Dissecting a Regular 2n-gon into Four Smaller 2n-gons

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This Demonstration shows a dissection of a regular 2-gon into four smaller 2-gons. Steps 1 and 2 remove two of the small 2-gons and step 3 transforms the rest into two other small 2-gons, which are symmetric in the origin.

Contributed by: Izidor Hafner (June 2016)
Open content licensed under CC BY-NC-SA



Figure 21.6 in [4] shows three symmetric assemblies of four dodecagons into one, each assembly requiring 12 pieces. Lindgren writes: "These are referred to, but not described, by H. M. Cundy and C. D. Langford, Mathematical Gazette, 44(46), 1960, Note 2875, (information by Greg N. Frederickson)."


[1] G. N. Frederickson, Dissections: Plane & Fancy, New York: Cambridge University Press, 2003 pp. 10–11.

[2] W. W. Rouse Ball and H. S. M. Coxeter, Mathematical Recreations and Essays, 13th ed., New York: Dover Publications, 1987 p. 142.

[3] Wikipedia. "Dodecagon." (Jun 3, 2016) en.wikipedia.org/wiki/Dodecagon.

[4] H. Lindgren, Geometric Dissections, Princeton, NJ: Van Nostrand, 1964.

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