Question 14
The rectangle $ABCD$ below has dimensions $AB=12\sqrt3$ and $BC=13\sqrt3.$ Diagonals $AC$ and $BD$ intersect at $P.$ If triangle $ABP$ is cut out and removed, edges $AP$ and $BP$ are joined, and the figure is then creased along segments $CP$ and $DP,$ we obtain a triangular pyramid, all four of whose faces are isosceles triangles. Find the volume of this pyramid.
