Any n-sided polygon which has n sides of equal length can be considered an equilateral. Not all equilaterals are convex geometric shapes: consider that for a pentagon two adjacent sides can be reflected in the line segment joining the two extreme vertices.
An equilateraltriangle is a triangle with all three sides of equal length
An equilateraltriangle is therefore a special case of an isosceles triangle having not just two, but all three sides equal.
Napoleon's theorem states that if three equilateraltriangles are drawn on the legs of any triangle (either all drawn inwards or outwards) and the centers of these triangles are connected, the result is another equilateraltriangle.
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