An eleven-sided, eleven-angled planar shape is called a hendecagon. An eleven-sided 3-dimensional shape is called a hendecahedron. It also has twenty edges.
The names for smaller-sided shapes usually combine Latin prefixes with the Greek -gon, such as in pentagon. However, the Greek ‘hen’ is used here instead to avoid the Latin ‘un(i)-‘. For the 3-dimensional shape, -hedron is of English origin.
A regular hendecagon has angles of 127.27 degrees, and has Schlaefli symbol {11}. For a regular hendecagon where the length of one side = a, the area is approximately equal to 9.36564 x a^2, as determined by the formula:
A = (11/4)a^2 cot (pi/11)
While a shape with any number of sides can be constructed so that all angles are identical, it is impossible to construct a hendecagon using the classic method of only a straightedge and a compass.
There is no regular hendecahedron.
Despite the unusual shape, three countries actually use the hendecagon as the template for some of their coins. The Canadian dollar coin, or ‘loonie’, was designed with eleven slightly-rounded edges to distinguish it for use by the blind. It was very popular right from its introduction, and is currently in extremely common use. The town of Echo Bay, Ontario, has erected a giant loonie statue in honour of its local creator. The number of sides was chosen so as not to be confused with some King George nickels which also were angular rather than round.
During the 2002 Winter Olympics, the Canadian ice-making company buried a loonie to mark centre ice. Both the Canadian men’s and women’s ice hockey teams went on to win gold medals.
The Indian two-rupee coin is also in common use. However, continual attempts by the United States to create a popular dollar-value coin have yet to be successful, and the 11-sided Susan B. Anthony dollar coin is no exception.
Hendecahedrons have been created mostly by esoteric gaming/dice companies, mostly because they could. Many hardcore gamers acquire one at some point, simply for their curiosity value, in much the same way as most hardcore gamers have a 100-sided die which is absolutely impractical to use. They have absolutely no uses in role playing, despite the temptation and the availability in equally esoteric gaming stores.
A hendecagram is an eleven-pointed planar shape. It thus has 22 external sides, two per point. An 11/2 regular star hendecagram is the symbol of the Aleister Crowley Foundation.
