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.[1]
^Coxeter, Regular and Semi-Regular Polytopes III, (1988), p318
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