Tetradecagon

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Regular tetradecagon
Regular polygon 14 annotated.svg
A regular tetradecagon
Type Regular polygon
Edges and vertices 14
Schläfli symbol {14}
Coxeter diagram CDel node 1.pngCDel 14.pngCDel node.png
Symmetry group D14, order 2×14
Internal angle (degrees) \approx 154.2857°
Dual polygon self
Properties convex, cyclic, equilateral, isogonal, isotoxal

In geometry, a tetradecagon (or tetrakaidecagon) is a polygon with 14 sides and angles.

Regular tetradecagon[edit]

The area of a regular tetradecagon of side length a is given by

A = \frac{14}{4}a^2\cot\frac{\pi}{14}\simeq 15.3345a^2

Numismatic use[edit]

The regular tetradecagon is used as the shape of some commemorative gold and silver Malaysian coins, the number of sides representing the 14 states of the Malaysian Federation.[1]

Construction[edit]

A regular tetradecagon cannot be constructed using a compass and straightedge.[2] The animation below gives an approximation of about 0.05° on the center angle:

Approximated Tetradecagon Inscribed in a Circle.gif
Construction of an approximated regular tetradecagon

Petrie polygons[edit]

Regular skew tetradecagons exist as Petrie polygon for many higher-dimensional polytopes, shown in these skew orthogonal projections, including:

A13 13-simplex t0.svg
13-simplex
BC7 7-cube t6.svg
7-orthoplex
7-cube t5.svg
Rectified 7-orthoplex
7-cube t4.svg
Birectified 7-orthoplex
7-cube t3.svg
Trirectified 7-cube
7-cube t2.svg
Birectified 7-cube
7-cube t1.svg
Rectified 7-cube
7-cube t0.svg
7-cube
BC7 4 21 t0 B7.svg
(421)
4 21 t1 B7.svg
t1(421)
4 21 t2 B7.svg
t2(421)
4 21 t3 B7.svg
t3(421)
2 41 t0 B7.svg
(241)
2 41 t1 B7.svg
t1(241)
1 42 t0 B7.svg
(142)
D8 8-cube t7 B7.svg
t6(151)
8-cube t6 B7.svg
t5(151)
8-cube t5 B7.svg
t4(151)
8-cube t4 B7.svg
t3(151)
8-cube t3 B7.svg
t2(151)
8-demicube t1 D8.svg
t1(151)
8-demicube t0 D8.svg
(151)

References[edit]

  1. ^ The Numismatist, Volume 96, Issues 7-12, Page 1409, American Numismatic Association, 1983.
  2. ^ Wantzel, Pierre (1837). "Recherches sur les moyens de Reconnaître si un Problème de géométrie peau se résoudre avec la règle et le compas". Journal de Mathématiques: 366–372. 

External links[edit]