Hexagonal prismatic honeycomb

Hexagonal prismatic honeycomb
Type	Uniform honeycomb
Schläfli symbol	t0{6,3} x {∞} t1,2{6,3} x {∞}
Coxeter-Dynkin diagram
Cell types	4.4.6
Face types	{4}, {6}
Edge figures	{3} and {4}
Vertex figure	triangular bipyramid
Cells/edges	3 and 4
Faces/edges	3 and 4
Cells/vertex	6
Faces/vertex	3 {6}, 6 {4}
Edges/vertex	5
Coxeter group	[6,3,2,∞] [3[3],2,∞]
Dual	Triangular prismatic honeycomb
Properties	vertex-transitive

The hexagonal prismatic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of hexagonal prisms.

It is constructed from a hexagonal tiling extruded into prisms.

It is one of 28 convex uniform honeycombs.

This honeycomb can be alternated into the gyrated tetrahedral-octahedral honeycomb, with pairs of tetrahedra existing in the alternated gaps (instead of a triangular bipyramid).

References

• George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
• Branko Grünbaum, Uniform tilings of 3-space. Geombinatorics 4(1994), 49 - 56.
• Norman Johnson Uniform Polytopes, Manuscript (1991)
• Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
  • (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 Uniform space-fillings)
• A. Andreini, Sulle reti di poliedri regolari e semiregolari e sulle corrispondenti reti correlative (On the regular and semiregular nets of polyhedra and on the corresponding correlative nets), Mem. Società Italiana della Scienze, Ser.3, 14 (1905) 75–129.
• Klitzing, Richard. "3D Euclidean Honeycombs hiph".
• Uniform Honeycombs in 3-Space: 16-Hiph