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- Waterman_polyhedron abstract "In geometry, the Waterman polyhedra are a family of polyhedra invented around 1990 by the mathematician Steve Waterman. A Waterman polyhedron is 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, then creating the convex hull of the resulting pack of spheres. 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.".
- Waterman_polyhedron thumbnail W5_sphere_cluster.jpg?width=300.
- Waterman_polyhedron wikiPageExternalLink 8428323.
- Waterman_polyhedron wikiPageExternalLink ccppoly.html.
- Waterman_polyhedron wikiPageExternalLink waterman.
- Waterman_polyhedron wikiPageExternalLink A119870.
- Waterman_polyhedron wikiPageExternalLink waterman.
- Waterman_polyhedron wikiPageExternalLink gen.
- Waterman_polyhedron wikiPageExternalLink watermanpolyhedron.com.
- Waterman_polyhedron wikiPageExternalLink Waterman_.htm.
- Waterman_polyhedron wikiPageExternalLink waterman.html.
- Waterman_polyhedron wikiPageExternalLink waterman-butterfly.
- Waterman_polyhedron wikiPageExternalLink plot-waterman.html.
- Waterman_polyhedron wikiPageExternalLink 93067.
- Waterman_polyhedron wikiPageExternalLink projPoly2.html.
- Waterman_polyhedron wikiPageExternalLink StellaManual.php?prod=stella4D.
- Waterman_polyhedron wikiPageExternalLink UsersModels.php.
- Waterman_polyhedron wikiPageExternalLink CART5.html.
- Waterman_polyhedron wikiPageExternalLink watermanpolyhedra1.html.
- Waterman_polyhedron wikiPageExternalLink watch?v=06-b-Mjr1eY.
- Waterman_polyhedron wikiPageExternalLink watch?v=3dkIIkyze2Y.
- Waterman_polyhedron wikiPageExternalLink watch?v=ajwR6ku5WGk&feature=related.
- Waterman_polyhedron wikiPageID "10723825".
- Waterman_polyhedron wikiPageLength "6741".
- Waterman_polyhedron wikiPageOutDegree "21".
- Waterman_polyhedron wikiPageRevisionID "682993488".
- Waterman_polyhedron wikiPageWikiLink Archimedean_solid.
- Waterman_polyhedron wikiPageWikiLink Category:Polyhedra.
- Waterman_polyhedron wikiPageWikiLink Circumscribed_sphere.
- Waterman_polyhedron wikiPageWikiLink Close-packing_of_equal_spheres.
- Waterman_polyhedron wikiPageWikiLink Convex_hull.
- Waterman_polyhedron wikiPageWikiLink Convex_polygon.
- Waterman_polyhedron wikiPageWikiLink Cubic_close_packing.
- Waterman_polyhedron wikiPageWikiLink Encyclopedia_of_Integer_Sequences.
- Waterman_polyhedron wikiPageWikiLink File:Waterman_Overview.png.
- Waterman_polyhedron wikiPageWikiLink Geometry.
- Waterman_polyhedron wikiPageWikiLink Integer-valued_polynomial.
- Waterman_polyhedron wikiPageWikiLink Mike_Bostock.
- Waterman_polyhedron wikiPageWikiLink On-Line_Encyclopedia_of_Integer_Sequences.
- Waterman_polyhedron wikiPageWikiLink Platonic_solid.
- Waterman_polyhedron wikiPageWikiLink Polyhedron.
- Waterman_polyhedron wikiPageWikiLink Rhombic_dodecahedron.
- Waterman_polyhedron wikiPageWikiLink Sphere_packing.
- Waterman_polyhedron wikiPageWikiLink Steve_Waterman_(mathematician).
- Waterman_polyhedron wikiPageWikiLink Truncated_cuboctahedron.
- Waterman_polyhedron wikiPageWikiLink Truncated_octahedron.
- Waterman_polyhedron wikiPageWikiLink Truncated_tetrahedron.
- Waterman_polyhedron wikiPageWikiLink File:W5_polyhedron.jpg.
- Waterman_polyhedron wikiPageWikiLink File:W5_sphere_cluster.jpg.
- Waterman_polyhedron wikiPageWikiLinkText "Waterman polyhedra".
- Waterman_polyhedron wikiPageWikiLinkText "Waterman polyhedron".
- Waterman_polyhedron hasPhotoCollection Waterman_polyhedron.
- Waterman_polyhedron wikiPageUsesTemplate Template:More_footnotes.
- Waterman_polyhedron wikiPageUsesTemplate Template:Sqrt.
- Waterman_polyhedron subject Category:Polyhedra.
- Waterman_polyhedron hypernym Family.
- Waterman_polyhedron type Article.
- Waterman_polyhedron type Article.
- Waterman_polyhedron type Page.
- Waterman_polyhedron type Polytope.
- Waterman_polyhedron comment "In geometry, the Waterman polyhedra are a family of polyhedra invented around 1990 by the mathematician Steve Waterman. A Waterman polyhedron is 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, then creating the convex hull of the resulting pack of spheres. Waterman polyhedra form a vast family of polyhedra.".
- Waterman_polyhedron label "Waterman polyhedron".
- Waterman_polyhedron sameAs Pluredro_de_Waterman.
- Waterman_polyhedron sameAs m.02qnb6v.
- Waterman_polyhedron sameAs Q12353886.
- Waterman_polyhedron sameAs Q12353886.
- Waterman_polyhedron wasDerivedFrom Waterman_polyhedron?oldid=682993488.
- Waterman_polyhedron depiction W5_sphere_cluster.jpg.
- Waterman_polyhedron isPrimaryTopicOf Waterman_polyhedron.
