en>David Eppstein: /* References */ authorlink antman

2014-12-21T02:25:33Z

References: authorlink antman

← Older revision		Revision as of 04:25, 21 December 2014
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	~~{\| class="wikitable" align="right" style="margin-left:10px" width="250"~~		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}}~~
	\|-
	~~\|bgcolor=#ffffff align=center colspan=2\|[[File:HC R1.png\|220px]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|Type\|\|[[convex uniform honeycomb]] dual~~
	\|-
	~~\|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}}~~
	\|-
	~~\|bgcolor=#e7dcc3\|Cell type\|\|[[Rhombic dodecahedron]] ''V3.4.3.4''~~
	\|-
	~~\|bgcolor=#e7dcc3\|Face types\|\|[[Rhombus]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|[[Space group]]\|\|Fm{{overline\|3}}m (225)~~
	\|-
	~~\|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>]>~~
	\|-
	~~\|bgcolor=#e7dcc3\|Dual\|\|[[tetrahedral-octahedral honeycomb]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|Properties\|\|[[edge-transitive]], [[face-transitive]], [[cell-transitive]]~~
	\|}

	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]]).~~

	~~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~~.

	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]].

	~~[[File:Rhombic_dodecahedra~~.~~png\|220px]]~~

	~~== References ==~~
	* {{The Geometrical Foundation of Natural Structure (~~book)\|page=168}}~~

	~~== External links ==~~
	~~{{Commons category\|Rhombic dodecahedral honeycomb}}~~
	* {{Mathworld \| urlname = Space-FillingPolyhedron \| title = Space-filling polyhedron}}
	* [http://~~www~~.~~archinstitute~~.~~blogspot~~.~~com Examples of Housing Construction using this geometry~~]

	~~[[Category:Honeycombs (geometry~~)]]

en>Bhny at 13:37, 17 May 2012

2012-05-17T13:37:37Z

New page

{| class="wikitable" align="right" style="margin-left:10px" width="250"
!bgcolor=#e7dcc3 colspan=2|{{PAGENAME}}
|-
|bgcolor=#ffffff align=center colspan=2|[[File:HC R1.png|220px]]
|-
|bgcolor=#e7dcc3|Type||[[convex uniform honeycomb]] dual
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]||{{CDD|node_fh|4|node|3|node|4|node}} = {{CDD|node_f1|3|node|split1-43|nodes}} {{CDD|node_f1|split1|nodes|split2|node}}
|-
|bgcolor=#e7dcc3|Cell type||[[Rhombic dodecahedron]] ''V3.4.3.4''
|-
|bgcolor=#e7dcc3|Face types||[[Rhombus]]
|-
|bgcolor=#e7dcc3|[[Space group]]||Fm{{overline|3}}m (225)
|-
|bgcolor=#e7dcc3|[[Coxeter notation]]||½<math>{\tilde{C}}_3</math>, [1+,4,3,4] <math>{\tilde{B}}_3</math>, [4,31,1] <math>{\tilde{A}}_3</math>×2, <[3[4]]>
|-
|bgcolor=#e7dcc3|Dual||[[tetrahedral-octahedral honeycomb]]
|-
|bgcolor=#e7dcc3|Properties||[[edge-transitive]], [[face-transitive]], [[cell-transitive]]
|}

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]]).

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.

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]].

[[File:Rhombic_dodecahedra.png|220px]]

== References ==
* {{The Geometrical Foundation of Natural Structure (book)|page=168}}

== External links ==
{{Commons category|Rhombic dodecahedral honeycomb}}
* {{Mathworld | urlname = Space-FillingPolyhedron | title = Space-filling polyhedron}}
* [http://www.archinstitute.blogspot.com Examples of Housing Construction using this geometry]

[[Category:Honeycombs (geometry)]]

Formal calculation - Revision history

en>David Eppstein: /* References */ authorlink antman

en>Bhny at 13:37, 17 May 2012