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Apr 16, 2022 at 2:01 comment added Sam Hopkins Although possibly this does not explain all the uses of "great" for polyhedra that you mention. Often for a "great" polyhedron there is also a "small" polyhedron which would have the same name, and the great/small is to distinguish those two.
Apr 16, 2022 at 1:43 history answered Sam Hopkins CC BY-SA 4.0