Fat Shellable Spheres

2025/09/25 by Joshua G. Hinman, Hinman, Joshua
Engineering · #Advanced Materials and Mechanics

paper · pdf · doi:10.48550/arxiv.2509.20771

Abstract

The fatness of a 4-polytope or 3-sphere is defined as (f₁+f₂-20)/(f₀+f₃-10). 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.

Citations

• Combining realization space models of polytopes
• The complete enumeration of 4-polytopes and 3-spheres with nine vertices
• Additive structures on f-vector sets of polytopes
• Small f-vectors of 3-spheres and of 4-polytopes
• New polytopes from products
• Face numbers of 4-Polytopes and 3-Spheres

Related

• Face numbers of 4-Polytopes and 3-Spheres
• Convex Polytopes: Extremal Constructions and f-Vector Shapes
• k-dimensional transversals for fat convex sets
• Projected Products of Polytopes
• Covering a reduced spherical body by a disk