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Full Idea
A building may be composed of proper parts which are themselves buildings; a particular pattern may be composed of proper parts which are themselves patterns (even the same pattern, on a smaller scale).
Gist of Idea
The parts may be the same type as the whole, like a building made of buildings
Source
Kathrin Koslicki (The Structure of Objects [2008], 7.2.12)
Book Ref
Koslicki,Kathrin: 'The Structure of Objects' [OUP 2008], p.195
A Reaction
This strikes me as a rather important observation, if you are (erroneously) trying to establish the identity of a thing simply by categorising its type.