Animations of some twist-hinged dissections of ring benches

The following animations, by Greg Frederickson, are of twist-hinged dissections that appear in the paper:

"Symmetry and Structure in Twist-Hinged Dissections of Polygonal Rings and Polygonal Anti-Rings", by Greg N. Frederickson,
Proceedings of Bridges Donostia: Mathematics, Music, Art, Architecture, Culture, San Sebastian, Spain (July 2007), pp. 21-28.

Here are animations of some of the twist-hinged dissections in the Bridges Donostia article, applied to polygonal benches, ring benches, and anit-ring benches:

Decagonal bench to two pentagonal anti-ring benches (illustrated in Figure 5).

Decagonal ring bench to two pentagonal benches (illustrated in Figure 7).

Dodecagonal ring bench to three square benches (illustrated in Figure 8).

Two dodecagonal rings to three octagonal ring benches (illustrated in Figure 9).
Actually, the animation shows just one dodecagonal ring bench to one and a half octagonal ring benches.

See videos of actual physical models of the third of the examples above.

For additional background material, see:

Hinged Dissections: Swinging & Twisting, by Greg N. Frederickson,
Cambridge University Press, 2002, pages 228-256.

If you are interested in building one of the ring-benches in the paper, but are puzzled by what the angles and dimensions should be, please send me a message ( gnf at cs.purdue.edu ) and I'll work them out for you.