Twin cores are a very rare occurrence in the wizarding world. The wand can be made from a different wood or a different length as long as both wands share the same core from the same magical animal. If twin cores try to do combat to each other then the wands will not do the desired spell but instead will reverse the last spells that the wands have cast. If both wands battle the same enemy then both the wands powers increase tenfold.[1]

Known twin wands

Wand Owners Core Core From:
Phoenix feather Fawkes
Horned Serpent horn Unnamed Horned Serpent