Hexeractic hexacomb

From Polytope Wiki
Jump to navigation Jump to search
Hexeractic hexacomb
Rank7
TypeRegular
SpaceEuclidean
Notation
Bowers style acronymAxh
Coxeter diagramx4o3o3o3o3o4o ()
Schläfli symbol{4,3,3,3,3,4}
Elements
ExaN hexeracts
Peta6N penteracts
Tera15N tesseracts
Cells20N cubes
Faces15N squares
Edges6N
VerticesN
Vertex figureHexacontatetrapeton, edge length 2
Related polytopes
ArmyAxh
RegimentAxh
DualHexeractic hexacomb
ConjugateNone
Abstract & topological properties
OrientableYes
Properties
SymmetryR7
ConvexYes
NatureTame

The hexeractic hexacomb or axh, also called the hexeractic honeycomb or 6-cubic honeycomb, is the only regular hexacomb or tessellation of 6D Euclidean space. 4 hexeracts join at each teron, and 64 join at each vertex of this honeycomb. It is the 6D hypercubic honeycomb.

Vertex coordinates[edit | edit source]

The vertices of a hexeractic hexacomb of edge length 1 are given by (i, j, k, l, m, n), where i, j, k, l, m, n are integers.

Representations[edit | edit source]

A hexeratic hexacomb has the following Coxeter diagrams:

  • x4o3o3o3o3o4o () (full symmetry)
  • o3o3o3o3o4x *b3o () (half symmetry)

External links[edit | edit source]