OK, let me try this way.....


examples of a symetrical core is the Swamp Monster, inferno, Throttle, THING, Sonic X.

examples of an asymetrical core are Freak, Hercules Mutant, Super Freak.


Let me ask this question then, The X Factor, It has that center piece (the flat circular piece) in the core that only goes through one side....but if you turn it around, it is futher out on one side and the other side has the flat area, would this make it symetrical or asymetrical?


I hope I worded that well

To further expand on what Ishmael said...with symmetrical cores, no matter which way you slice them in half, both halves will have the same shape and mass.  With "asymmetrical" or "mass bias" cores there is always a direction in which they can be sliced in half and produce two halves with different masses (although the shape may or may not be identical).

You mentioned the X-Factor cores.  Storm uses different masses on each side of the disk to produce the mass bias although the shape of the core is uniform.  The Freak, for example, uses protrusions on one side or the other of the core to create the mass bias.