What are the body diagonals of a cube and how do you calculate them?

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SUMMARY

The body diagonals of a cube connect opposite corners, extending from one vertex to the furthest vertex in three-dimensional space. For example, if you start at the near-top-right corner of the cube, the body diagonal extends to the far-bottom-left corner. This concept is analogous to the diagonals of a square but applied in three dimensions. The calculation of the length of a body diagonal can be derived using the formula \(d = a\sqrt{3}\), where \(d\) is the diagonal length and \(a\) is the length of a side of the cube.

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Can some one tell me what are the diagonals of a cube?
Picture is better
 
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Firstly, think of a diagonal of a square.

A---------------B






C---------------D

It would A to D, D to A, C to B, or B to C. With a three dimensional cube, similarly, it is from one corner to the other "extreme" corner. That is the corner most farthest away. So if you are at the near-top-right corner, the diagonal would be a line to the far-bottom-left corner.
 

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