The Banach-Tarski Theorem describes how to split a sphere and re-arrange the pieces to make two spheres of volume equal to the original sphere.

Turns out it works on dragons, too.

(Cover taken from http://mlp.wikia.com/wiki/File:Spike_ID_S3E05.png and slightly modified)

For other stories of similarly duplicated characters, take a look at Second Sun by Carabas and Amphelion by Monokeras.