Magic Square Tetraflexagon

A magic square is a grid of numbers where all the rows, columns, and diagonals add up to the same number. A flexagon is an origami-like construction folded from a strip of paper that can be flexed to rearrange and reveal faces. You can combine these two concepts to make a magic square that can be rearranged while retaining its "magic" properties.

In the following square tetraflexagon, all the rows, columns and major diagonals in the magic square sum to 34. You can flex the flexagon to rearrange the magic square in four different ways. Even though each flex swaps around the rows, columns, and diagonals, they still continue to sum to 34.

To see this magic square tetraflexagon in action, watch the video. To make the flexagon, click on the following image to get the full sized version. Print and cut out.

template

flexing instructions

To flex from the arrangement with 3 in the upper left to the one with 6 in the corner, fold the top half of the square backwards until it's flat against the back face. You can then open up the flexagon from the top, folding the back half downwards until you again have a square.

To flex from the arrangement with 6 in the upper left to the one with 9 in the corner, fold the left half of the square backwards until it's flat against the back face. You can then open up the flexagon from the left, folding the back half to the right until you again have a square.

To flex from the arrangement with 9 in the upper left to the one with 16 in the corner, fold the top half of the square backwards until it's flat against the back face. You can then open up the flexagon from the top, folding the back half downwards until you again have a square.

Learn all about flexagons in The Secret World of Flexagons

More information on square tetraflexagons

More magic flexagons from flexagon.net

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