quarter tesseractic honeycomb (No image)TypeUniform 4-honeycombFamilyQuarter hypercubic honeycombSchläfli symbolr{4,3,3,4}r{4,31,1}r{4,31,1}q{4,3,3,4}Coxeter-Dynkin diagram =
= 4-face typeh{4,32}, h3{4,32}, Cell type{3,3}, t1{4,3}, Face type{3}{4}Edge figureSquare pyramidVertex figureElongated {3,4}×{}Coxeter group = [4,3,3,4] = [4,31,1] = [31,1,1,1]DualPropertiesvertex-transitive In four-dimensional Euclidean geometry, the rectified tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a rectification of a tesseractic honeycomb which creates new vertices on the middle of all the original edges, rectifying the cells into rectified tesseracts, and adding new 16-cell facets at the original vertices. Its vertex figure is an octahedral prism, {3,4}×{}.
It is also called a quarter tesseractic honeycomb since it has half the vertices of the 4-demicubic honeycomb, and a quarter of the vertices of a tesseractic honeycomb.Coxeter, Regular and Semi-Regular Polytopes III, (1988), p318
Related honeycombs
See also Regular and uniform honeycombs in 4-space: Tesseractic honeycomb Demitesseractic honeycomb 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] See p318 George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) o4x3o3o4o, o3o3o *b3x4o, x3o3x *b3o4o, x3o3x *b3o *b3o - rittit - O87