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Hendecagon

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Regular hendecagon
Regular hendecagon
Edges and vertices 11
Schläfli symbols {11}
Coxeter–Dynkin diagrams CDW ringCDW 11CDW dot
Symmetry group Dihedral (D11)
Area
(with a = edge length)
A=\frac{11}{4}\cot\left(\frac{\pi}{11}\right)a^2\simeq 9.36a^2
Internal angle
(degrees)
180°×(1-2/11)
=147°.27

In geometry, a hendecagon (also undecagon[1]) is an 11-sided polygon. The name "undecagon" is often seen as incorrect, but the matter is up for debate. The Greek prefix 'hen', is preferable to the Latin 'uni' or 'un' [2]. A regular hendecagon has internal angles of 147.27 degrees. The area of a regular hendecagon with side length a is given by

A=\frac{11}{4}\cot\left(\frac{\pi}{11}\right)a^2\simeq9.36a^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

Related shapes

The hendecagon shares the same set of 11 vertices with four regular hendecagrams, {11/2}, {11/3}, {11/4}, {11/5}.

Petrie polygons

The regular hendecagon is the Petrie polygon for 10-dimensional uniform polytopes of the simplex family, projected in a skew orthogonal projection.[1][2]


10-simplex t0
10-simplex
10-simplex t1
Rectified 10-simplex
10-simplex t2
Birectified 10-simplex
10-simplex t3
Trirectified 10-simplex
10-simplex t4
Quadrirectified 10-simplex

External links


ar:أحادي عشري

ast:Endecágonu cs:Jedenáctiúhelníkeo:Dekunulaterogl:Endecágono it:Endecagono hu:Tizenegyszög nl:Elfhoekno:Hendekagon nn:Hendekagon pt:Hendecágono sr:Једанаестоугао th:รูปสิบเอ็ดเหลี่ยม


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