Chazelle polyhedron

Chazelle polyhedron is a non-convex polyhedron constructed by removing pieces of wedges from both top and bottom of a cube's sides, leaving the notches. Its saddle surface can be considered as the set of line segments that lie forming the hyperbolic paraboloid with an equation ${\displaystyle z=xy}$.^[1] This polyhedron is named after Bernard Chazelle.^[2]

The Chazelle polyhedron

Originally, the Chazelle polyhedron was intended to prove the quadratic lower bound of complexity on the decomposition of convex polyhedra in three dimensions.^[1] The later applications are used regarding the problem related to the construction of lower bounds as in the binary space partition,^[3] bounding volume hierarchy for collision detection,^[4] decomposability of fat-polyhedra,^[5] and optimal triangulation in mesh generation with its element's size.^[6]