1 52 honeycomb

{{DISPLAYTITLE:1 52 honeycomb}} 152 honeycomb(No image)TypeUniform tessellationFamily1k2 polytopeSchläfli symbol {3,35,2}Coxeter symbol 152Coxeter-Dynkin diagramnodea 3a nodea 3a branch_01lr 3a nodea 3a nodea 3a nodea 3a nodea 3a nodea8-face types142 25px151 25px7-face types132 25px141 25px6-face types122 25px{31,3,1} 25px{35} 25px5-face types121 25px{34} 25px4-face type111 25px{33} 25pxCells{32} 25pxFaces{3}25pxVertex figurebirectified 8-simplex:t2{37} 25pxCoxeter group, [35,2,1] In geometry, the 152 honeycomb is a uniform tessellation of 8-dimensional Euclidean space. It contains 142 and 151 facets, in a birectified 8-simplex vertex figure. It is the final figure in the 1k2 polytope family. Construction It is created by a Wythoff construction upon a set of 9 hyperplane mirrors in 8-dimensional space. The facet information can be extracted from its Coxeter-Dynkin diagram. nodea 3a nodea 3a branch_01lr 3a nodea 3a nodea 3a nodea 3a nodea 3a nodea Removing the node on the end of the 2-length branch leaves the 8-demicube, 151. nodea 3a branch_01lr 3a nodea 3a nodea 3a nodea 3a nodea 3a nodea Removing the node on the end of the 5-length branch leaves the 142. nodea 3a nodea 3a branch_01lr 3a nodea 3a nodea 3a nodea 3a nodea The vertex figure is determined by removing the ringed node and ringing the neighboring node. This makes the birectified 8-simplex, 052. nodea 3a nodea 3a nodea_1 3a nodea 3a nodea 3a nodea 3a nodea 3a nodea Related polytopes and honeycombs See also 521 honeycomb 251 honeycomb References Coxeter The Beauty of Geometry: Twelve Essays, Dover Publications, 1999, 978-0-486-40919-1 (Chapter 3: Wythoff's Construction for Uniform Polytopes) Coxeter Regular Polytopes (1963), Macmillan Company Regular Polytopes, Third edition, (1973), Dover edition, 0-486-61480-8 (Chapter 5: The Kaleidoscope) 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, wiley.com, 978-0-471-01003-6, GoogleBook (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3–45] Category:9-polytopes Category:E8 (mathematics) Category:Honeycombs (geometry)