Geodesic
Acute Triangulations of Doubly Covered Convex Quadrilaterals
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 933-938

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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. 
@article{BUMI_2007_8_10B_3_a32,
     author = {Yuan, Liping and Zamfirescu, Carol T.},
     title = {Acute {Triangulations} of {Doubly} {Covered} {Convex} {Quadrilaterals}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {933--938},
     publisher = {mathdoc},
     volume = {Ser. 8, 10B},
     number = {3},
     year = {2007},
     zbl = {1185.52018},
     mrnumber = {2507906},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a32/}
}
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Yuan, Liping; Zamfirescu, Carol T. Acute Triangulations of Doubly Covered Convex Quadrilaterals. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 933-938. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a32/