The rectangle A B C D at the right has dimensions A B=12 \sqrt{3} and B C=13 \sqrt{3}. Diagonals \overline{A C} and \overline{B D} intersect at P. If triangle A B P is cut out and removed, edges \overline{A P} and \overline{B P} are joined, and the figure is then creased along segments \overline{C P} and \overline{D P}, we obtain a triangular pyramid, all four of whose faces are isosceles triangles. Find the volume of this pyramid.
