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| | The author's name is Christy. My wife and I reside in Mississippi and I adore every working day residing right here. Office supervising is what she does for a residing. To climb is some thing she would by no means give up.<br><br>Here is my web site ... tarot readings ([http://help.ksu.edu.sa/node/65129 click here!]) |
| !bgcolor=#e7dcc3 colspan=2|{{PAGENAME}}
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| |bgcolor=#ffffff align=center colspan=2|[[File:HC R1.png|220px]]
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| |bgcolor=#e7dcc3|Type||[[convex uniform honeycomb]] dual
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| |bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]||{{CDD|node_fh|4|node|3|node|4|node}} = {{CDD|node_f1|3|node|split1-43|nodes}}<BR>{{CDD|node_f1|split1|nodes|split2|node}}
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| |bgcolor=#e7dcc3|Cell type||[[Rhombic dodecahedron]] ''V3.4.3.4''
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| |bgcolor=#e7dcc3|Face types||[[Rhombus]]
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| |bgcolor=#e7dcc3|[[Space group]]||Fm{{overline|3}}m (225)
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| |bgcolor=#e7dcc3|[[Coxeter notation]]||½<math>{\tilde{C}}_3</math>, [1<sup>+</sup>,4,3,4]<BR><math>{\tilde{B}}_3</math>, [4,3<sup>1,1</sup>]<BR><math>{\tilde{A}}_3</math>×2, <[3<sup>[4]</sup>]>
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| |bgcolor=#e7dcc3|Dual||[[tetrahedral-octahedral honeycomb]]
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| |bgcolor=#e7dcc3|Properties||[[edge-transitive]], [[face-transitive]], [[cell-transitive]]
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| The '''rhombic dodecahedra honeycomb''' is a space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) in Euclidean 3-space. It is the [[Voronoi diagram]] of the [[face-centered cubic]] sphere-packing, which is believed to be the densest possible packing of equal spheres in ordinary space (see [[Kepler conjecture]]). | |
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| It consists of copies of a single [[Cell (mathematics)|cell]], the [[rhombic dodecahedron]]. All faces are [[rhombi]], with diagonals in the ratio 1:√2. Three cells meet at each edge. The honeycomb is thus [[cell-transitive]], [[face-transitive]] and [[edge-transitive]]; but it is not [[vertex-transitive]], as it has two kinds of vertex. The vertices with the obtuse rhombic face angles have 4 cells. The vertices with the acute rhombic face angles have 6 cells.
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| The rhombic dodecahedron can be twisted on one of its hexagonal cross-sections to form a [[trapezo-rhombic dodecahedron]], which is the cell of a somewhat similar tessellation, the [[Voronoi diagram]] of hexagonal [[close-packing]].
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| [[File:Rhombic_dodecahedra.png|220px]]
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| == References ==
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| * {{The Geometrical Foundation of Natural Structure (book)|page=168}}
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| == External links ==
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| {{Commons category|Rhombic dodecahedral honeycomb}}
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| * {{Mathworld | urlname = Space-FillingPolyhedron | title = Space-filling polyhedron}}
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| * [http://www.archinstitute.blogspot.com Examples of Housing Construction using this geometry]
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| [[Category:Honeycombs (geometry)]]
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The author's name is Christy. My wife and I reside in Mississippi and I adore every working day residing right here. Office supervising is what she does for a residing. To climb is some thing she would by no means give up.
Here is my web site ... tarot readings (click here!)