Acute Triangulation of Constant Curvature Polygonal Complexes

TL;DR

This paper proves that any 2D polygonal complex with polygons of constant curvature can be triangulated with only acute simplices, regardless of finiteness or local finiteness.

Contribution

It establishes the existence of acute triangulations for a broad class of 2D complexes with constant curvature polygons, extending previous results.

Findings

Every such complex admits an acute triangulation.

No finiteness or local finiteness restrictions are needed.

The result applies to complexes with finitely many isometry classes of polygons.

Abstract

We prove that every 2-dimensional polygonal complex, where each polygon is given a constant curvature metric and belongs to one of finitely many isometry classes can be triangulated using only acute simplices. There is no requirement on the complex to be finite or even locally finite.