Tagging named rock faces like 'Eiger Nordwand'

lately I was editing a lot of natural features in alpine regions. Often times I come across steep rock faces, which have commonly known names - sometimes very famous ones like the ‘Eiger Nordwand’, which is very important for the history of alpinism and as a landmark.
So far I used the generic tag place=natural, but I would think that a dedicated value for the natural-tag would be more appropiate (f.e. natural=rock_face).
Is there any other tag that is more appropiate than place=locality for such features?

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