What is the mathematical formula to calculate "a" for a given "b" in the picture below of a tetrahedron with sides "b" inside of a truncated tetrahedron with sides "a". I think that this is a more challenging problem that what it appears to be.

THis is your assignment , what do you think the answer is. We can only help once you show us what you have done.

I have tried to approach the solution to this problem by having 2 tetrahedrals - one inside and enclosed by the truncated tetrahedral, and a second outside that encloses the truncated tetrahedral. But then I got stuck and could not get any further without making assumptions that I was not sure were right.

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Originally Posted by andrewvecsey

I have tried to approach the solution to this problem by having 2 tetrahedrals - one inside and enclosed by the truncated tetrahedral, and a second outside that encloses the truncated tetrahedral. But then I got stuck and could not get any further without making assumptions that I was not sure were right. Something like it is right in the middle, but then what. why am I asked all the time to increase my answer by 5 characters. Again by 5 characters

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Have tried to approach the solution to this problem by having 2 tetrahedrals - one inside and enclosed by the truncated tetrahedral, and a second outside that encloses the truncated tetrahedral. But then I got stuck and could not get any further without making assumptions that I was not sure were right. Something like it is right in the middle, but then what. Why am I asked all the time to increase my answer by 5 characters. Again by 5 characters

Andrew - I'm not following what you mean by a truncated tetrahedron with sides 'a'. It looks from the figures like 'a' is the length of the pieces of the tetrahedron that are cut off, but there is no indication of the length of the remaining part of the truncated tetrahedron. Hence the length 'a' does not define the size of the truncated tetrahedron.

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Originally Posted by ebaines

..... It looks from the figures like 'a' is the length of the pieces of the tetrahedron that are cut off, but there is no indication of the length of the remaining part of the truncated tetrahedron. Hence the length 'a' does not define the size of the truncated tetrahedron.

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The length "a" defines the truncated tetrahedron. It has 8 sides all with length "a", like all truncated tetrahedrons have. The tetrahedron that is enclosed by the truncated tetrahedron has 4 sides with length "b", like all tetrahedrons have. The question to solve is - what must "a" be so that the 4 corners of an enclosed tetrahedron with side "b" coincides with the 4 center triangle faces of the truncated tetrahedron?