Acute triangulations of the regular icosahedral surface.(English)Zbl 1062.51014

The authors prove that the surface of the regular icosahedron admits a triangulation with eight non-obtuse triangles, as well as a triangulation with twelve acute triangles. There are no triangulations with fewer than eight or twelve, respectively, non-obtuse or acute triangles.

MSC:

 51M20 Polyhedra and polytopes; regular figures, division of spaces 52C20 Tilings in $$2$$ dimensions (aspects of discrete geometry)
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