Math Wiki
Regular hendecagon
Regular hendecagon.svg
Edges and vertices 11
Schläfli symbols {11}
Coxeter–Dynkin diagrams CDW ring.pngCDW 11.pngCDW dot.png
Symmetry group Dihedral (D11)
(with = edge length)
Internal angle

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 is given by

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


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.svg
10-simplex t1.svg
Rectified 10-simplex
10-simplex t2.svg
Birectified 10-simplex
10-simplex t3.svg
Trirectified 10-simplex
10-simplex t4.svg
Quadrirectified 10-simplex

External links

ar:أحادي عشري ast:Endecágonu cs:Jedenáctiúhelník eo:Dekunulatero gl:Endecágono it:Endecagono hu:Tizenegyszög nl:Elfhoek no:Hendekagon nn:Hendekagon pt:Hendecágono sr:Једанаестоугао th:รูปสิบเอ็ดเหลี่ยม

  1. Coxeter, H. S. M. Petrie Polygons. Regular Polytopes, 3rd ed. New York: Dover, 1973. (sec 2.6 Petrie Polygons pp. 24–25)
  2. Humphreys, James E. (1992), Reflection Groups and Coxeter Groups, Cambridge University Press, pp. 80 (Section 3.16, Coxeter Elements, table 2, Coxeter number for An is n+1), ISBN 978-0-521-43613-7,