Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Rhombic dodecahedral honeycomb
open-in-new
<table><tbody><tr><th colspan="2">Rhombic dodecahedral honeycomb</th></tr><tr><td colspan="2"></td></tr><tr><td>Type</td><td><a href="/facts/Convex_uniform_honeycomb/78IkTl7A">convex uniform honeycomb</a> dual</td></tr><tr><td><a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagram</a></td><td> = </td></tr><tr><td>Cell type</td><td><a href="/facts/Rhombic_dodecahedron/X3npAlmr">Rhombic dodecahedron</a> <i>V3.4.3.4</i></td></tr><tr><td>Face types</td><td><a href="/facts/Rhombus/T4pU50GF">Rhombus</a></td></tr><tr><td><a href="/facts/Space_group/2XQx0J7M">Space group</a></td><td>Fm3m (225)</td></tr><tr><td><a href="/facts/Coxeter_notation/ArUw6goe">Coxeter notation</a></td><td>½ C ~ 3 {\displaystyle {\tilde {C}}_{3}} , [1+,4,3,4] B ~ 3 {\displaystyle {\tilde {B}}_{3}} , [4,31,1] A ~ 3 {\displaystyle {\tilde {A}}_{3}} ×2, <[3[4]]></td></tr><tr><td>Dual</td><td><a href="/facts/Tetrahedral-octahedral_honeycomb/mX4CxSvp">tetrahedral-octahedral honeycomb</a></td></tr><tr><td>Properties</td><td><a href="/facts/Edge-transitive/p5j7GhwX">edge-transitive</a>, <a href="/facts/Face-transitive/ukLVQlK2">face-transitive</a>, <a href="/facts/Cell-transitive/ukLVQlK2">cell-transitive</a></td></tr></tbody></table> <p>The rhombic dodecahedral honeycomb (also dodecahedrille) is a space-filling <a href="/facts/Tessellation/7BWDywXC">tessellation</a> (or <a href="/facts/Honeycomb_(geometry)/seyRBcel">honeycomb</a>) in Euclidean 3-space. It is the <a href="/facts/Voronoi_diagram/AhQY5LD8">Voronoi diagram</a> of the <a href="/facts/Face-centered_cubic/92Co7BKM">face-centered cubic</a> sphere-packing, which has the densest possible packing of equal spheres in ordinary space (see <a href="/facts/Kepler_conjecture/5cFNDqwA">Kepler conjecture</a>). </p>