Consider the diagonals $A_1A_3, A_2A_4, A_3A_5, A_4A_6, A_5A_4$ and $A_6A_2$ of a convex hexagon $A_1A_2A_3A_4A_5A_6$. The hexagon whose vertices are the points of intersection of the diagonals is regular. Can we conclude that the hexagon $A_1A_2A_3A_4A_5A_6$ is also regular?