Flexing one of these flexagons will truly produce magic! Magic flexagons are flexagons where patterns of numbers on the faces add up to magic numbers. They are like magic squares, magic stars, etc. but have the dynamic property where flexed faces will always have magic number properties even though the faces get rearranged. Some magic flexagons are more similar to magic cube than a magic square as in the second model below. Flexagons are a wonderful base for creating number magic! Below I give several templates for magic flexagons that I am sure you will find facinating and clearly show the potential for infinite variations. These are great meditative devices for calming the mind and, as we get older, for keeping the mind number sharp in this age of calculators and computers.
Unlike flexagons, magic squares have deep historical roots going back thousands of years. Flexagons present new ways to create beauty with a combination of patterns in numbers and art. Square flexagons have obvious synergy with magic squares. If we create or select magic squares where the sub squares also add up to magic numbers, we can create square flexagons that will be magic on all flexagon faces, even though the faces are rearranged during flexing. For example, for a 4x4 magic square, if all the four number groups in each corner add up to the same number, it will retain magic totals for the rows and columns when we flex the flexagon faces of a square flexagon. Below is a 4 sided cyclic square flexagon you can download and make for yourself.
This Magic Tetratetraflexagon flexagon features famous magic squares created by; Heinrich Cornelius Agrippa, Albrecht Dürer, Josep Maria Subirachs, and Benjamin Franklin. More history on these magic squares is contained on the template. More on all these Magic Flexagons can be found the the Blog tab.
For this next magic flexagon you wil find that the three numbers on all triangles add up to 42 on all flexagon faces. The sum of the numbers around the inside center point will always add up to twice 42 or 84. The outside numbers around every face will always add up to 168.
Super Magic Star Trihexaflexagon
For the following super magic star flexagon, the four same colored numbers connecting each of the points of the stars on all six flexagon faces will add up to 26. Each face has 6 sets of these 4 numbers. The 6 numbers on the six points of all the stars also add up to 26. This flexagon is constructed from the only six possible “Super Magic Stars.” Super magic stars have the special feature that the points of the stars add up to the magic number as well as the arms. You will also find that the 12 numbers around the center of each face will add up to twice 26 or 52. For super magic star details see: http://www.geocities.com/~harveyh/order6.htm .