Tesseractic tetracomb

Tesseractic tetracomb
Rank	5
Type	Regular
Space	Euclidean
Notation
Bowers style acronym	Test
Coxeter diagram	x4o3o3o4o ()
Schläfli symbol	{4,3,3,4}
Elements
Tera	N tesseracts
Cells	4N cubes
Faces	6N squares
Edges	4N
Vertices	N
Vertex figure	Hexadecachoron, edge length √2
Related polytopes
Army	Test
Regiment	Test
Dual	Tesseractic tetracomb
Conjugate	None
Topological properties
Orientable	Yes
Properties
Symmetry	R5
Convex	Yes

The tesseractic tetracomb or test, also called the tesseractic honeycomb, is one of three regular tetracombs or tessellations of 4D Euclidean space. 4 tesseracts join at each face, and 16 join at each vertex of this honeycomb. It is the 4D hypercubic honeycomb.

Vertex coordinates

The vertices of a tesseractic tetracomb of edge length 1 are given by (i, j, k, l), where i, j, k, and l are integers.

Representations

A tesseractic tetracomb has the following Coxeter diagrams:

• x4o3o3o4o (full symmetry)
• x4o3o3o4x (as expanded tesseractic tetracomb)
• o3o3o *b3o4x (S5 symmetry, tesseracts of two types)

External links

• Klitzing, Richard. "test".

• Wikipedia Contributors. "Tesseractic honeycomb".