Acute and nonobtuse triangulations of polyhedral surfaces

In this paper, we prove the existence of acute triangulations for general polyhedral surfaces. We also show how to obtain nonobtuse subtriangulations of triangulated polyhedral surfaces.Massachusetts Institute of Technology (UROP Program

Acute Triangulations of the Cuboctahedral Surface

In this paper we prove that the surface of the cuboctahedron can be triangulated into 8 non-obtuse triangles and 12 acute triangles. Furthermore, we show that both bounds are the best possible.Comment: 16 pages, 8 figures, presented on CGGA201

A Dihedral Acute Triangulation of the Cube

It is shown that there exists a dihedral acute triangulation of the three-dimensional cube. The method of constructing the acute triangulation is described, and symmetries of the triangulation are discussed.Comment: Minor edits for journal version. Added some material to the introductio

Survey of two-dimensional acute triangulations

AbstractWe give a brief introduction to the topic of two-dimensional acute triangulations, mention results on related areas, survey existing achievements–with emphasis on recent activity–and list related open problems, both concrete and conceptual