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Regular Hendecagon


RegularHendecagon

The regular hendecagon is the regular polygon with 11 sides, as illustrated above, and has Schläfli symbol {11}.

The regular hendecagon cannot be constructed using the classical Greek rules of geometric construction.

Susan B. Anthony dollar coin

The rim of the U.S. Susan B. Anthony dollar coin was a regular hendecagon, as illustrated above.

The inradius, circumradius, and area of the regular hendecagon with unit side lengths are

r=1/2cot(1/(11)pi) approx 1.70284
(1)
R=1/2csc(1/(11)pi) approx 1.77473
(2)
A=(11)/4cot(1/(11)pi) approx 9.67103.
(3)

These can be written exactly as the polynomial roots

r=(11264x^(10)-42240x^8+29568x^6-5280x^4+220x^2-1)_(10)
(4)
R=(11x^(10)-55x^8+77x^6-44x^4+11x^2-1)_(10)
(5)
A=(1024x^(10)-154880x^8+6559168x^6-113379904x^4+857435524x^2-2357947691)_(10).
(6)

See also

Constructible Polygon, Decagon, Dodecagon, Hendecagon, Polygon, Regular Polygon, Trigonometry Angles--Pi/11

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References

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 194-200, 1996.

Cite this as:

Weisstein, Eric W. "Regular Hendecagon." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RegularHendecagon.html

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