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math.CO2026
Neighborly Murai spheres and the Simplicial Steinitz Problem
Ivan Limonchenko, AleÅ¡ VavpetiÄ
We provide a classification of neighborly Murai spheres, which implies that all of them are polytopal. Furthermore, we show that each neighborly -sphere with no more than …
math.CO2024
Simplicial vs. cubical spheres, polyhedral products and the Nevo-Petersen conjecture
Ivan Limonchenko, Rade ŽivaljeviÄ
We prove that a Murai sphere is flag if and only if it is a nerve complex of a flag nestohedron and classify all the polytopes arising in this way. Our classification implies that…