A regular enneadecagon
|Edges and vertices||19|
|Symmetry group||Dihedral (D19), order 2×19|
|Internal angle (degrees)||≈161.052°|
|Properties||Convex, cyclic, equilateral, isogonal, isotoxal|
Another animation of an approximate construction.
Based on the unit circle r = 1 [unit of length]
- Constructed side length of the enneadecagon in GeoGebra = 0.329189180561468... [unit of length]
- Side length of the enneadecagon = = 0.329189180561467788... [unit of length]
- Absolute error of the constructed side length = 2.12...E-16 [unit of length]
- Constructed central angle of the enneadecagon in GeoGebra = 18.94736842105263...°
- Central angle of the enneadecagon = = 18.947368421052631578...°
- Absolute error of the constructed central angle = -1.578...E-15°
Example to illustrate the error
- At a radius r = 1 billion km (the light would need about 55 min for this distance) the absolute error of the side length constructed would be approx. 0.21 mm.
These 4 symmetries can be seen in 4 distinct symmetries on the enneadecagon. John Conway labels these by a letter and group order. Full symmetry of the regular form is r38 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.
Each subgroup symmetry allows one or more degrees of freedom for irregular forms. Only the g19 subgroup has no degrees of freedom but can seen as directed edges.
- 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.
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, (2008) The Symmetries of Things, ISBN 978-1-56881-220-5 (Chapter 20, Generalized Schaefli symbols, Types of symmetry of a polygon pp. 275-278)