Which Platonic solid is in the middle?

Geometry Level 3

If each of the Platonic solid is circumscribed exactly within a given sphere then sorted into volume order, then which Platonic solid is in the middle of the list?

Dodecahedron Impossible to determine Icosahedron Cube Tetrahedron Octahedron

A Former Brilliant Member by A Former Brilliant Member

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1 solution

In a sphere of volume 1, here are the respective volumes: Tetrahedron 0.122518 Octahedron 0.31831 Cube 0.367553 Icosahedron 0.605461 Dodecahedron 0.664909 \begin{array}{ll} \text{Tetrahedron} & 0.122518 \\ \text{Octahedron} & 0.31831 \\ \text{Cube} & 0.367553 \\ \text{Icosahedron} & 0.605461 \\ \text{Dodecahedron} & 0.664909 \\ \end{array}

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