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.


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