Smoothing of singular intersections of ellipsoids: pyramitoid

TL;DR

This paper explores smoothing techniques for 3D manifolds with singularities derived from ellipsoid intersections, introducing the concept of n-pyramitoid as a generalization of n-pyramid.

Contribution

It advances the understanding of smoothings of singular 3-manifolds from Coxeter orbifolds and introduces the new concept of n-pyramitoid.

Findings

Developed methods for smoothing singular intersections of ellipsoids.

Generalized the n-pyramid to n-pyramitoid.

Contributed to the study of 3-manifold topology and orbifold smoothings.

Abstract

The goal of this work is to continue the study the smoothings of 3-dimensional manifolds with singularities obtained as small covers of non simple right-angle Coxeter polyhedral orbifolds. They appear in the study of coaxial intersections of ellipsoids. In particular we introduce the concept of $n$-pyramitoid generalizing the $n$-pyramid.