Cantitruncated cubic honeycomb

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Cantitruncated cubic honeycomb
Schläfli symbol	t0,1,2{4,3,4} h0,1,2,3{4,3,4}
Coxeter-Dynkin diagrams
Type	Uniform honeycomb
Coxeter group	[4,3,4] [4,31,1]
Dual	Dual cantitruncated cubic honeycomb
Properties	vertex-transitive

The cantitruncated cubic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space, made up of truncated cuboctahedra, truncated octahedra, and cubes in a ratio of 1:1:3.

Contents 1 Uniform colorings 2 Edge framework 3 Alternation 4 References

[edit] Uniform colorings

Cells can be shown in two different symmetries. The linear Coxeter-Dynkin diagram form can be drawn with one color for each cell type. The bifurcating diagram form can be drawn with two types (colors) of truncated cuboctahedron cells alternating.

[edit] Edge framework

[edit] Alternation

This image shows a partial honeycomb of the alternation of the cantitruncated cubic honeycomb. It contains three types of uniform cells: semiregular snub cubes, regular icosahedra (snub tetrahedron), and regular tetrahedra. In addition the gaps created at the alternated vertices form irregular tetrahedral cells. This honeycomb exists in two mirror image forms.

[edit] References

• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X.  Chapter 5 (Polyhedral packing and spacing filling): Fig. 5-13, p.176 shows this honeycomb. Fig. 5-34 p.197 shows a partial honeycomb of the alternation with only snub cube cells show.