Chazelle polyhedron is a non-convex

polyhedron In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal Face (geometry), faces, straight Edge (geometry), edges and sharp corners or Vertex (geometry), vertices. The term "polyhedron" may refer ...

constructed by removing pieces of

wedge A wedge is a triangle, triangular shaped tool, a portable inclined plane, and one of the six simple machines. It can be used to separate two objects or portions of an object, lift up an object, or hold an object in place. It functions by conver ...

s 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 In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry. Every pla ...

with an equation

z = xy

. This polyhedron is named after Bernard Chazelle. Originally, the Chazelle polyhedron was intended to prove the quadratic lower bound of complexity on the decomposition of convex polyhedra in three dimensions. The later applications are used regarding the problem related to the construction of lower bounds as in the binary space partition,

bounding volume hierarchy A bounding volume hierarchy (BVH) is a tree structure on a set of geometric objects. All geometric objects, which form the leaf nodes of the tree, are wrapped in bounding volumes. These nodes are then grouped as small sets and enclosed within lar ...

for

collision detection Collision detection is the computational problem of detecting an intersection of two or more objects in virtual space. More precisely, it deals with the questions of ''if'', ''when'' and ''where'' two or more objects intersect. Collision detect ...

, decomposability of fat-polyhedra, and optimal triangulation in

mesh generation Mesh generation is the practice of creating a polygon mesh, mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells. Often these cells form a simplicial complex. Usually the cells partition the geometric ...

with its element's size.

References

{{reflist Nonconvex polyhedra