The classic Risk map (published 1959 and 2003) is spatially skewed in that, for any two countries, the connections and pathing distance may be visually distorted. For instance, the pathing distance from Southern Europe to Iceland is three hops which is slightly less than four inches on the printed board map. Using the same three hops you can path all the way to Venezuela crossing a third of Africa and the entire Brazilian Amazon. The distortion is even more pronounced in terms of real world distances. You need only consult a globe to see that the distances of Rome to Reykjavik and Rome to Caracas differ by a factor of three. The real world distortion is because the Risk board map is a Mercator projection from a sphere to a rectangle. However, the pathing distortion is purely the result of the country borders selected by the original Risk board map designer.
One of the key features of the classic Risk map is that all countries have at most six adjacent countries and no crossed connections. This indicates that the Risk map could be spatially normalized into a regular triagonal/hexagonal tiling. An example of a crossed connection would be Four Corners USA where the borders four states: Arizona, Utah, Colorado, New Mexico meet in a 4-way intersection. The connections Arizona-Colorado and Utah-New Mexico cross each other.
The image above was first described by Ray E. Bornert in 2004 as the Xisk Map intending to suggest the idea of a hexagon. It shows the best possible visual spatial relationship between all of the countries on the Risk board map. A fully normalized triangular grid would mean that all 42 countries would cleanly rest on a unique vertice, and all 83 adjoining connections would rest upon a clean edge between vertices. The Risk map cannot be fully tiled but only partially so. All of the countries except Southern Europe rest cleanly on a unique grid vertice. All but 12 connections rest cleanly on a triangle edge. The skewed connections are: Southern Europe to all, North Africa to Western Europe and Brazil, Yakutsk to Siberia and Kamchatka, Middle East to East Africa and Ukraine. Southern Europe could be moved to a vertice but that would increase the spatial distortion for at least 2 connections which goes against the goal of accurately depicting the spatial relationship of each country with every neighbor (which is a higher priority).