T H E R E U L E A U X

The Reuleaux triangle can be understood as an extension of the Vesica Piscis through the addition of an arc with the same curvature as the arcs of the original circumferences,so that from the two equilateral triangles that remained enclosed in the original construction, only one is left. The three resulting arcs of the new intersection have the same length and, moreover, the distance from each point of the curve to the opposite vertex is constant.
This means it will roll between two fixed parallel lines as would a wheel over a horizontal plane.