Cartesian coordinates for the vertices of a rectified hexacross, centered at the origin, edge length
are all permutations of: The 60 vertices represent the root vectors of the simple Lie group D6.
The 60 roots of D6 can be geometrically folded into H3 (Icosahedral symmetry), as to , creating 2 copies of 30-vertex icosidodecahedra, with the Golden ratio between their radii:[1] The birectified 6-orthoplex can tessellation space in the trirectified 6-cubic honeycomb.
Cartesian coordinates for the vertices of a rectified hexacross, centered at the origin, edge length
These polytopes are a part a family of 63 Uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.