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There are 6 ways:
1. The four points form a square.
2. Three points form an equilateral triangle and the fourth point is at the center of that triangle.
3. Points A, B, and C form an equilateral triangle and points D, B, and C form another equilateral triangle.
4. Points A, B, and C form an equilateral triangle, point D sticks out from point A, perpendicular to line BC to a distance equal to the sides on the equilateral triangle.
5. Points A, B, and C form an equilateral triangle. Line AD bisects line BC.
6. The four points make a trapezoid with the base of the trapezoid equal to the diagonals, and the other three lines equal in length.
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