Waterman Polyhedron
Waterman polyhedra were invented around 1990 by the mathematician Steve Waterman.
Waterman polyhedra are created by packing spheres according to the cubic close(st) packing (CCP), then sweeping away the spheres that are farther from the center than a defined radius. The resulting pack of spheres is then convex hulled, and thereby a polyhedron is created.
-
Cubic Close(st) Packed spheres with radius sqrt(2*24)
-
Waterman Polyhedron W24 Origin 1
Waterman polyhedra form a vast family of polyhedra. Some of them have a number of nice properties such as multiple symmetries, or interesting and regular shapes. Others are just a collection of faces formed from irregular convex polygons.
The most popular Waterman polyhedra are those with centers at the point (0,0,0) and built out of hundreds of polygons. Such polyhedra resemble spheres. In fact, the more faces a Waterman polyhedron has, the more it resembles its circumscribed sphere in volume and total area.
With each point of 3D space we can associate a family of Waterman polyhedra with different values of radii of the circumscribed spheres. Therefore, from a mathematical point of view we can consider Waterman polyhedra as a 4D space W(x, y, z, r), where x, y, z are coordinates of a point in 3D, and r is a positive number greater than 1.
Read more about Waterman Polyhedron: Seven Origins of Cubic Close(st) Packing (CCP), Waterman Polyhedra and Platonic / Archimedean Solids, Generalized Waterman Polyhedra (GWP)