Gyrated triangular prismatic honeycomb

Gyrated triangular prismatic honeycomb
Type	Convex uniform honeycomb
Schläfli symbol	{3,6}:g x {∞}
Cell types	(3.4.4)
Face types	{3}, {4}
Edge figures	?
Vertex figure
Cells/edges	E1:(3.4.4)5 E2: (3.4.4)4
Faces/edges	E1: 3.4.4.4.4 E2: 3.4.3.4
Cells/vertex	(3.4.4)12
Faces/vertex	{3}3.{4}8
Edges/vertex	8
Coxeter group	[6,3,2+]
Dual	?
Properties	vertex-transitive

wireframe

The gyrated triangular prismatic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of triangular prisms. It is vertex-uniform with 12 triangular prisms per vertex.

It can be seen as parallel planes of square tiling with alternating offsets caused by layers of paired triangular prisms. The prisms in each layer are rotated by a right angle to those in the next layer.

It is one of 28 convex uniform honeycombs.

See also

• cubic honeycomb

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)
• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X.
• Critchlow, Keith (1970). Order in Space: A design source book. Viking Press. ISBN 0-500-34033-1.
• 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.
• D. M. Y. Sommerville, An Introduction to the Geometry of n Dimensions. New York, E. P. Dutton, 1930. 196 pp. (Dover Publications edition, 1958) Chapter X: The Regular Polytopes
• Klitzing, Richard. "3D Euclidean Honeycombs gyro( x∞o x3o6o ) - gytoph - O12".