Stackfolding dissections

In the late summer and fall of 2007, I became interested in folding dissections that have only one assemblage. To mimic a dissection such as two equal squares to one, I would have the smaller square be in a "tower" twice as high as that of the larger square. I wrote the following article,

"Unfolding an 8-high Square, and Other New Wrinkles", by Greg N. Frederickson,
which was the basis for my talk at the Eighth Gathering for Gardner, in March 2008.

For the time being, I'll include just a few animations of stackfolding dissections:

A simple animation of a stackfolding dissection of a 1-high square to an 8-high square, which seemed particularly appropriate for G4G8.

A 1-high star to a 3-high star. It seems necessary to fold some pieces part of the way, fold others all the way around, and then complete the initial folds.

A 1-high Latin cross to a 2-high Latin cross. It seems necessary to fold four of the pieces simultaneously.

A 1-high Greek cross to a 9-high Greek cross. It was not so easy to beat this down to 27 pieces, nor to get the sequence of foldings. Note that the pieces are colored so that all pieces on one level of the 9-high cross are colored the same.

For additional background material, see:

Piano-Hinged Dissections: Time to Fold!, by Greg N. Frederickson,
A K Peters, 2006.