A tetrahedron T has edges of length 6cm. Find the volume of the solid S that has its vertices at the centre of each face of the tetrahedron. What kind of solid is S?

What kind of solid do you get if you repeat this process on the solid S, and how is its volume related to the volume of the original tetrahedron?

What happens if you start with a cube with edges of length 6cm instead of a tetrahedron?