Polygonal Numbers

Triangle a number

({()({}[()])}{})

Square a number

({({})({}[()])}{})

Pentagon a number

({({})({}[()])({})}{})

String formula for arbitrary n-gon (n > 3)

"({({})({}[()])"+"({})"*(n-4)+"}{})"

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Negative general Polygonal numbers

Polygonal numbers can be generalized and projected onto the negative numbers.

The Anti-n-gon is the result of passing -n into the general form of the general formula for the n-gon.

Both Square and Triangle have a vertical axis of symmetry.

Anti-Pentagon a number

({({})({})({}[()])}{})

String formula for arbitrary anti-n-gon (n > 2)

"({"+"({})"*(n-3)+"({}[()])}{})"