Tridecagon

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Regular tridecagon
Regular polygon 13 annotated.svg
A regular tridecagon
Type Regular polygon
Edges and vertices 13
Schläfli symbol {13}
Coxeter diagram CDel node 1.pngCDel 13.pngCDel node.png
Symmetry group Dihedral (D13), order 2×13
Internal angle (degrees) \approx 152.308°
Dual polygon self
Properties convex, cyclic, equilateral, isogonal, isotoxal

In geometry, a tridecagon (or triskaidecagon) is a polygon with 13 sides and angles.

Regular tridecagon[edit]

The measure of each internal angle of a regular tridecagon is approximately 152.308 degrees, and the area with side length a is given by

A = \frac{13}{4}a^2 \cot \frac{\pi}{13} \simeq 13.1858\,a^2.

Numismatic use[edit]

The regular tridecagon is used as the shape of the Czech 20 korun coin.[1]

Related polygons[edit]

A tridecagram is a 13-sided star polygon. There are 5 regular forms given by Schläfli symbols: {13/2}, {13/3}, {13/4}, {13/5}, {13/6}.

Triskaidecagrams.svg

Construction[edit]

A regular tridecagon is not constructible with compass and straightedge. However, it is constructible using a Neusis construction.[2]

Petrie polygons[edit]

The regular tridecagon is the Petrie polygon for a number of higher-dimensional polytopes, projected in a skew orthogonal projection, including from the A12, 12-simplex family:

A12 12-simplex t0.svg
12-simplex
12-simplex t1.svg
Rectified 12-simplex
12-simplex t2.svg
Birectified 12-simplex
12-simplex t3.svg
trirectified 12-simplex
12-simplex t4.svg
quadrirectified 12-simplex
12-simplex t5.svg
quintirectified 12-simplex

References[edit]

  1. ^ Colin R. Bruce, II, George Cuhaj, and Thomas Michael, 2007 Standard Catalog of World Coins, Krause Publications, 2006, ISBN 0896894290, p. 81.
  2. ^ Gleason, Andrew M. (1988), Angle trisection, the heptagon, and the triskaidecagon, American Mathematical Monthly 95 (3): 185–194, doi:10.2307/2323624, MR 935432 .

External links[edit]