## Math formula(e) needed: tesseract model construction?

Although I CAN do this without the math formula(e) to figure it all out, I would like to have it for a quicker method of figuring out size, etc. so I didn't have to use up so much material in guessing.

I would like to construct the tesseract I have pictured here, using rigid clear plastic sheets or panels.

Given a said size for the "inner cube" say 2 inches (approx. 5 cm or about 51 mm) what formula(e) must I use to calculate the panels' dimensions to connect to the larger cube (knowing full well this will depend on the size of the larger cube....say approx. 4 inches across (about 10 cm or 102 mm)?

The reason I'd like the formula(e) is that I may need to increase the size of the center cube by an inch or so, and this would allow me to do so without having to go through the "trial and error" thing so many times.

I would, of course, want the center cube to be "centered", if possible or shall I say as close as possible.

Thanks....

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^{2}= SUM s_{i}^{2}where s_i is the length of the i

^{th}side. For the case of an N-cube with side s, this reduces to s*sqrt(N).For your nested cubes, Goodhart, with sides L and M (L > M), each of your red lines is just half the difference of the two body diagonals:

[sqrt(3)L - sqrt(3)M] / 2 = (L-M) sqrt(3)/2

which is BritLuv's solution.

a(squared) + b(squared) = c(squared)

All you need to do is work out the square root of c and you have the length of the red lines.

Providing the cube in the middle is perfectly central, all of the red lines would be the same.

Hope this helps.

b is the side length of the bigger cube and a of the smaller.