Hexeractic hexacomb
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Hexeractic hexacomb | |
---|---|
Rank | 7 |
Type | Regular |
Space | Euclidean |
Notation | |
Bowers style acronym | Axh |
Coxeter diagram | x4o3o3o3o3o4o () |
Schläfli symbol | {4,3,3,3,3,4} |
Elements | |
Exa | N hexeracts |
Peta | 6N penteracts |
Tera | 15N tesseracts |
Cells | 20N cubes |
Faces | 15N squares |
Edges | 6N |
Vertices | N |
Vertex figure | Hexacontatetrapeton, edge length √2 |
Related polytopes | |
Army | Axh |
Regiment | Axh |
Dual | Hexeractic hexacomb |
Conjugate | None |
Abstract & topological properties | |
Orientable | Yes |
Properties | |
Symmetry | R7 |
Convex | Yes |
Nature | Tame |
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]
- Klitzing, Richard. "axh".
- Wikipedia contributors. "6-cubic honeycomb".