Difference between revisions of "Template:Cubic cell tessellations"

Revision as of 11:48, 18 September 2017

In geometry, there are a sequence of regular polytopes and honeycombs, {4,3,p}, with cubic cells. The first is the finite tesseract in 4-dimensional space. The second is the cubic honeycomb that tessellates Euclidean 3-space. The next two tessellate hyperbolic 3-space.

{4,3,p} regular honeycombs
Space	S³	E³	H³
Form	Finite	Affine	Compact	Paracompact	Noncompact
Name File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel p.png File:CDel node.png	{4,3,3} File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node.png	{4,3,4} File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel split1.png File:CDel nodes.png File:CDel labelinfin.png File:CDel branch 10.png File:CDel 2.png File:CDel labelinfin.png File:CDel branch 10.png File:CDel 2.png File:CDel labelinfin.png File:CDel branch 10.png	{4,3,5} File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 5.png File:CDel node.png	{4,3,6} File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 6.png File:CDel node.png File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel split1.png File:CDel branch.png File:CDel node 1.png File:CDel ultra.png File:CDel node.png File:CDel split1.png File:CDel branch.png File:CDel uaub.png File:CDel nodes 11.png	{4,3,7} File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 7.png File:CDel node.png	{4,3,8} File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 8.png File:CDel node.png File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel split1.png File:CDel branch.png File:CDel label4.png	... {4,3,∞} File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel infin.png File:CDel node.png File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel split1.png File:CDel branch.png File:CDel labelinfin.png
Image	60px	60px	80px	80px	60px	60px	60px
Vertex figure File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel p.png File:CDel node.png	60px {3,3} File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node.png	60px {3,4} File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png File:CDel node 1.png File:CDel split1.png File:CDel nodes.png	60px {3,5} File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 5.png File:CDel node.png	60px {3,6} File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 6.png File:CDel node.png File:CDel node 1.png File:CDel split1.png File:CDel branch.png	60px {3,7} File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 7.png File:CDel node.png	60px {3,8} File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 8.png File:CDel node.png File:CDel node 1.png File:CDel split1.png File:CDel branch.png File:CDel label4.png	60px {3,∞} File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel infin.png File:CDel node.png File:CDel node 1.png File:CDel split1.png File:CDel branch.png File:CDel labelinfin.png

References

Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8. (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
The Beauty of Geometry: Twelve Essays (1999), Dover Publications, LCCN Expression error: Unrecognized punctuation character "[". 99-Expression error: Unrecognized punctuation character "[".Template:Only in print, ISBN 0-486-40919-8 (Chapter 10, Regular Honeycombs in Hyperbolic Space) Table III
N. W. Johnson, R. Kellerhals, J. G. Ratcliffe, S. T. Tschantz, Commensurability classes of hyperbolic Coxeter groups, (2002) H³: p130. [1]

@@ Line 21: / Line 21: @@
 ![[Order-5 cubic honeycomb|{4,3,5}]]<BR>{{CDD|node_1|4|node|3|node|5|node}}
 ![[Order-6 cubic honeycomb|{4,3,6}]]<BR>{{CDD|node_1|4|node|3|node|6|node}}<BR>{{CDD|node_1|4|node|split1|branch}}<BR>{{CDD|node_1|ultra|node|split1|branch|uaub|nodes_11}}
-!{4,3,7}<BR>{{CDD|node_1|4|node|3|node|7|node}}
+![[Order-7 cubic honeycomb|{4,3,7}]]<BR>{{CDD|node_1|4|node|3|node|7|node}}
-!{4,3,8}<BR>{{CDD|node_1|4|node|3|node|8|node}}<BR>{{CDD|node_1|4|node|split1|branch|label4}}
+![[Order-8 cubic honeycomb|{4,3,8}]]<BR>{{CDD|node_1|4|node|3|node|8|node}}<BR>{{CDD|node_1|4|node|split1|branch|label4}}
-!... {4,3,&infin;}<BR>{{CDD|node_1|4|node|3|node|infin|node}}<BR>{{CDD|node_1|4|node|split1|branch|labelinfin}}
+!... [[Infinite-order cubic honeycomb|{4,3,&infin;}]]<BR>{{CDD|node_1|4|node|3|node|infin|node}}<BR>{{CDD|node_1|4|node|split1|branch|labelinfin}}
 |- style="text-align:center;"
 !Image

Difference between revisions of "Template:Cubic cell tessellations"

Revision as of 11:48, 18 September 2017

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