A regular decagon
|Edges and vertices||10|
|Symmetry group||Dihedral (D10), order 2×10|
|Internal angle (degrees)||144°|
|Properties||convex, cyclic, equilateral, isogonal, isotoxal|
An alternative formula is where d is the distance between parallel sides, or the height when the decagon stands on one side as base, or the diameter of the decagon's inscribed circle. By simple trigonometry,
and it can be written algebraically as
An alternative (but similar) method is as follows:
- Construct a pentagon in a circle by one of the methods shown in constructing a pentagon.
- Extend a line from each vertex of the pentagon through the center of the circle to the opposite side of that same circle. Where each line cuts the circle is a vertex of the decagon.
- The five corners of the pentagon constitute alternate corners of the decagon. Join these points to the adjacent new points to form the decagon.
- Decagonal number and centered decagonal number, figurate numbers modeled on the decagon
- Decagram, a star polygon with the same vertex positions as the regular decagon
- Sidebotham, Thomas H. (2003), The A to Z of Mathematics: A Basic Guide, John Wiley & Sons, p. 146, ISBN 9780471461630.
- Wenninger, Magnus J. (1974), Polyhedron Models, Cambridge University Press, p. 9, ISBN 9780521098595.
- The elements of plane and spherical trigonometry, Society for Promoting Christian Knowledge, 1850, p. 59. Note that this source uses a as the edge length and gives the argument of the cotangent as an angle in degrees rather than in radians.
- Ludlow, Henry H. (1904), Geometric Construction of the Regular Decagon and Pentagon Inscribed in a Circle, The Open Court Publishing Co..
- Weisstein, Eric W., "Decagon", MathWorld.
- Definition and properties of a decagon With interactive animation