Small rhombated tesseractic tetracomb

Small rhombated tesseractic tetracomb
Rank5
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymSrittit
Coxeter diagramx4o3x3o4o ()
Elements
Tera4N octahedral prisms, N icositetrachora, N small rhombated tesseracts
Cells32N triangular prisms, 8N+16N octahedra, 4N small rhombicuboctahedra
Faces32N+64N triangles, 6N+48N squares
Edges24N+96N
Vertices24N
Vertex figureSquare pyramidal prism, edge lengths 1 (base cube) and 2 (sides and top edge)
Related polytopes
ArmySrittit
RegimentSrittit
ConjugateQuasirhombated tesseractic tetracomb
Abstract & topological properties
OrientableYes
Properties
SymmetryR5
ConvexYes
NatureTame

The small rhombated tesseractic tetracomb or srittit, also called the cantellated tesseractic tetracomb is a convex uniform tetracomb. 4 small rhombated tesseracts, 2 icositetrachora, and 1 octahedral prism join at each vertex of this tessellation. As the name suggests, it is the cantellation of the tesseractic tetracomb.

Vertex coordinates

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

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

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

Representations

A small rhombated tesseractic tetracomb has the following Coxeter diagrams:

• x4o3x3o4o () (full symmetry)
• o3x3o4x *b3o () (half symmetry)