# The disphenoid

**Geometry**Level 5

\[\large { P(x) = x^3 - 17x^2 + 93x - 161 } \]

Find the closed form of the volume of the *disphenoid* whose edge lengths are the roots of the polynomial above.

GIve your answer to 3 decimal places.

**Definition**: A disphenoid is a non-regular tetrahedron whose faces have the same perimeter/area, and thus consist of congruent triangles.

Try this easier problem.