Rhombs inscribed in spheres bounding strictly-convex regions

TL;DR

This paper extends the class of n-spheres known to inscribe an (n+1)-rhomb in a given direction, building on recent and earlier geometric work.

Contribution

It generalizes previous results on inscribed rhombs in spheres by incorporating recent advances and classical theorems.

Findings

Extended the class of spheres inscribing (n+1)-rhombs

Connected recent work of Fung with classical results of Hadwiger, Larman, and Mani

Provided new geometric conditions for inscribed rhombs in spheres

Abstract

We use some recent work of Fung and an earlier paper of Hadwiger, Larman and Mani to extend the class of $n$-spheres which are known to inscribe an $(n + 1)$-rhomb in a given direction.