## Acute triangulations of doubly covered convex quadrilaterals.(English)Zbl 1185.52018

A doubly covered convex set is a surface homeomorphic to the sphere consisting of two planar isometric convex sets, with boundaries glued in accordance with the isometry. In this paper it is shown that every doubly covered convex quadrilateral can be triangulated by at most 20 triangles having all their angles less than $$\pi /2$$.

### MSC:

 52C20 Tilings in $$2$$ dimensions (aspects of discrete geometry)