bitruncated tesseractic honeycomb
class="wikitable" align="right" style="margin-left:10px" width="360"
!bgcolor=#e7dcc3 colspan=2|Bitruncated tesseractic honeycomb | |
bgcolor=#ffffff align=center colspan=2|(No image) | |
bgcolor=#e7dcc3|Type | Uniform 4-honeycomb |
bgcolor=#e7dcc3|Schläfli symbol | t1,2{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 type | Bitruncated tesseract 40px Truncated 16-cell 40px |
bgcolor=#e7dcc3|Cell type | Octahedron 20px Truncated tetrahedron 20px Truncated octahedron 20px |
bgcolor=#e7dcc3|Face type | {3}, {4}, {6} |
bgcolor=#e7dcc3|Vertex figure | 80px Square-pyramidal pyramid |
bgcolor=#e7dcc3|Coxeter group | = [4,3,3,4] = [4,31,1] = [31,1,1,1] |
bgcolor=#e7dcc3|Dual | |
bgcolor=#e7dcc3|Properties | vertex-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
Regular and uniform honeycombs in 4-space:
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}}