+-------------D /| /| / | / | / | / | / | / | C-------------+ | | | | | | B--------|----+ | / | / | / | / | / | / |/ |/ +-------------AA, B, C and D are non-adjacent vertices of a cube. There is a point P in space such that PA=3, PB=5, PC=7, and PD=6. Find the distance from P to the other four vertices and find the length of the edge of the cube.

There are two answers, one with P outside the cube and one with P inside the cube.