The answer depends on whether the shape is 2-dimensional or 3-d. For a 2-dimensional polygon with n sides, the minimum number is n-3 diagonals.
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A rigid shape is when you cant push/pull on it and make it turn into a different shape. You can make shapes rigid by adding "braces", which are lines that you put inside the shape to make triangles (which are rigid). For instance, a square is notrigid. To make it rigid, you would put a brace inside diagonally. This would create TWO triangles, and therefore, rigid. ~xDragonx
35 diagonals
There are 54 diagonals in a 12 sided shape
A nanogon has no diagonals because there is no such shape. A nonagon, on the other hand, has 9*(9-3)/2 = 27 diagonals.
I am sure that a shape with six side has 9 diagonals. (I found out cause I really wanted to help people.)