# Rectified 6-orthoplexes

In six-dimensional geometry, a **rectified 6-orthoplex** is a convex uniform 6-polytope, being a rectification of the regular 6-orthoplex.

There are unique 6 degrees of rectifications, the zeroth being the 6-orthoplex, and the 6th and last being the 6-cube. Vertices of the rectified 6-orthoplex are located at the edge-centers of the 6-orthoplex. Vertices of the birectified 6-orthoplex are located in the triangular face centers of the 6-orthoplex.

The *rectified 6-orthoplex* is the vertex figure for the demihexeractic honeycomb.

There are two Coxeter groups associated with the *rectified hexacross*, one with the C_{6} or [4,3,3,3,3] Coxeter group, and a lower symmetry with two copies of pentacross facets, alternating, with the D_{6} or [3^{3,1,1}] Coxeter group.

The 60 vertices represent the root vectors of the simple Lie group D_{6}. The vertices can be seen in 3 hyperplanes, with the 15 vertices rectified 5-simplices cells on opposite sides, and 30 vertices of an expanded 5-simplex passing through the center. When combined with the 12 vertices of the 6-orthoplex, these vertices represent the 72 root vectors of the B_{6} and C_{6} simple Lie groups.

The 60 roots of D_{6} can be geometrically folded into H_{3} (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.

It can also be projected into 3D-dimensions as --> , a dodecahedron envelope.

These polytopes are a part a family of 63 Uniform 6-polytopes generated from the B_{6} Coxeter plane, including the regular 6-cube or 6-orthoplex.