I have a polyhedron, an elongated hexagonal bipyramid,
created in affine space and would like to translate this [these] into 3D
Cartesian space such that it tessellates the latter, with the
following constraints. That the transformation performed allows for the
indexing of each of the tessellated component structures. I have thought of
ways of doing this but this might involve "recreating the wheel," if
one does already exist in a package such as yours.

Hopefully, one or more of
your users would comment on this.

There are other operations to be performed latter but this is the main step.

Thanks!