Rectified tesseractic tetracomb

Rectified tesseractic tetracomb
Rank	5
Type	Quasiregular
Space	Euclidean
Notation
Bowers style acronym	Rittit
Coxeter diagram	o4x3o3o4o ()
Elements
Tera	N hexadecachora, N rectified tesseracts
Cells	16N tetrahedra, 4N cuboctahedra
Faces	32N triangles, 6N squares
Edges	24N
Vertices	4N
Vertex figure	Octahedral prism, edge lengths 1 (base) and √2 (sides
Related polytopes
Army	Rittit
Regiment	Rittit
Dual	Joined tesseractic tetracomb
Conjugate	None
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R5
Convex	Yes

The rectified tesseractic tetracomb, or rittit, is a convex uniform tetracomb. 2 hexadecachora and 8 rectified tesseracts join at each vertex of this tessellation. As the name suggests, it is the rectification of the tesseractic tetracomb.

Vertex coordinates

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

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

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

Representations

A rectified tesseractic tetracomb has the following Coxeter diagrams:

• o4x3o3o4o (full ysmmetry)
• o3o3o *b3x4o (half symmetry, tetratetrahedral prism verf)
• x3o3x *b3o4o (half symmetry, octahedral frustum verf)
• x3o3x *b3o *b3o (quarter symmetry, tetratetrahedral frustum verf)

External links

• Klitzing, Richard. "rittit".

• Wikipedia Contributors. "Rectified tesseractic honeycomb".