Heptadecagon

Heptadecagon
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Coxeter diagram	x17o
Schläfli symbol	{17}
Elements
Edges	17
Vertices	17
Vertex figure	Dyad, length 2cos(π/17)
Measures (edge length 1)
Circumradius	$\frac{1}{2\sin\frac{\pi}{17}} ≈ 2.72110$
Inradius	$\frac{1}{2\tan\frac{\pi}{17}} ≈ 2.67476$
Area	$\frac{17}{4\tan\frac{\pi}{17}} ≈ 22.73549$
Angle	$\frac{15\pi}{17} ≈ 158.82353°$
Central density	1
Number of pieces	17
Level of complexity	1
Related polytopes
Army	{17}
Dual	Heptadecagon
Conjugate	7 total
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	I2(17), order 34
Convex	Yes
Nature	Tame

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

Measures

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

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

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

Stellations

• 2-heptadecagram
• 3-heptadecagram
• 4-heptadecagram
• 5-heptadecagram
• 6-heptadecagram
• 7-heptadecagram
• 8-heptadecagram

External links

• Bowers, Jonathan. "Regular Polygons and Other Two Dimensional Shapes".

• Wikipedia Contributors. "Heptadecagon".