I corrected a mistake on Tutte’s map conversion. This one is the fixed version. Face number 25 surrounding all the other faces on the original map, is the ocean of the rectangular and circular maps.

Same map converted into rectangular and circular (using different colors):

Here is a presentation I made with Prezi and a video with the application to generate maps (circular and rectangular) on Youtube.

Please, feel yourself at home and you are very welcome to take a look around, leave comments, ask questions, send ideas, corrections and so on.

Bye

And please, if my english gets too incomprehensible, tell me.

All regular maps can be topologically transformed into rectangular of circular maps (see T2).

Here is the computerized and colored version: Conversion of famous maps UPDATED

CORRECTED!

All regular maps can be topologically transformed into rectangular of circular maps (see T2).

This is the conversion of Tutte’s map, made by hand, into a rectangular map. The colored and computerized version will follow.

These conversion are done just for fun and have not theoretical interest. The theorem in T2 proves that all regular maps (basically all maps of interest to the four color theorem) can be converted into circular of rectangular maps.

Tutte’s map on the left and the map made of rectangles right below it, are exacly the same map. Face number 25 correspond to the surrounding area (the ocean) of the rectangular map.

Conversion of famous maps UPDATED

Original image taken from:

http://en.wikipedia.org/wiki/Four_color_theorem

Same image converted into circular and rectangular (using different colors):

I am converting some famous maps into rectangular maps. You can check some converted maps here: Conversion of famous maps.

First steps are explained here: First steps.