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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 ''n''×''n'' pandiagonal magic square can be regarded as having 8''n''2 orientations.
==3×3 panmagic squares==
It is easily shown that non-trivial pandiagonal numerical magic squares of order 3 do not exist. However, if the magic square concept is generalized to include geometric shapes instead of numbers—the geometric magic squares discovered by Lee Sallows—a 3×3 panmagic square does exist.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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