November 2015 - Dividing the Tetrahedron

There is a regular tetrahedron, with a point at the centre. This point divides the tetrahedron into 4 smaller congruent (irregular) tetrahedra. Each smaller tetrahedron has surface area 18√2+36√3.

Find the volume of the regular tetrahedron (and then divide it by √2 to get a whole number answer).

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