Rectified heptapeton

The rectified heptapeton, or ril, also called the rectified 6-simplex, is a convex uniform polypeton. It consists of 7 regular hexatera and 7 rectified hexatera. Two hexatera and 5 rectified hexatera join at each pentachoric prismatic vertex. As the name suggests, it is the rectification of the heptapeton.

It is isogonal under the 7-2-3 step prism symmetry, and is a 7-2-3 triple step prism.

It is also a convex segmentopeton, as a hexateron atop rectified hexateron.

Vertex coordinates
The vertices of a rectified heptapeton of edge length 1 can be given in seven dimensions as all permutations of:


 * $$\left(\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,0,\,0,\,0,\,0,\,0\right).$$

Representations
A rectified heptapeton has the following Coxeter diagrams:


 * o3x3o3o3o3o (full symmetry)
 * xo3ox3oo3oo3oo&#x (A5 axial, hexateron atop rectified hexateron)
 * oxo3oox3ooo3ooo oxo&#xt (A4×A1 symmetry, vertex-first)
 * oxo3oox3ooo oxo3xoo&#xt (A3×A2 symmetry, triangle-first)
 * xoxo3oxoo3oooo3oooo&#xr (A4 axial only)
 * oxoox ooooo3ooxoo3oxoxo&#xr (A3×A1 axial only)

Related polytopes
The rectified heptapeton is the colonel of a regiment of 7 members.