Hypermap representations of ordinary maps II

This diagram summarizes the map operations needed to go directly from an ordinary map to its representations as a hypermap (having 2-valent hyperedges.)

In the diagram, for any map operation Mp, Mp'() = Mp(Du()), and Mp*() = Du(Mp()).

The map operation here named meta (following Conway) is sometimes called full bisection, barycentric subdivision, 2-D subdivision or dual triangle quadrisection.

The map operation here named bevel (following most of the map operations literature) is sometimes called omnitruncation.

The map operation here named parallel is sometimes called parallelization.

The map operation here named subdivide is sometimes called Su1 or 1-dimensional subdivision.

The composite map operation ring is given by: Ri() = Me(Su()).