| bgcolor=#e7dcc3 colspan=2 | Omnitruncated 5-simplex honeycomb | |
|---|---|---|
| bgcolor=#ffffff align=center colspan=2 | (No image) | |
| Type | Uniform honeycomb | |
| Family | Omnitruncated simplectic honeycomb | |
| Schläfli symbol | t012345 | |
| Coxeter–Dynkin diagram | ||
| 5-face types | ||
| 4-face types | t0123 ×t012 × | |
| Cell types | t012 x | |
| Face types | ||
| Vertex figure | Irr. 5-simplex | |
| Symmetry | {\tilde{A}}5 | |
| Properties | vertex-transitive |
The facets of all omnitruncated simplectic honeycombs are called permutahedra and can be positioned in n+1 space with integral coordinates, permutations of the whole numbers (0,1,..,n).
The A lattice (also called A) is the union of six A5 lattices, and is the dual vertex arrangement to the omnitruncated 5-simplex honeycomb, and therefore the Voronoi cell of this lattice is an omnitruncated 5-simplex.
∪ ∪ ∪ ∪ ∪ = dual of
The omnitruncated 5-simplex honeycomb can be projected into the 3-dimensional omnitruncated cubic honeycomb by a geometric folding operation that maps two pairs of mirrors into each other, sharing the same 3-space vertex arrangement:
Regular and uniform honeycombs in 5-space: