A tetrahedron puzzle

This post is about a 3D geometry Riddler puzzle involving spheres and tetrahedra! Here is the problem:

We want to create a new gift for fall, and we have a lot of spheres, of radius 1, left over from last year’s fidget sphere craze, and we’d like to sell them in sets of four. We also have a lot of extra tetrahedral packaging from last month’s Pyramid Fest. What’s the smallest tetrahedron into which we can pack four spheres?

Here is my solution:
[Show Solution]

One thought on “A tetrahedron puzzle”

  1. Do the tetrahedrons have to be perfectly symmetrical in faces, edges, and vertices? If so, we don’t have to account for the top sphere sinking into the bottom three’s “divot”.

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