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}, t{7}
Coxeter diagram CDel node 1.pngCDel 14.pngCDel node.png
CDel node 1.pngCDel 7.pngCDel node 1.png
Symmetry group Dihedral (D14), order 2×14
Internal angle (degrees) ≈154.2857°
Dual polygon Self
Properties Convex, cyclic, equilateral, isogonal, isotoxal

A tetradecagon or 14-gon is a shape with 14 sides and 14 corners.

Regular tetradecagon[change | change source]

A regular tetradecagon has Schläfli symbol {14} and can be constructed as a quasiregular truncated heptagon, t{7}, which alternates two types of edges.

Area[change | change source]

The amount of space a regular tetradecagon takes up is

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

a is the length of one of its sides.

Dissection[change | change source]

Coxeter states that every parallel-sided 2m-gon can be divided into m(m-1)/2 rhombs. For the regular tetradecagon, m=7, and it can be divided into 21: 3 sets of 7 rhombs. This decomposition is based on a Petrie polygon projection of a 7-cube, with 21 of 672 faces. [1] The list A006245 defines the number of solutions as 24698, including up to 14-fold rotations and chiral forms in reflection.

Dissection into 21 rhombs
7-cube graph.svg 14-gon-dissection.svg

Numismatic use[change | change source]

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.[2]

References[change | change source]

  1. Coxeter, Mathematical recreations and Essays, Thirteenth edition, p.141
  2. The Numismatist, Volume 96, Issues 7-12, Page 1409, American Numismatic Association, 1983.

External links[change | change source]