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How do I obtain the coordinates of the centers of triangles composing the Koch snowflake?

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Please search the site properly for existing answers before asking a new question. Following the answer by @Mark McClure here , getting the centers of the Koch snowflake triangles is a very easy job.

Centers at level n=2

(Mean /@ triangles[2])

Visualize them. Thx to the answer I linked above.

enter image description here

Graphics[{Table[{Darker[LightYellow, 1 - 1/1.2^(k - 1)], 
    EdgeForm[{Thin, Directive[Opacity@.3, Gray]}], 
    Polygon[triangles[k]], Darker[Red, 1 - 1/2^(k - 1)], 
    Point /@ (Mean /@ triangles[k])}, {k, 1, level}], {Orange, 
   Line[edges]}}]
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