $I ¨ (d + 1, k) = \frac{1}{2} [(d - k ⌈( d + 1 ) /2 ⌉) + (d - k ⌊( d + 1 ) /2 ⌋)]$ . Rec…