Tesseractic tetracomb

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Tesseractic tetracomb
Rank5
TypeRegular
SpaceEuclidean
Notation
Bowers style acronymTest
Coxeter diagramx4o3o3o4o ()
Schläfli symbol{4,3,3,4}
Elements
TeraN tesseracts
Cells4N cubes
Faces6N squares
Edges4N
VerticesN
Vertex figureHexadecachoron, edge length 2
Related polytopes
ArmyTest
RegimentTest
DualTesseractic tetracomb
ConjugateNone
Abstract & topological properties
OrientableYes
Properties
SymmetryR5
ConvexYes
NatureTame

The tesseractic tetracomb or test, also called the tesseractic honeycomb, is one of three regular tetracombs or tessellations of 4D Euclidean space. 4 tesseracts join at each face, and 16 join at each vertex of this honeycomb. It is the 4D hypercubic honeycomb.

Vertex coordinates[edit | edit source]

The vertices of a tesseractic tetracomb of edge length 1 are given by (i, j, k, l), where i, j, k, and l are integers.

Representations[edit | edit source]

A tesseractic tetracomb has the following Coxeter diagrams:

  • x4o3o3o4o () (full symmetry)
  • x4o3o3o4x () (as expanded tesseractic tetracomb)
  • o3o3o4x *b3o () (S5 symmetry, tesseracts of two types)

External links[edit | edit source]