Hendecagon

Hendecagon

[hen-dek-uh-gon]
Regular hendecagon
Edges and vertices 11
Schläfli symbols {11}
Coxeter–Dynkin diagrams - Symmetry group Dihedral (D11)
Area
(with t=edge length)
A = frac{11}{4}t^2 cot frac{pi}{11} simeq 9.36564 t^2.
Internal angle
(degrees)
180°×(1-2/11)
=147°.2727...

In geometry, a hendecagon (also undecagon) is an 11-sided polygon. The name "undecagon" is often seen as incorrect, but the matter is up for debate. The prefix should be the Greek 'hen', not the Latin 'un' (which is also of Greek origin) . A hendecagon has 11 sides. A regular hendecagon has internal angles of 147.272727... degrees. The area of a regular hendecagon with side length a is given by

A = frac{11}{4}a^2 cot frac{pi}{11} simeq 9.36564,a^2.
A regular hendecagon is not constructible with compass and straightedge.

Use in coinage

The Canadian dollar coin, the loonie, is patterned on a regular hendecagonal prism, as is the Indian two-rupee coin.

It was also patterned on the Susan B. Anthony dollar of the United States from 1979-1981 and again in 1999.

See also

References

External links

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