Rectified tesseractic honeycomb

quarter cubic honeycomb
(No image)
Type	Uniform 4-honeycomb
Family	Quarter hypercubic honeycomb
Schläfli symbol	r{4,3,3,4} r{4,31,1} r{4,31,1} q{4,3,3,4}
Coxeter-Dynkin diagram	= = = =
4-face type	h{4,32}, h3{4,32},
Cell type	{3,3}, t1{4,3},
Face type	{3} {4}
Edge figure	Square pyramid
Vertex figure	Elongated {3,4}×{}
Coxeter group	${\displaystyle {\tilde {C}}_{4}}$ = [4,3,3,4] ${\displaystyle {\tilde {B}}_{4}}$ = [4,31,1] ${\displaystyle {\tilde {D}}_{4}}$ = [31,1,1,1]
Dual
Properties	vertex-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.^[1]