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A Tetrahedral Volume Puzzle (Posted on 2016-07-28) Difficulty: 2 of 5
A tetrahedron has all four of its faces equal to an area of 12*sqrt(3). What is the largest and smallest possible volumes it can have?

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The volume can be made as small as one desires.  Take a regular tetrahedron and squash it by bringing two non-intersecting edges close together.  All of the sides deform and approach 45-45-90 triangles as the volume goes to zero.

A regular tetrahedron is the most efficient tetrahedron (I think) meaning it can enclose the greatest volume for a given surface area.
The side length of this is 4*sqrt(3) and volume 16*sqrt(6)

  Posted by Jer on 2016-07-28 10:30:10
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