Acute Triangulations of Doubly Covered Convex Quadrilaterals

Motivated by various applications triangulations of surfaces using only acute triangles have been recently studied. Triangles and quadrilaterals can be triangulated with at most 7, respectively 10, acute triangles. Doubly covered triangles can be triangulated with at most 12 acute triangles. In this paper we investigate the acute triangulations of doubly covered convex quadrilaterals, and show that they can be triangulated with at most 20 acute triangles. Recentemente, motivate da varie applicazioni, sono state studiate le triangolazioni di superfici utilizzando soltanto triangoli acutangoli. I triangoli e i quadrilateri possono essere triangolati, rispettivamente, con ∗E-mail: [email protected], [email protected]. This author was supported by Tianyuan Fund for Mathematics (10426013) and Fund of Hebei Province for Doctorate (B2004114). †E-mail: [email protected]