Tetradecagon
In geometry, a tetradecagon (or tetrakaidecagon) is a fourteen-sided polygon or 14-gon.
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.
The area of a regular tetradecagon of side length a is given by
Construction
As 14 = 2 × 7, a regular tetradecagon cannot be constructed using a compass and straightedge. However, it is constructible using neusis, or with an angle trisector. The animation below gives an approximation of about 0.05° on the center angle:
Construction of an approximated regular tetradecagon
Symmetry
The regular tetradecagon has Dih14 symmetry, order 28. There are 3 subgroup dihedral symmetries: Dih7, Dih2, and Dih1, and 4 cyclic group symmetries: Z14, Z7, Z2, and Z1.
These 8 symmetries can be seen in 10 distinct symmetries on the tetradecagon, a larger number because the lines of reflections can either pass through vertices or edges. John Conway labels these by a letter and group order. Full symmetry of the regular form is r28 and no symmetry is labeled a1. The dihedral symmetries are divided depending on whether they pass through vertices (d for diagonal) or edges (p for perpendiculars), and i when reflection lines path through both edges and vertices. Cyclic symmetries in the middle column are labeled as g for their central gyration orders.
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