Xiao Feng, Liping Yuan and Tudor Zamfirescu: Acute Triangulations of Archimedean Surfaces. The Truncated Tetrahedron, p.271-282

Abstract:

In this paper we prove that the surface of the regular truncated tetrahedron can be triangulated into 10 non-obtuse geodesic triangles, and also into 12 acute geodesic triangles. Furthermore, we show that both triangulations have minimal size.

Key Words: Archimedean surface, regular truncated tetrahedron, acute triangulation, cut locus.

2000 Mathematics Subject Classification: Primary: 52B10;
Secondary: 52B05, 53C45.

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