Take an arbitrary triangle ABC. Construct external regular triangles on its sides. Then construct the centroids of these regular triangles and join them to get a new triangle. When we drag the points A, B and C we can see that the new triangle A₁B₁C₁ is regular too.

This fact is known as Napoleon Theorem: The centroids of the regular triangles constructed externally on the sides of an arbitrary triangle are vertices of a regular triangle.