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