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1.
A winged unicorn. A combonation of a unicorn and a pegasus. Sometimes known as a unipeg.
"The alicorn flew overhead, its horn prominent on its head, shining in the sunlight."
by Rose-Pose January 18, 2006
 
2.
The spiral horn of a unicorn.
"If you cut the alicorn, she'll die."
by Ceveri November 12, 2005
 
3.
An Alicorn is a winged Unicorn.

Mostly said by bronies.

Another word for Alicorn is Pegacorn.
Princess Luna is an alicorn also Princess Celestia is an alicorn.
by 20%Brony December 04, 2011