Pentadecagon
In geometry, a pentadecagon (or pentakaidecagon) is a fifteen-sided polygon or 15-gon.
Regular pentadecagon
A regular pentadecagon is represented by Schläfli symbol {15}.
A regular pentadecagon has interior angles of 156°, and with a side length a, has an area given by
Uses
A regular triangle, decagon, and pentadecagon can completely fill a plane vertex.
Construction
As 15 = 3 × 5, a regular pentadecagon is constructible using compass and straightedge: The following constructions of regular pentadecagons with given circumcircle are similar to the illustration of the proposition XVI in Book IV of Euclid's Elements.
Comparison the construction according Euclid in this image: Pentadecagon
In the construction for given circumcircle: 
is a side of equilateral triangle and 
is a side of a regular pentagon.
The point 
divides the radius 
in golden ratio: 
Compared with the first animation (with green lines) are in the following two images the two circular arcs (for angles 36° and 24°) rotated 90° counterclockwise shown. They do not use the segment 
, but rather they use segment 
as radius 
for the second circular arc (angle 36°).
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