All the vertices lie in parallel realms in which they form alternated cubic honeycombs, the tetrahedra being either tops of the rectified 5-cell or the bases of the 5-cell, and the octahedra being the bottoms of the rectified 5-cell.
The 20 vertices of its vertex figure, the runcinated 5-cell represent the 20 roots of the
The A*4 lattice[5] is the union of five A4 lattices, and is the dual to the omnitruncated 5-simplex honeycomb, and therefore the Voronoi cell of this lattice is an omnitruncated 5-cell The tops of the 5-cells in this honeycomb adjoin the bases of the 5-cells, and vice versa, in adjacent laminae (or layers); but alternating laminae may be inverted so that the tops of the rectified 5-cells adjoin the tops of the rectified 5-cells and the bases of the 5-cells adjoin the bases of other 5-cells.
This inversion results in another non-Wythoffian uniform convex honeycomb.
Its vertex figure is a tetrahedral antiprism, with 2 regular tetrahedron, 8 triangular pyramid, and 6 tetragonal disphenoid cells, defining 2 5-cell, 8 truncated 5-cell, and 6 bitruncated 5-cell facets around a vertex.
It can be constructed as five sets of parallel hyperplanes that divide space into two half-spaces.
The 3-space hyperplanes contain quarter cubic honeycombs as a collection facets.
[9] The facets of all omnitruncated simplectic honeycombs are called permutohedra and can be positioned in n+1 space with integral coordinates, permutations of the whole numbers (0,1,..,n).