bitruncated tesseractic honeycomb

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!bgcolor=#e7dcc3 colspan=2|Bitruncated tesseractic honeycomb

bgcolor=#ffffff align=center colspan=2|(No image)
bgcolor=#e7dcc3|TypeUniform 4-honeycomb
bgcolor=#e7dcc3|Schläfli symbolt1,2{4,3,3,4} or 2t{4,3,3,4}
t1,2{4,31,1} or 2t{4,31,1}
t2,3{4,31,1}
q2{4,3,3,3,4}
bgcolor=#e7dcc3|Coxeter-Dynkin diagram{{CDD|node|4|node_1|3|node_1|3|node|4|node}}

{{CDD|node|4|node_1|3|node_1|split1|nodes}}

{{CDD|nodes_11|split2|node_1|3|node|4|node}}

{{CDD|nodes_10ru|split2|node_1|split1|nodes_10lu}} = {{CDD|node_1|split1|nodes|4a4b|nodes_h1h1}}

bgcolor=#e7dcc3|4-face typeBitruncated tesseract 40px
Truncated 16-cell 40px
bgcolor=#e7dcc3|Cell typeOctahedron 20px
Truncated tetrahedron 20px
Truncated octahedron 20px
bgcolor=#e7dcc3|Face type{3}, {4}, {6}
bgcolor=#e7dcc3|Vertex figure80px
Square-pyramidal pyramid
bgcolor=#e7dcc3|Coxeter group{\tilde{C}}_4 = [4,3,3,4]
{\tilde{B}}_4 = [4,31,1]
{\tilde{D}}_4 = [31,1,1,1]
bgcolor=#e7dcc3|Dual
bgcolor=#e7dcc3|Propertiesvertex-transitive

In four-dimensional Euclidean geometry, the bitruncated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a bitruncation of a tesseractic honeycomb. It is also called a cantic quarter tesseractic honeycomb from its q2{4,3,3,4} construction.

Other names

  • Bitruncated tesseractic tetracomb (batitit)

Related honeycombs

{{C4_honeycombs}}

{{B4_honeycombs}}

{{D4_honeycombs}}

See also

Notes

{{reflist}}

References

  • 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}} [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html]
  • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318 [https://books.google.com/books?id=fUm5Mwfx8rAC&dq=%22quarter+cubic+honeycomb%22+q%7B4%2C3%2C4%7D&pg=PA318]
  • George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
  • {{KlitzingPolytopes|flat.htm|4D|Euclidean tesselations#4D}} x3x3x *b3o *b3o, x3x3x *b3o4o, o3x3o *b3x4o, o4x3x3o4o - batitit - O92
  • {{cite book |author=Conway JH, Sloane NJH |year=1998 |title=Sphere Packings, Lattices and Groups |publisher=Springer |edition=3rd |isbn=0-387-98585-9 |url-access=registration |url=https://archive.org/details/spherepackingsla0000conw_b8u0 }}

{{Honeycombs}}

Category:5-polytopes

Category:Honeycombs (geometry)

Category:Bitruncated tilings