Tetradecagon
A tetradecagon or 14-gon is a shape with 14 sides and 14 corners.
| Regular tetradecagon | |
|---|---|
 A regular tetradecagon | |
| Type | Regular polygon |
| Edges and vertices | 14 |
| Schläfli symbol | {14}, t{7} |
| Coxeter diagram |     |
| Symmetry group | Dihedral (D14), order 2×14 |
| Internal angle (degrees) | ≈154.2857° |
| Dual polygon | Self |
| Properties | Convex, cyclic, equilateral, isogonal, isotoxal |
Regular tetradecagon
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
The amount of space a regular tetradecagon takes up is
The area of a regular tetradecagon of side length a is given by
- [math]\displaystyle{ \begin{align}A &= \frac{14}{4}a^2\cot\frac{\pi}{14}=\frac{14}{4}a^2\left(\frac{\sqrt{7}+4\sqrt{7}\cos\left({\frac{2}{3}\arctan{\frac{\sqrt{3}}{9}}}\right)}{3}\right)\\ &\simeq 15.3345a^2\end{align} }[/math]
a is the length of one of its sides.
Dissection
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.
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Numismatic use
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]
Tetradecagon Media
Tetradecagon with given circumcircle:*An animation (1 min 47 s) from a neusis construction with radius of circumcircle \overline{OA} = 6,*according to Andrew M. Gleason, based on the angle trisection by means of the tomahawk.
Tetradecagon with given side length:*An animation (1 min 20 s) from a neusis construction with marked ruler, according to David Johnson Leisk (Crockett Johnson).
Symmetries of a regular tetradecagon. Vertices are colored by their symmetry positions. Blue mirrors are drawn through vertices, and purple mirrors are drawn through edge. Gyration orders are given in the center.
en:14-cube, A13 projection
14-gon rhombic dissection-size2
en:Tetradecagon dissection by rhombi in star symmetry
14-gon rhombic dissection2
14-gon rhombic dissectionx
References
Other websites
- Weisstein, Eric W., "Tetradecagon" from MathWorld.