Cubic-triangular tiling honeycombTypeParacompact uniform honeycombSchläfli symbol{(3,6,3,4)} or {(4,3,6,3)}Coxeter diagrams or Cells{4,3} {3,6} r{4,3} Facestriangular {3}square {4}hexagon {6}Vertex figurerhombitrihexagonal tilingCoxeter group[(6,3,4,3)]PropertiesVertex-transitive, edge-transitive In the geometry of hyperbolic 3-space, the cubic-triangular tiling honeycomb is a paracompact uniform honeycomb, constructed from cube, triangular tiling, and cuboctahedron cells, in a rhombitrihexagonal tiling vertex figure. It has a single-ring Coxeter diagram, , and is named by its two regular cells.
See also Convex uniform honeycombs in hyperbolic space List of regular polytopes
References Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296) Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II, III, IV, V, p212-213) Jeffrey R. Weeks The Shape of Space, 2nd edition (Chapter 16-17: Geometries on Three-manifolds I, II) Norman Johnson Uniform Polytopes, Manuscript 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