Symmetry and Structure in Twist-Hinged Dissections of Polygonal Rings and Polygonal Anti-Rings

Greg N. Frederickson
Bridges Donostia: Mathematics, Music, Art, Architecture, Culture (2007)
Pages 21–28


A geometric dissection is a cutting of a geometric figure into pieces that we can rearrange to form another figure. Twist-hinged dissections have the amazing property that all pieces are connected by special hinges that allow the one figure to be converted to the other by means of twists. This paper explores such dissections for ringlike figures based on regular polygons. The twist-hinged dissections of these figures can be adapted to create reconfigurable benches that ring a pillar or tree, exhibiting remarkable symmetry and making singular design statements.