Small prismated heptapeton

The small prismated heptapeton or spil, also called the runcinated heptapeton or runcinated 6-simplex, is a convex uniform polypeton. It consists of 7 dodecatera, 7 small prismated hexatera, 21 rectified pentachoric prisms, and 35 triangular-tetrahedral duoprisms. 1 dodecateron, 3 small prismated hexatera, 3 rectified pentachoric prisms, and 3 triangular-tetrahedral duoprisms join at each vertex. As the name suggests, it is the runcination of the heptapeton.

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


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

Representations
A small prismated heptapeton has the following Coxeter diagrams:


 * x3o3o3x3o3o (ful symmetry)
 * ooo3oox3xx3o3ooo3oxx&#xt (A5 axial, dodecateron-first)

Related polytopes
The small prismated heptapeton is the colonel of a regiment with 138 uniform members plus 15 fissaries.