Stellated decagram

Stellated decagram
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Sadag
Schläfli symbol	{10/4}
Elements
Components	2 pentagrams
Edges	10
Vertices	10
Vertex figure	Dyad, length (√5–1)/2
Measures (edge length 1)
Circumradius	$\sqrt{\frac{5-\sqrt5}{10}} ≈ 0.52573$
Inradius	$\sqrt{\frac{5-2\sqrt5}{20}} ≈ 0.16246$
Area	$\sqrt{\frac{25-10\sqrt5}{4}} ≈ 0.81230$
Angle	36°
Central density	4
Number of pieces	20
Level of complexity	2
Related polytopes
Army	Dec
Dual	Stellated decagram
Conjugate	Stellated decagon
Convex core	Decagon
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	I2(10), order 20
Convex	No
Nature	Tame

The stellated decagram or sadag is a polygon compound composed of two pentagrams. As such it has 10 edges and 10 vertices.

It is the third stellation of the decagon.

Its quotient prismatic equivalent is the pentagrammic retroprism, which is three-dimensional.

Vertex coordinates

Coordinates for the vertices of a stellated decagram of edge length 1 centered at the origin are given by:

• $\left(±\frac12,\,±\sqrt{\frac{5-2\sqrt5}{20}}\right),$
• $\left(±\frac{\sqrt5-1}{4},\,±\sqrt{\frac{5+\sqrt5}{40}}\right),$
• $\left(0,\,±\sqrt{\frac{5-\sqrt5}{10}}\right).$

External links

• Bowers, Jonathan. "Regular Polygons and Other Two Dimensional Shapes".