Tesseractic honeycomb

Tesseractic honeycomb

Perspective projection of a 3x3x3x3 red-blue chessboard.
Type Regular 4-space honeycomb
Uniform 4-honeycomb
Family Hypercubic honeycomb
Schläfli symbols {4,3,3,4}
t0,4{4,3,3,4}
{4,3,31,1}
{4,4}(2)
{4,3,4}×{∞}
{4,4}×{∞}(2)
{∞}(4)
Coxeter-Dynkin diagrams




4-face type {4,3,3}
Cell type {4,3}
Face type {4}
Edge figure {3,4}
(octahedron)
Vertex figure {3,3,4}
(16-cell)
Coxeter groups , [4,3,3,4]
, [4,3,31,1]
Dual self-dual
Properties vertex-transitive, edge-transitive, face-transitive, cell-transitive, 4-face-transitive

In four-dimensional euclidean geometry, the tesseractic honeycomb is one of the three regular space-filling tessellations (or honeycombs), represented by Schläfli symbol {4,3,3,4}, and consisting of a packing of tesseracts (4-hypercubes).

Its vertex figure is a 16-cell. Two tesseracts meet at each cubic cell, four meet at each square face, eight meet on each edge, and sixteen meet at each vertex.

It is an analog of the square tiling, {4,4}, of the plane and the cubic honeycomb, {4,3,4}, of 3-space. These are all part of the hypercubic honeycomb family of tessellations of the form {4,3,...,3,4}. Tessellations in this family are self-dual.