Bitruncated tesseractic tetracomb

Bitruncated tesseractic tetracomb
Rank	5
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Batitit
Coxeter diagram	o4x3x3o4o ()
Elements
Tera	N truncated hexadecachora, N tesseractihexadecachora
Cells	4N octahedra, 16N truncated tetrahedra, 4N truncated octahedra
Faces	32N triangles, 6N squares, 32N hexagons
Edges	24N+48N
Vertices	24N
Vertex figure	Square scalene, edge lengths 11 (base square), √2 (top edge), and √3 (sides)
Related polytopes
Army	Batitit
Regiment	Batitit
Conjugate	None
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R5
Convex	Yes

The bitruncated tesseractic tetracomb, or batitit, is a convex uniform tetracomb. 2 truncated hexadecachora and 4 tesseractihexadecachora join at each vertex of this tessellation. As the name suggests, it is the bitruncation of the tesseractic tetracomb.

Vertex coordinates

The vertices of a bitruncated tesseractic tetracomb of edge length 1 are given by all permutations of:

• $\left(2\sqrt2i,\,±\frac{\sqrt2}{2}+2\sqrt2j,\,\sqrt2+2\sqrt2k,\,\sqrt2+2\sqrt2l\right),$

where i, j, k, and l range over the integers.

Representations

A bitruncated tesseractic tetracomb has the following Coxeter diagrams:

• o4x3x3o4o (full symmetry)
• o3x3o *b3x4o (half symmetry, rectangular scalene verf)
• x3x3x *b3o4o (half symmetry, square pyramidal pyramid verf)
• x3x3x *b3o *b3o (quarter symmetry, rectangular pyramidal pyramid verf)

External links

• Klitzing, Richard. "batitit".

• Wikipedia Contributors. "Bitruncated tesseractic honeycomb".