Pandiagonal magic square

A pandiagonal magic square or panmagic square (also diabolic square, diabolical square or diabolical magic square) is a magic square with the additional property that the broken diagonals, i.e. the diagonals that wrap round at the edges of the square, also add up to the magic constant.

A pandiagonal magic square remains pandiagonally magic not only under rotation or reflection, but also if a row or column is moved from one side of the square to the opposite side. As such, an ${\displaystyle n\times n}$ pandiagonal magic square can be regarded as having ${\displaystyle 8n^{2}}$ orientations.