Hendecagon

The hendecagon, or heng, is a polygon with 11 sides. A regular hendecagon has equal sides and equal angles.

The combining prefix is hen-, as in hentet, or han-, as in handip.

It has four stellations, these being the small hendecagram, the hendecagram, the great hendecagram, and the grand hendecagram.

It is the smallest regular convex polygon that cannot form a planar vertex with only other regular convex polygons.

Higher polytopes containing regular hendecagons that are "interesting" in some sense are rare. An exception is three members of the family of pairwise augmented cupolae, which are 11-4-3 acrohedra (all faces are regular).

Naming
The name hendecagon is derived from the Ancient Greek ' (11) and ' (angle), referring to the number of vertices.

Other names include:


 * heng, Bowers style acronym, short for "hendecagon"

Vertex coordinates
Vertex coordinates for a hendecagon of edge length $$2\sin(\pi/11)$$, centered at the origin, are:


 * $$(1,\,0)$$,
 * $$(\cos(2\pi/11),\,\pm\sin(2\pi/11))$$,
 * $$(\cos(4\pi/11),\,\pm\sin(4\pi/11))$$,
 * $$(\cos(6\pi/11),\,\pm\sin(6\pi/11))$$,
 * $$(\cos(8\pi/11),\,\pm\sin(8\pi/11))$$,
 * $$(\cos(10\pi/11),\,\pm\sin(10\pi/11))$$.