Icosagon

Icosagon
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Coxeter diagram	x20o
Schläfli symbol	{20}
Elements
Edges	20
Vertices	20
Vertex figure	Dyad, length $\sqrt{2+\sqrt{\frac{5+\sqrt{5}}{2}}}$
Measures (edge length 1)
Circumradius	$\sqrt{3+\sqrt{5}+\sqrt{\frac{25+11\sqrt{5}}{2}}} ≈ 3.19623$
Inradius	$\frac{1+\sqrt{5}+\sqrt{5+2\sqrt{5}}}{2} ≈ 3.15688$
Area	$5(1+\sqrt{5}+\sqrt{5+2\sqrt{5}}) ≈ 31.56876$
Angle	162°
Central density	1
Number of pieces	20
Level of complexity	1
Related polytopes
Army	{20}
Dual	Icosagon
Conjugates	Small icosagram, icosagram, great icosagram
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	I2(20), order 40
Convex	Yes
Nature	Tame

The icosagon is a polygon with 20 sides. A regular icosagon has equal sides and equal angles.

Icosagons are the largest polygon currently known to appear in a CRF polytope that is not part of ann infinite series, as augmentations of certain icosagon-based duoprisms are CRF.

Stellations

• 2-icosagram (compound of 2 decagons)
• 3-icosagram
• 4-icosagram (compound of 4 pentagons)
• 5-icosagram (compound of 5 squares)
• 6-icosagram (compound of 2 decagrams)
• 7-icosagram
• 8-icosagram (compound of 4 pentagrams)
• 9-icosagram

External links

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

• Wikipedia Contributors. "Icosagon".