Celliprismatotruncated tesseractic tetracomb

Celliprismatotruncated tesseractic tetracomb
Rank	5
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Captatit
Coxeter diagram	x4x3o3x4x ()
Elements
Tera	4N truncated cubic prisms, 3N octagonal duoprisms, N prismatorhombated hexadecachora
Cells	32N triangular prisms, 24N+8N cuboctahedra, 24N octagonal prisms, 8N truncated cubes
Faces	64N triangles, 24N+48N+96N squares, 48N octagons
Edges	96N+192N
Vertices	96N
Vertex figure	Rectangular scalene, base edge lengths 1 and √2, remaining edge lengths √2 (5) and √2+√2 (4)
Related polytopes
Army	Captatit
Regiment	Captatit
Conjugate	Quasiquasicelliprismatotruncated tesseractic tetracomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R5×2
Convex	Yes
Nature	Tame

The celliprismatotruncated tesseractic tetracomb or captatit, also called the steriruncitruncated tesseractic tetracomb is a convex uniform tetracomb. 2 prismatorhombated hexadecachora, 2 truncated cubic prisms, and 2 octagonal duoprisms join at each vertex of this tessellation. As the name suggests, it is the steriruncitruncation of the tesseractic tetracomb.

Vertex coordinates

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

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

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

External links

• Klitzing, Richard. "captatit".
• Wikipedia contributors. "Steriruncitruncated tesseractic honeycomb".