Flexible polyhedra are, in a sense, a three-dimensional extension of the notion of a flexagon. The flexacube, for instance, reveals hidden faces as it is manipulated. More surprising still, the Yoshimoto cube reveals two star-shaped solids.
The flexacube
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The flexacube is a structure made up of eight cubes linked to one another along certain edges, with the connection between two cubes being flexible. Every cube making up the structure has six faces of different colors. In the example used in this article, the blue and red faces are opposite, as are the green and yellow faces, and the orange and purple faces.
When "folded", the cubes (which we will assume have unit side length) take on two stable parallelepiped shapes: either a cube with side 2 or a 4 × 2 × 1 rectangular parallelepiped.
In the cube with side 2, opposite faces are the same color.
