Order-5 tesseractic honeycomb explained

bgcolor=#e7dcc3 colspan=2	Order-5 tesseractic honeycomb
bgcolor=#ffffff align=center colspan=2	(No image)
Type	Hyperbolic regular honeycomb
Schläfli symbol
Coxeter diagram
4-faces
Cells
Faces
Face figure
Edge figure
Vertex figure
Dual	Order-4 120-cell honeycomb
Coxeter group	4, [5,3,3,4]
Properties	Regular

In the geometry of hyperbolic 4-space, the order-5 tesseractic honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol, it has five 8-cells (also known as tesseracts) around each face. Its dual is the order-4 120-cell honeycomb, .

Related polytopes and honeycombs

It is related to the Euclidean 4-space (order-4) tesseractic honeycomb,, and the 5-cube, in Euclidean 5-space. The 5-cube can also be seen as an order-3 tesseractic honeycomb on the surface of a 4-sphere.

See also

• List of regular polytopes

References

• Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II, III, IV, V, p212-213)