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Weird Universes

Age 16 to 18 Challenge Level:

Four identical robots and their enemies, the stick men, live in small universes based on squares with the opposites sides identified (i.e. corresponding to the same points in space) in various ways, as shown in the diagrams below:

Consider these universes. In which ways could the stick men shoot the robots? Which create a geometry which can be made in 3 dimensions out of a sheet of paper? Perhaps you might like to experiment with other universes?
Did you know ... ?

String theory suggests that each point we see in 3D space is in fact a higher dimensional surface wrapped up in very specific ways.