Folding Pseudo-Stars that are Cyclicly Hinged

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Greg N. Frederickson: Folding Pseudo-Stars that are Cyclicly Hinged. In: Bridges 2015. Pages 1–8



Motivated by a (layered) folding dissection of a 2-high {10/3}-star to a 4-high {5/2}-star, we identify an infinite class of folding dissections for pseudo-stars for which the dissections are cyclicly hinged. In addition to folding dissections of 2-high to 4-high pseudo-stars, the class includes folding dissections of 2-high to (2h)-high pseudo-stars for any whole number h, as well as folding dissections of (2h)-high to (2h′)-high pseudo-stars where h and h′ are whole numbers such that gcd(h, h′) = 1. The total number of pieces in each of these folding dissections is the sum of the number of points in both stars.

Extended Abstract


 author      = {Greg N. Frederickson},
 title       = {Folding Pseudo-Stars that are Cyclicly Hinged },
 pages       = {1--8},
 booktitle   = {Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture},
 year        = {2015},
 editor      = {Kelly Delp, Craig S. Kaplan, Douglas McKenna and Reza Sarhangi},
 isbn        = {978-1-938664-15-1},
 issn        = {1099-6702},
 publisher   = {Tessellations Publishing},
 address     = {Phoenix, Arizona},
 note        = {Available online at \url{ }},
 url         = { },

Used References

[1] C. S. Elliott. An extension to polygram shapes and some new dissections. Journal of Recreational Mathematics, 27(4):277–284, 1995.

[2] Greg N. Frederickson. Dissections Plane & Fancy. Cambridge University Press, New York, 1997.

[3] Greg N. Frederickson. Hinged Dissections: Swinging and Twisting. Cambridge University Press, New York, 2002.

[4] Greg N. Frederickson. Piano-Hinged Dissections: Time to Fold! A K Peters, Wellesley, MA, 2006.

[5] Greg N. Frederickson. Dissecting and folding stacked geometric figures. Powerpoint presentation at the DIMACS Workshop on Algorithmic Mathematical Art: Special Cases and Their Applications, Rutgers University, Piscataway, NJ., 2009.

[6] Greg N. Frederickson. My parade of algorithmic mathematical art. In Robert Bosch, DouglasMcKenna, and Reza Sarhangi, editors, Bridges Towson: Mathematics, Music, Art, Architecture, Culture, Proceedings 2012, pages 41–48, Towson, MD, 2012. Tessellations Publishing.

[7] Harry Lindgren. Geometric Dissections. D. Van Nostrand Company, Princeton, New Jersey, 1964.


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