# Challenge 392: Operation Octahedron

Investigate this octahedron...

An octahedron has vertices A, B, C , D, X and Y.

ABCD is a square, with X above the plane containing ABCD and Y below this plane.

All the faces of the octahedron are equilateral triangles.

Given that the volume of the octahedron is 288cm^{3}, find the total length of all its edges in the form a√2 cm, where a is an integer.

What is the ratio of the octahedron's surface area to its volume, in its simplest form?