How to draw combinatorial map? From graphs and edges to corner rotations   and permutations
  In this article we consider combinatorial maps approach to graphs on surfaces, and how between them can be establish terminological uniformity in favor of combinatorial maps in way rotations are set as base structural elements and all other notions are derived from them. We set this approach as rotational prevalence principle. We consider simplest way how to draw combinatorial map, and ask how this approach in form of rotational prevalence could be used in graphs drawing practice and wider in algorithms. We try to show in this paper that the use of corners in the place of halfedges is much more natural than that of halfedges. Formally there is no difference between both choices, but corner approach is much more clear and concise, thus we advocate for that. 
Dainis Zeps (IMCS), Paulis Kikusts (IMCS)
math.GM