Octahedron atop cuboctahedron

Octahedron atop cuboctahedron, or octaco, is a CRF segmentochoron (designated K-4.29 on Richard Klitzing's list). As the name suggests, it consists of an octahedron and a cuboctahedron as bases, connected by 8 further octahedra and 6 square pyramids.

It can also be seen as a rectification of the CRF octahedral pyramid.

Two octahedron atop cuboctahedron segmentochora can be attached at their cuboctahedral bases, to form the regular icositetrachoron.

Vertex coordinates
The vertices of an octahedron atop cuboctahedron segmentochoron of edge length 1 are given by:
 * $$\left(±\frac{\sqrt2}{2},\,0,\,0,\,\frac{\sqrt2}{2}\right)$$ and all permutations of first three coordinates
 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0\right)$$ and all permuations of first three coordinates

Representations
an octahedron atop cuboctahedron segmentochoron has the following Coxeter diagrams:


 * oo4ox3xo&#x (BC3 axial)
 * ox3xo3ox&#x (A3 axial)