Flexagons are perfect for creating dynamic magic squares (magic stars etc.)  There are a great number of ideas that can be explored.  Square flexagons are a nice place to start as they already have the geometry of a magic square.  Starting with 4x4 or 8x8  magic squares where the sub 2x2 and 4x4 squares are also magic, square flexagons can be created that retain magic sums even after flexing.  I created a template for one of these you can download from the Magic Flexagons menu tab.  I choose 4 famous magic squares to display on each of the 4 sides of a cyclic square flexagon. It is easy to make and of course has a "Magic" sense to it.  This idea can be expanded into any of the infinite varieties of square flexagons.

Magic Flexagons can also be created from a traditional three-sided hexaflexagon with excellent dynamic properties.  For example, check out the Magic Trihexaflexagon template on the Magic Flexagon tab.  For this template, the three numbers in the corners of all triangles add up to 42 on all flexagon faces.   The sum of the six numbers around the inside center point on each flexagon face will always add up to twice 42 or 84.  The outside numbers around every face will always add up to 168.  When trying to create 6 magic sums for each of the 6 triangles on the faces of the flexagon while at the same time trying to make magic sums for the two rings of 6 and 12 numbers on the faces of the flexagons and preserving these sums even when the faces are jumbled by flexing is challenging.   I found one way to construct the numbers for this flexagon is to create a 3x6 magic rectangle for each face such that the unique conditions of the flexagon are all met.  As it turns out, 3x6 magic rectangles using the numbers 1-18 is not possible.  Magic rectangles can only be created from rows and columns that are both even or odd (except 2x2).  That is why my flexagon faces have numbers greater than 18 in it. I believe it is possible to created 3x6 magic rectangles with prime numbers, but my initial look at it showed there would be a lot of 3 and maybe 4 digit numbers in the solution.  I am sure there are numerous other solutions using interesting numbers sequences for this flexagon.

Now to look at a Magic Flexagon with even more interesting number combinations, I created a Super Magic Star Trihexaflexagon.  I considered six pointed magic stars (six is the magic number for hexaflexagons!) where there are 4 numbers arranged from each star point to another star point. There are 6 of these four number groups in each super magic star.  Each of these number sums add to 26 and in this case every super magic star face has only the numbers from 1-12.  I chose magic stars where not only the arms add up to the magic number, but also the points add up to the magic number of 26.  There are only six - 6 pointed Super Magic Stars where the points of the star also add up to the magic number (26).  The 3 sided hexaflexagon has exactly 6 face variations.  I decided this was a perfect match and created a Magic star flexagon where each face displays one of the six - 6 pointed Super Magic Stars.  I color coded all the variations so each magic star is easily seen on all six of the flexagon faces.  Download a template for this flexagon also from the Magic Flexagon tab.  The unique concept for this flexagon was in creating a design that would represent Super Magic Stars on the flexagon faces.  The result makes for a fascinating flexagon and also stimulates dozens of new ideas for other Magic Flexagons!  I can imagine a huge number of Magic Flexagons of many different types can be created from the infinite flexagon bestiary.  I would love hearing from anyone who makes these models.