Truncated tesseractic tetracomb

Truncated tesseractic tetracomb
Rank	5
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Tattit
Coxeter diagram	x4x3o3o4o ()
Elements
Tera	N hexadecachora, N truncated tesseracts
Cells	16N tetrahedra, 4N truncated cubes
Faces	32N triangles, 6N octagons
Edges	4N+24N
Vertices	8N
Vertex figure	Octahedral pyramid, edge lengths 1 (base) and √2+√2 (sides)
Related polytopes
Army	Tattit
Regiment	Tattit
Conjugate	Quasitruncated tesseractic tetracomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R5
Convex	Yes
Nature	Tame

The truncated tesseractic tetracomb, or tattit, is a convex uniform tetracomb. 1 hexadecachoron and 8 truncated tesseracts join at each vertex of this tessellation. As the name suggests, it is the truncation of the tesseractic tetracomb.

Vertex coordinates

The vertices of a truncated cubic honeycomb of edge length 1 are given by all permutations of:

• $\left(\pm {\frac {1}{2}}+(1+{\sqrt {2}})i,\,\pm {\frac {1+{\sqrt {2}}}{2}}+(1+{\sqrt {2}})j,\,\pm {\frac {1+{\sqrt {2}}}{2}}+(1+{\sqrt {2}})k,\,\pm {\frac {1+{\sqrt {2}}}{2}}+(1+{\sqrt {2}})l\right)$,

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

Representations

A truncated tesseractic tetracomb has the following Coxeter diagrams:

• x4x3o3o4o () (full symmetry)
• o3o3x4x *b3o () (half symmetry)

External links

• Klitzing, Richard. "tattit".
• Wikipedia contributors. "Truncated tesseractic honeycomb".