Learn English – the preposition associated with “admiration”

Possibly there's a US/UK divide here. I don't much like OP's example usage.

It's not obvious why the adjective "great" should affect the acceptable preposition either, but I must say "He had an admiration of Washington Irving" sounds awful to me. I'd always use for, and drop the article...

He had great admiration for Washington Irving.

EDIT: As @Armen Ծիրունյան's answer points out, admiration of still occurs fairly often, but it usually occurs in "adjectival" constructions involving [to be] in admiration of. Where admiration has a more overt "noun" sense, we use [to have] [an] admiration for...

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Note that the "alternative" versions (was in admiration for, had admiration of) don't occur often enough to show on the chart. Clearly the vast majority of writers use for in OP's context.