Octahedron Platonic

What is the ratio of Geometric Platonic Solids?
I am doing a Geometry project in which i have to place a cube inside a dodecahedron, and a tetrahedron inside the cube and an octahedron inside the tetrahedron, but the catch is they must be fit snugly inside each solid and my teacher told us there is a ratio for these solids. Does anyone know this ratio?
Thanks
Hope this helps. I know that an icosahedron can be inscribed in an octahedron so that each vertex of the icosahedron divides the edge of the octahedron in the golden ratio (phi).
phi = 1/2(1 + sq rt5)
Octahedral Coil
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