Rank2
TypeRegular
Notation
Coxeter diagramx17o ()
Schläfli symbol{17}
Elements
Edges17
Vertices17
Vertex figureDyad, length ${\displaystyle 2\cos(\pi /17)}$
Measures (edge length 1)
Circumradius${\displaystyle {\frac {1}{2\sin {\frac {\pi }{17}}}}\approx 2.72110}$
Inradius${\displaystyle {\frac {1}{2\tan {\frac {\pi }{17}}}}\approx 2.67476}$
Area${\displaystyle {\frac {17}{4\tan {\frac {\pi }{17}}}}\approx 22.73549}$
Angle${\displaystyle {\frac {15\pi }{17}}\approx 158.82353^{\circ }}$
Central density1
Number of external pieces17
Level of complexity1
Related polytopes
Conjugate7 total
Abstract & topological properties
Flag count34
Euler characteristic0
OrientableYes
Properties
SymmetryI2(17), order 34
Flag orbits1
ConvexYes
NatureTame

The heptadecagon is a polygon with 17 sides. A regular heptadecagon has equal sides and equal angles.

Because 17 is a Fermat prime, the heptadecagon is a constructable polygon.

## Measures

As ${\displaystyle \sin {\tfrac {\pi }{17}}}$ is expressible with real radicals, the circumradius can be given as
${\displaystyle {\frac {2}{\sqrt {8-{\sqrt {30+2{\sqrt {17}}-2{\sqrt {34-2{\sqrt {17}}}}+2{\sqrt {68+12{\sqrt {17}}+2{\sqrt {34-2{\sqrt {17}}}}+16{\sqrt {34+2{\sqrt {17}}}}-2{\sqrt {578-34{\sqrt {17}}}}}}}}}}}}$,

${\displaystyle {\sqrt {\frac {15+{\sqrt {17}}+{\sqrt {34-2{\sqrt {17}}}}+{\sqrt {68+12{\sqrt {17}}-2{\sqrt {34-2{\sqrt {17}}}}-16{\sqrt {34+2{\sqrt {17}}}}+2{\sqrt {578-34{\sqrt {17}}}}}}}{64-8{\sqrt {30+2{\sqrt {17}}-2{\sqrt {34-2{\sqrt {17}}}}+2{\sqrt {68+12{\sqrt {17}}+2{\sqrt {34-2{\sqrt {17}}}}+16{\sqrt {34+2{\sqrt {17}}}}-2{\sqrt {578-34{\sqrt {17}}}}}}}}}}}}$,
${\displaystyle 17{\sqrt {\frac {15+{\sqrt {17}}+{\sqrt {34-2{\sqrt {17}}}}+{\sqrt {68+12{\sqrt {17}}-2{\sqrt {34-2{\sqrt {17}}}}-16{\sqrt {34+2{\sqrt {17}}}}+2{\sqrt {578-34{\sqrt {17}}}}}}}{256-32{\sqrt {30+2{\sqrt {17}}-2{\sqrt {34-2{\sqrt {17}}}}+2{\sqrt {68+12{\sqrt {17}}+2{\sqrt {34-2{\sqrt {17}}}}+16{\sqrt {34+2{\sqrt {17}}}}-2{\sqrt {578-34{\sqrt {17}}}}}}}}}}}}$.