Octadecagon

Regular octadecagon
Edges and vertices	18
Schläfli symbol	{18}
Coxeter–Dynkin diagram
Symmetry group	Dihedral (D18)
Area (with t=edge length)	$\frac{18}{4}t^2 \cot \frac{\pi}{18}$
Internal angle (degrees)	160°
Properties	convex, cyclic, equilateral, isogonal, isotoxal

An octadecagon is a polygon with 18 sides and 18 vertices. Another name for an octadecagon is octakaidecagon.

Construction

A regular octadecagon cannot be constructed using compass and straightedge.

Petrie polygons

The regular octadecagon is the Petrie polygon for a number of higher dimensional polytopes, shown in these skew orthogonal projections from Coxeter planes:

A17	17-simplex
BC9	9-orthoplex	Rectified 9-orthoplex	Birectified 9-orthoplex	Trirectified 9-orthoplex	Quadrirectified 9-cube	Trirectified 9-cube	Birectified 9-cube	Rectified 9-cube	9-cube
D10	t8(171)	t7(171)	t6(171)	t5(171)	t4(171)	t3(171)	t2(171)	t1(171)	10-demicube (171)
E7	(321)	t1(321)	t2(321)	(231)	t1(231)	t1(132)	(132)

External links

• Weisstein, Eric W., "Octadecagon" from MathWorld.

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