Acute triangulations of double planar convex bodies
Liping Yuan, Tudor I. Zamfirescu · Publicationes Mathematicae Debrecen · 2012
A (2-dimensional) double convex body 2K is a surface homeomorphic to the sphere consisting of two planar isometric compact convex bodies, K and K ′ , with boundaries glued in the obvious way.In this note we prove that, if K admits two perpendicular axes of symmetry and bdK satisfies a certain curvature condition, then 2K admits an acute triangulation of size 72.In particular, each double ellipse admits such a triangulation.