# Heptadecagon

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Heptadecagon
Rank2
TypeRegular
SpaceSpherical
Info
Coxeter diagramx17o
Schläfli symbol{17}
SymmetryI2(17), order 34
Army{17}
Elements
Vertex figureDyad, length 2cos(π/17)
Edges17
Vertices17
Measures (edge length 1)
Circumradius${\displaystyle \frac{1}{2\sin\frac{\pi}{17}} ≈ 2.72110}$
Inradius${\displaystyle \frac{1}{2\tan\frac{\pi}{17}} ≈ 2.67476}$
Area${\displaystyle \frac{17}{4\tan\frac{\pi}{17}} ≈ 22.73549}$
Angle${\displaystyle \frac{15\pi}{17} ≈ 158.82353°}$
Central density1
Euler characteristic0
Related polytopes
DualHeptadecagon
Properties
ConvexYes
OrientableYes
NatureTame

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

## Measures

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

the inradius as
${\displaystyle \sqrt{\frac{15+\sqrt{17}+\sqrt{34-2\sqrt{17}}+\sqrt{68+12\sqrt{17}-2\sqrt{34-2\sqrt{17}}-16\sqrt{34+2\sqrt{17}}+2\sqrt{578-34\sqrt{17}}}}{64-8\sqrt{30+2\sqrt{17}-2\sqrt{34-2\sqrt{17}}+2\sqrt{68+12\sqrt{17}+2\sqrt{34-2\sqrt{17}}+16\sqrt{34+2\sqrt{17}}-2\sqrt{578-34\sqrt{17}}}}}}}$,

and the area as
${\displaystyle 17\sqrt{\frac{15+\sqrt{17}+\sqrt{34-2\sqrt{17}}+\sqrt{68+12\sqrt{17}-2\sqrt{34-2\sqrt{17}}-16\sqrt{34+2\sqrt{17}}+2\sqrt{578-34\sqrt{17}}}}{256-32\sqrt{30+2\sqrt{17}-2\sqrt{34-2\sqrt{17}}+2\sqrt{68+12\sqrt{17}+2\sqrt{34-2\sqrt{17}}+16\sqrt{34+2\sqrt{17}}-2\sqrt{578-34\sqrt{17}}}}}}}$.