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Holly
"Yes, thirteen-and-a-half inches. Yew. Curious indeed how these things happen. The wand chooses the wizard, remember... I think we must expect great things from you, Mr. Potter... After all, He-Who-Must-Not-Be-Named did great things – terrible, yes, but great."
Harry shivered. He wasn't sure he liked Mr. Ollivander too much. He paid seven gold Galleons for his wand, and Mr. Ollivander bowed them from his shop.
As he closed the door, walking between the shelves towards the back of his shop, stroking a few of the boxes containing wands on the way, Garrick Ollivander was still pondering the recent encounter.
Phoenix feather. Really, who was actually dumb enough to believe that a phoenix of all creatures would donate a feather for a wizard it did not know? Not that the other so-called wand cores were any more realistic. Combining the fire-based magic of a dragon's heart, the heat of the beast's rage still contained therein, with a piece of wood? And anybody trying to get a hair from a unicorn was likely to be gored by the silvery horn of the animal.
Even if one were to gain these materials, though, they would not be useful when creating a magical focus. The mere idea...
No, those were not actual materials. Instead, they were code words, roughly declaring the temperament of a wizard's magic. Gentle and shy as a unicorn, battle oriented like a dragon, or somewhere in between – like a phoenix.
The old wandmaker gazed around at his creations. Pieces of wood, different in shape and origin, not magical at all – yet prepared, by rituals as well as the runes on the tools used to shape them, to accept, condense and solidify a part of their wielder's magic.
That was the true core of any wand, formed the moment the inert piece of wood was first picked up by one whose magic liked it. Without such a core of solidified magic, a wand was just as dead as any other stick.
There had been other foci, long ago, so long that most did not remember. Formed out of nothing but magic and power of will. Shaped by imagination and destiny. Wizards had grown so annoyingly complacent...
Still, today had at least been interesting.
The shared wand core... or rather, that part of Mr. Potter's solidified magic which felt so remarkably similar to the one he had felt a little over fifty years ago...
And Holly, of all things. That damned wood was so annoyingly ambiguous!
Holly, the crown of the winter solstice, ruler of the white realm, king of the darker half of the year. A reminder that life is possible even on the darkest and coldest of days, and yet also a constant reminder of said days themselves. Would that child be the next darkness... or the light within the darkness?
Probably the latter. He was not blind, not yet at least, and that familiar magic had come from the child's forehead and the scar residing there. The lightning-shaped scar. And Holly was said to repel lightning.
There was hope.
And yet, Holly was also a symbol of hard-won battles...
He sighed, hoping to survive whatever was to come...
The first two paragraphs are quite obviously taken directly from the book. In fact, this story consists of two paragraphs from the first Harry Potter book and half an hour of research into the symbolism of holly, carefully tied together by the conclusions most of you would have reached (at least if you found the same or similar sources as I did).
In order to stay with my usual theme, I decorated all of that with hints and pieces of my version of the magical world. Specifically, you should assume that wands have a comparatively minor role in my planned story.
Regarding wand cores, though, I really think that combining any material contaminated by fire-based magic with wood of all things would not be a safe thing to do. So why not use the magic of the wielder, in a more concentrated form, as the real core? The process of the magic rushing into the prepared wood (which it would only do if it liked the wood) and condensing into a wand core would also explain the sparks.
I might, at some later point, write additional chapters about the wands of other characters, but the main idea is written down, so for now, this is a oneshot.
Last word of advice: Don't ever try to pluck a hair from a unicorn's tail.