The inner Napoleon triangle is the Triangle formed by the centers of internally erected Equilateral Triangles , , and on the sides of a given Triangle . It is an Equilateral Triangle.
The outer Napoleon triangle is the Triangle formed by the centers of externally erected Equilateral Triangles , , and on the sides of a given Triangle . It is also an Equilateral Triangle.
See also Equilateral Triangle, Napoleon Points, Napoleon's Theorem
References
Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 60-65, 1967.