Loops On The Dot (Digital Diagram)

 

Since the board has no boundary and all pieces on it can move without limit of steps, players will find that the experience of playing “Dot” is totally different from any other board game, especially the movements of pieces along the looping routes.

 

Although the Dot is a 3-dimensional sphere, the surface of it is essentially a 2-dimensional membrane without borders, because it only needs two sets of volumes—the longitude and the latitude—to pinpoint a location on its surface. Since the surface of the Dot is essentially a 2-dimensional membrane, surely it can be displayed as a 2-dimensional and rectangular chart—just like the flat chessboard—by seven specific steps of transmogrification.

 

There are twenty loops on the surface of the Dot in total, which are eight latitudinal loops, four longitudinal loops, four clockwise helix loops and four counterclockwise helix loops. If all these loops are displayed on a 2-dimensional and rectangular chart, and the lines of the loops remain connected, it will look like this diagram exactly.

 

 

 

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2D