Octadecagon

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Regular octadecagon
Regular polygon 18 annotated.svg
A regular octadecagon
Type Regular polygon
Edges and vertices 18
Schläfli symbol {18}
Coxeter diagram CDel node 1.pngCDel 18.pngCDel node.png
Symmetry group D18, order 2×18
Internal angle (degrees) 160°
Dual polygon self
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[edit]

A regular octadecagon cannot be constructed using a compass and straightedge.

Uses[edit]

3.9.18 vertex.png
A regular triangle, enneagon, and octadecagon can completely fill a plane vertex.

Petrie polygons[edit]

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 t0.svg
17-simplex
BC9 9-cube t8.svg
9-orthoplex
9-cube t7.svg
Rectified 9-orthoplex
9-cube t6.svg
Birectified 9-orthoplex
9-cube t5.svg
Trirectified 9-orthoplex
9-cube t4.svg
Quadrirectified 9-cube
9-cube t3.svg
Trirectified 9-cube
9-cube t2.svg
Birectified 9-cube
9-cube t1.svg
Rectified 9-cube
9-cube t0.svg
9-cube
D10 10-cube t9 B9.svg
t8(171)
10-cube t8 B9.svg
t7(171)
10-cube t7 B9.svg
t6(171)
10-cube t6 B9.svg
t5(171)
10-cube t5 B9.svg
t4(171)
10-cube t4 B9.svg
t3(171)
10-cube t3 B9.svg
t2(171)
10-cube t2 B9.svg
t1(171)
10-demicube.svg
10-demicube
(171)
E7 Up2 3 21 t0 E7.svg
(321)
Up2 3 21 t1 E7.svg
t1(321)
Up2 3 21 t2 E7.svg
t2(321)
Up2 2 31 t0 E7.svg
(231)
Up2 2 31 t1 E7.svg
t1(231)
Up2 1 32 t1 E7.svg
t1(132)
Up2 1 32 t0 E7.svg
(132)

External links[edit]