Rectified pentacontahexapentacosiheptacontahexaexon

The rectified pentacontahexapentacosiheptacontahexaexon, or rolaq, also called the rectified 231 polytope, is a convex uniform polyexon. It has 56 rectified icosiheptaheptacontadipeta, 126 demihexeracts, and 576 rectified heptapeta. 2 demihexeracts, 6 rectified icosiheptaheptacontadipeta, and 6 rectified heptapeta join at each rectified hexateric prismatic vertex. As the name suggests, it is the rectification of the pentacontahexapentacosiheptacontahexaexon.

The rectified pentacontahexapentacosiheptacontahexaexon contains the vertices and edges of a small prismated demihexeractic prism, a truncated tetrahedral duoprismatic prism, a triangular-celliprismated hexateric duoprism, a hexagonal-small birhombidodecateral duoprism, a small trirhombihexadecaexon, and a petiprismated hexadecaexon.

Vertex coordinates
The vertices of a rectified pentacontahexapentacosiheptacontahexaexon of edge length 1, centered at the origin, are given by:


 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac32\right)$$ and all even sign changes of the first six coordinates
 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0,\,±1\right)$$ and all permutations of first 6 coordinates
 * $$\left(\frac{3\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac12\right)$$ and all permutations and even sign changes of the first six coordinates
 * $$\left(±\sqrt2,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0,\,0,\,0\right)$$ and all permutations of first 6 coordinates
 * $$\left(\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,0\right)$$ and all even sign changes of the first six coordinates

Representations
A rectified pentacontahexapentacosiheptacontahexaexon has the following Coxeter diagrams:


 * o3x3o3o *c3o3o3o (full symmetry)


 * oxooo3xoooo3ooxoo3oxoxo *c3oooox3oooxo&#xt (E6 axial, rectified icosiheptaheptacontadipeton-first)
 * xox(ou)xox3oxo(oo)oxo3ooo(oo)ooo *b3ooo(xo)ooo3oox(oo)xoo3ooo(xo)ooo&#xt (D6 axial, demihexeract-first)