Waterman polyhedron: Difference between revisions

Revision as of 11:45, 1 March 2019

Revision as of 23:11, 28 December 2019

Line 13:

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 spacespaces 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.<ref>[http://www.mupad.com/mathpad/2006/majewski/index.php Visualizing Waterman Polyhedra with MuPAD] by M. Majewski</ref>

==Seven origins of cubic close(st) packing (CCP)==