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?
The volume can be made as small as one desires. Take a regular tetrahedron and squash it by bringing two nonintersecting edges close together. All of the sides deform and approach 454590 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 20160728 10:30:10 