Hendecagon
In geometry, a hendecagon (also undecagon or endecagon) is an eleven-sided polygon or 11-gon. (The name hendecagon, from Greek hendeka "eleven" and gon– "corner", is often preferred to the hybrid undecagon, whose first part is formed from Latin undecim "eleven".)
Regular hendecagon
A regular hendecagon is represented by Schläfli symbol {11}.
A regular hendecagon has internal angles of 147.27 degrees. The area of a regular hendecagon with side length a is given by
As 11 is not a Fermat prime, the regular hendecagon is not constructible with compass and straightedge. Because 11 is not a Pierpont prime, construction of a regular hendecagon is still impossible even with the usage of an angle trisector.
Close approximations to the regular hendecagon can be constructed, however. For instance, the ancient Greek mathematicians approximated the side length of a hendecagon inscribed in a unit circle as being 14/25 units long.
Symmetry
The regular hendecagon has Dih11 symmetry, order 22. Since 11 is a prime number there is one subgroup with dihedral symmetry: Dih1, and 2 cyclic group symmetries: Z11, and Z1.
Podcasts:
