Enneadecagon
Regular enneadecagon | |
---|---|
A regular enneadecagon | |
Type | Regular polygon |
Edges and vertices | 19 |
Schläfli symbol | {19} |
Coxeter diagram |
![]() ![]() ![]() |
Symmetry group | Dihedral (D19), order 2×19 |
Internal angle (degrees) | ≈161.052° |
Dual polygon | self |
Properties | convex, cyclic, equilateral, isogonal, isotoxal |
In geometry an enneadecagon is a polygon with 19 sides and angles.[1] It is also known as an enneakaidecagon or a nonadecagon.[2]
A regular enneadecagon is represented by Schläfli symbol {19}.
Regular form
The radius of the circumcircle of the regular enneadecagon with side length t is
(angle in degrees). The area, where t is the edge length, is
Construction
A regular enneadecagon cannot be constructed using a compass and straightedge. However, it is constructible using neusis, or an angle trisector.
Related polygons
A enneadecagram is a 19-sided star polygon. There are 9 regular forms given by Schläfli symbols: {19/2}, {19/3}, {19/4}, {19/5}, {19/6}, {19/7}, {19/8}, and {19/9}.
Picture | ![]() {19/2} |
![]() {19/3} |
![]() {19/4} |
![]() {19/5} |
---|---|---|---|---|
Interior angle | ≈142.105° | ≈123.158° | ≈104.211° | ≈85.2632° |
Picture | ![]() {19/6} |
![]() {19/7} |
![]() {19/8} |
![]() {19/9} |
Interior angle | ≈66.3158° | ≈47.3684° | ≈28.4211° | ≈9.47368° |
Petrie polygons
The regular enneadecagon is the Petrie polygon for one higher-dimensional polytope, projected in a skew orthogonal projection:
![]() 18-simplex (18D) |
References
- ↑ Borges, Samantha; Morgan, Matthew (2012), Children's Miscellany: Useless Information That's Essential to Know, Chronicle Books, p. 110, ISBN 9781452119731.
- ↑ McKinney, Sueanne; Hinton, KaaVonia (2010), Mathematics in the K-8 Classroom and Library, ABC-CLIO, p. 67, ISBN 9781586835224.
External links
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