Rectified pentacontatetrapeton

The rectified pentacontatetrapeton, or ram, also called the rectified 122 polytope, is a convex uniform polypeton. It consists of 54 penteractitriacontaditera and 72 dodecatera. 2 dodecatera and 6 penteractitriacontaditera join at each triangular duoprismatic prismatic vertex. As the name suggests, it is the rectification of the pentacontatetrapeton. It is also the birectified icosiheptaheptacontadipeton.

The rectified pentacontatetrapeton contains the vertices of a cellirhombidodecateral prism and a hexagonal trioprism.

It can tile 6-dimensional Euclidean space by itself, forming the rectified-pentacontatetrapetic hexacomb.

Representations
A rectified pentacontatetrapeton has the following Coxeter diagrams:


 * o3o3x3o3o *c3o (full symmetry)
 * oxooo3xoxox3oooxo *b3oxoxo3ooxoo&#xt (D5 axial, penteractitriacontaditeron-first)
 * oox(uoo)xoo3oxo(oox)oxo3xox(ouo)xox3oxo(xoo)oxo3oox(oou)xoo&#xt (A5 axial, dodecateron-first)

Vertex coordinates
The vertices of a unit rectified pentacontatetrapeton are given by all permutations of the first five coordinates of:


 * $$\biggl(\pm\frac{\sqrt{2}}{2},\pm\frac{\sqrt{2}}{2},\pm\frac{\sqrt{2}}{2},0,0,\pm\frac{\sqrt{6}}{2}\biggr)$$


 * $$\biggl(\pm\sqrt{2},\pm\frac{\sqrt{2}}{2},\pm\frac{\sqrt{2}}{2},0,0,0\biggr)$$

As well as all permutations of the first five coordinates and even sign changes of


 * $$\biggl(\frac{3\sqrt{2}}{4},\frac{3\sqrt{2}}{4},\frac{\sqrt{2}}{4},\frac{\sqrt{2}}{4},\frac{\sqrt{2}}{4},\frac{\sqrt{6}}{4}\biggr)$$