Celligreatorhombated tesseractic tetracomb

The celligreatorhombated tesseractic tetracomb or cagratit, also called the stericantitruncated tesseractic tetracomb, is a convex uniform tetracomb. 1 great rhombated tesseract, 1 prismatorhombated tesseract, 1 small rhombicuboctahedral prism, 2 great rhombicuboctahedral prisms, and 1 square-octagonal duoprism join at each vertex of this tessellation. As the name suggests, it is the stericantitruncation of the tesseractic tetracomb.

Celligreatorhombated tesseractic tetracomb
Rank5
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymCagratit
Coxeter diagramx4x3x3o4x ()
Elements
Tera6N square-octagonal duoprisms, 4N small rhombicuboctahedral prisms, 4N great rhombicuboctahedral prisms, N great rhombated tesseracts, N prismatorhombated tesseracts
Cells32N triangular prisms, 24N+24N+48N cubes, 32N hexagonal prisms, 16N truncated tetrahedra, 24N octagonal prisms, 8N small rhombicuboctahedra, 8N great rhombicuboctahedra
Faces64N triangles, 48N+96N+96N+96N+96N squares, 64N hexagons, 24N octagons
Edges96N+96N+192N+192N
Vertices192N
Vertex figureIsosceles trapezoidal pyramidal pyramid, base edge lengths 1, 2, 2, 2, remaining edge lengths 2 (6), 3 (2), and 2+2 (1)
Related polytopes
ArmyCagratit
RegimentCagratit
ConjugateQuasicelligreatoquasirhombated tesseractic tetracomb
Abstract & topological properties
OrientableYes
Properties
SymmetryR5
ConvexYes
NatureTame

Vertex coordinates edit

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

  •  ,

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

External links edit