Rectified octaexon

The rectified octaexon, or roc, also called the rectified 7-simplex, is a convex uniform polyexon. It consists of 8 regular heptapeta and 8 rectified heptapeta. Two heptapeta and 6 rectified heptapeta join at each hexateric prismatic vertex. As the name suggests, it is the rectification of the octaexon.

It is also a convex segmentoexon, as heptapeton atop rectified heptapeton.

The hecatonicosihexapentacosiheptacontahexaexon, or 321 polytope, can be obtained as the convex hull of two oppositely oriented rectified octaexa.

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


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

Representations
A rectified octaexon has the following Coxeter diagrams:


 * o3x3o3o3o3o3o (full symmetry)
 * xo3ox3oo3oo3oo3oo&#x (A6 axial, heptapeton atop rectified heptapeton)
 * oxo oxo3oox3ooo3ooo3ooo&#xt (A5×A1 axial, vertex-first)
 * xoo3oxo oxo3oox3ooo3ooo&#xt (A4×A2 axial, triangle-first)
 * oxo3xoo3ooo oxo3oox3ooo&#xt (A3×A3 axial, octahedron-first)