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

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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

## Snapshots

## Details

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)."

References

[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.

## Permanent Citation

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

http://demonstrations.wolfram.com/DissectingARegular2nGonIntoFourSmaller2nGons/

Wolfram Demonstrations Project

Published: June 6 2016