Rectified 24-cell honeycomb(No image)TypeUniform 4-honeycombSchläfli symbolr{3,4,3,3}rr{3,3,4,3}r2r{4,3,3,4}r2r{4,3,31,1}Coxeter-Dynkin diagrams =
= 4-face typeTesseract Rectified 24-cell Cell typeCube Cuboctahedron Face typeSquareTriangleVertex figureTetrahedral prismCoxeter groups, [3,4,3,3], [4,3,3,4], [4,3,31,1], [31,1,1,1]PropertiesVertex transitive In four-dimensional Euclidean geometry, the rectified 24-cell honeycomb is a uniform space-filling honeycomb. It is constructed by a rectification of the regular 24-cell honeycomb, containing tesseract and rectified 24-cell cells.
Alternate names Rectified icositetrachoric tetracomb Rectified icositetrachoric honeycomb Cantellated 16-cell honeycomb Bicantellated tesseractic honeycomb
Symmetry constructions
There are five different symmetry constructions of this tessellation. Each symmetry can be represented by different arrangements of colored rectified 24-cell and tesseract facets. The tetrahedral prism vertex figure contains 4 rectified 24-cells capped by two opposite tesseracts.
Coxeter groupCoxeterdiagramFacetsVertex figureVertexfiguresymmetry(order)= [3,4,3,3]4: 1: , [3,3,2](48)3: 1: 1: , [3,2](12)= [4,3,3,4]2,2: 1: , [2,2](8)= [31,1,3,4]1,1: 2: 1: , (4)= [31,1,1,1]1,1,1,1:1: , [](2)
See also Regular and uniform honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb
References Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, p. 296, Table II: Regular honeycombs 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, (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) Model 93 , o3o3o4x3o, o4x3o3x4o - ricot - O93