View source for Cubic-triangular tiling honeycomb

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!bgcolor=#e7dcc3 colspan=2|Cubic-triangular tiling honeycomb
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|bgcolor=#e7dcc3|Type||Paracompact uniform honeycomb
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|bgcolor=#e7dcc3|[[Schläfli symbol]]||{(3,6,3,4)} or {(4,3,6,3)}
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|bgcolor=#e7dcc3|Coxeter diagrams||{{CDD|label6|branch|3ab|branch_10l|label4}} or {{CDD|label6|branch|3ab|branch_01l|label4}}
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|bgcolor=#e7dcc3|Cells||[[Cube|{4,3}]] [[File:Uniform_polyhedron-43-t0.png|40px]]<BR>[[Triangular tiling|{3,6}]] 40px<BR>[[Cuboctahedron|r{4,3}]] [[File:Uniform_polyhedron-43-t1.png|40px]]
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|bgcolor=#e7dcc3|Faces||triangular {3}<BR>[[Square|square]] {4}<BR>[[Hexagon|hexagon]] {6}
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|bgcolor=#e7dcc3|Vertex figure||[[File:Uniform tiling 63-t02.png|80px]]<BR>[[Rhombitrihexagonal tiling|rhombitrihexagonal tiling]]
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|bgcolor=#e7dcc3|[[Coxeter group]]||[(6,3,4,3)]
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|bgcolor=#e7dcc3|Properties||Vertex-transitive, edge-transitive
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In the [[Geometry|geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''cubic-triangular tiling honeycomb''' is a paracompact uniform honeycomb, constructed from [[Cube|cube]], [[Triangular tiling|triangular tiling]], and [[Cuboctahedron|cuboctahedron]] cells, in a [[Rhombitrihexagonal tiling|rhombitrihexagonal tiling]] [[Vertex figure|vertex figure]]. It has a single-ring Coxeter diagram, {{CDD|label6|branch|3ab|branch_10l|label4}}, and is named by its two regular cells.

{{Honeycomb}}

== See also ==
* Convex uniform honeycombs in hyperbolic space
* List of regular polytopes

== References ==
*Coxeter, ''Regular Polytopes'', 3rd. ed., Dover Publications, 1973. {{isbn|0-486-61480-8}}. (Tables I and II: Regular polytopes and honeycombs, pp.&nbsp;294–296)
*Coxeter, ''The Beauty of Geometry: Twelve Essays'', Dover Publications, 1999 {{isbn|0-486-40919-8}} (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II, III, IV, V, p212-213)
* [[Biography:Jeffrey Weeks (mathematician)|Jeffrey R. Weeks]] ''The Shape of Space, 2nd edition'' {{isbn|0-8247-0709-5}} (Chapter 16-17: Geometries on Three-manifolds I, II)
* [[Biography:Norman Johnson (mathematician)|Norman Johnson]] ''Uniform Polytopes'', Manuscript
** [[Biography:Norman Johnson (mathematician)|N.W. Johnson]]: ''The Theory of Uniform Polytopes and Honeycombs'', Ph.D. Dissertation, University of Toronto, 1966 
** N.W. Johnson: ''Geometries and Transformations'', (2018) Chapter 13: Hyperbolic Coxeter groups

{{DEFAULTSORT:Order-4 Dodecahedral Honeycomb}}
[[Category:Honeycombs (geometry)]]

{{Sourceattribution|Cubic-triangular tiling honeycomb}}