Decagram (geometry)

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Regular decagram
Star polygon 10-3.svg
A regular decagram
Type Regular polygon
Edges and vertices 10
Schläfli symbol {10/3}
t{5/3}
Coxeter diagram CDel node 1.pngCDel 10.pngCDel rat.pngCDel d3.pngCDel node.png
CDel node 1.pngCDel 5-3.pngCDel node 1.png
Symmetry group Dihedral (D10)
Internal angle (degrees) 72°
Dual polygon self
Properties star, cyclic, equilateral, isogonal, isotoxal
Lengths in a regular decagram

In geometry, a decagram is a 10-sided star polygon. There is one regular decagram star polygon, {10/3}, containing the vertices of a regular decagon, but connected by every third point.

Star figures[edit]

There are two regular decagram star figures: {10/2} and {10/4}, connected by every second and every fourth point respectively.

Decagram 10 2.png
{10/2} or 2{5} is a compound of 2 pentagons.
Decagram 10 4.png
{10/4} or 2{5/2} is a compound of 2 pentagrams.

Other decagrams[edit]

An isotoxal decagram has two types of vertices at alternating radii, for example, this tripled-wrapped figure. This only has D5 symmetry.
Isotoxal pentagram.png

See also[edit]