# 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.

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

Disphenoid

Try this easier problem.

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