MathDB

A convex octahedron in Cartesian space contains the origin in its interior. Two of its vertices are on the

x

-axis, two are on the

y

-axis, and two are on the

z

-axis. One triangular face

F

has side lengths

\sqrt{17}

\sqrt{37}

\sqrt{52}

. A second triangular face

F_0

has side lengths

\sqrt{13}

\sqrt{29}

\sqrt{34}

. What is the minimum possible volume of the octahedron?

Problem Statement