One of the mysteries of the English language finally explained.
Definition of flexagon in US English:
flexagon
noun
MathematicsOriginally: a strip of paper marked with equilateral triangles, alternately upright and inverted and each typically decorated with a pattern or colour, which can be folded into the shape of a regular hexagon in a number of different ways; a hexagon made in this way, which can be manipulated to display different faces in different combinations. In later use also: any regular polygon made in this way.
Origin
1950s; earliest use found in Mathematical Gazette. Blend of flex and hexagon.