To accompany Folding and Unfolding in Computational Geometry:Part III: Ch.4.1: Folding a Polygon

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**Evolution of the hexahedron folded from a square.**

In each applet below, a square is shown which represents the unfolding of
a hexahedron. In each, the distance between the moveable red slider and the
leftmost black vertex is equivalent to the distance between the pink vertices
on the edge of the square. As the distance between the pink points changes,
the folding of the hexahedron changes slightly, and two points are transition
point, where the edges of the hexahedron have some noticeable change. Each
of the three resulting ranges is shown below.

**Move the red slider between the black dots**

The second range requires one fewer fold than the first: note the orange fold above is gone.

Note the green edge switches directions after the slider reaches the third black dot: at this point the faces which this edge separates become coplanar so that this switch is possible.

Created with Cinderella

applet created by Melody Donoso