The basic difference is this:
1.If you take a symmetrical core and cut it in half from top to bottom, both pieces will be exactly alike.
2.If you take an asymmetrical core and cut it in half from top to bottom, both pieces will be unique.
An asymmetric core will have a difference in shape from one side of it to the other while a symmetric core is the same all the way around.
The oddly shaped side of the asymmetric core is what is used to create a stronger mass bias than is found in symmetric balls.
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