Birectified 16-cell honeycomb(No image)TypeUniform honeycombSchläfli symbolt2{3,3,4,3}Coxeter-Dynkin diagram = 4-face typeRectified tesseract Rectified 24-cell Cell typeCube Cuboctahedron Tetrahedron Face type{3}, {4}Vertex figure{3}×{3} duoprismCoxeter group = [3,3,4,3] = [4,3,31,1] = [31,1,1,1]Dual?Propertiesvertex-transitive In four-dimensional Euclidean geometry, the birectified 16-cell honeycomb (or runcic tesseractic honeycomb) is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Symmetry constructions There are 3 different symmetry constructions, all with 3-3 duoprism vertex figures. The symmetry doubles on in three possible ways, while contains the highest symmetry.
Affine Coxeter group[3,3,4,3][4,3,31,1][31,1,1,1]Coxeter diagramVertex figureVertex figuresymmetry[3,2,3](order 36)[3,2](order 12)(order 6)4-facesCells
Related honeycombs
See also Regular and uniform honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb
Notes
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, (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) x3o3x *b3x *b3o, x3o3o *b3x4o, o3o3x4o3o - bricot - O106