Pentagon
From Wikipedia, the free encyclopedia
(Redirected from Pentagonal)
 | This article needs additional citations for verification. Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (July 2008) |
| Regular pentagon | |
|---|---|
 A regular pentagon | |
| Edges and vertices | 5 |
| Schläfli symbol | {5} |
| Coxeter–Dynkin diagram |    |
| Symmetry group | Dihedral (D5) |
| Internal angle (degrees) | 108° |
| Properties | convex, cyclic, equilateral, isogonal, isotoxal |
 | Look up pentagon in Wiktionary, the free dictionary. |
This article is about the geometric figure. For the headquarters of the United States Department of Defense, see The Pentagon. For other uses, see Pentagon (disambiguation).
In geometry, a pentagon From the Greek number 5 (pente) is any five-sided polygon. A pentagon may be simple or self-intersecting. The internal angles in a simple pentagon total 540°. A pentagram is an example of a self-intersecting pentagon.
Contents[show] |
[edit] Regular pentagons
A regular pentagon has all sides of equal length and all interior angles are equal measure (108°). It has five lines of reflectional symmetry and it has rotational symmetry of order 5 (through 72°, 144°, 216° and 288°). Its Schläfli symbol is {5}. The chords of a regular pentagon are in golden ratio to its sides.
The area of a regular convex pentagon with side length t is given by
A pentagram or pentangle is a regular star pentagon. Its Schläfli symbol is {5/2}. Its sides form the diagonals of a regular convex pentagon – in this arrangement the sides of the two pentagons are in the golden ratio.
When a regular pentagon is inscribed in a circle with radius R, its edge length t is given by the expression
