# Icosagon

Icosagon
Rank2
TypeRegular
Notation
Bowers style acronymIc
Coxeter diagramx20o ()
Schläfli symbol{20}
Elements
Edges20
Vertices20
Vertex figureDyad, length ${\displaystyle {\sqrt {2+{\sqrt {\frac {5+{\sqrt {5}}}{2}}}}}}$
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {3+{\sqrt {5}}+{\sqrt {\frac {25+11{\sqrt {5}}}{2}}}}}\approx 3.19623}$
Inradius${\displaystyle {\frac {1+{\sqrt {5}}+{\sqrt {5+2{\sqrt {5}}}}}{2}}\approx 3.15688}$
Area${\displaystyle 5(1+{\sqrt {5}}+{\sqrt {5+2{\sqrt {5}}}})\approx 31.56876}$
Angle162°
Central density1
Number of external pieces20
Level of complexity1
Related polytopes
ArmyIc
DualIcosagon
ConjugatesSmall icosagram, icosagram, great icosagram
Abstract & topological properties
Flag count40
Euler characteristic0
OrientableYes
Properties
SymmetryI2(20), order 40
Flag orbits1
ConvexYes
NatureTame

The icosagon, or ic, 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 an infinite series, as augmentations of certain icosagon-based duoprisms are CRF. Also, uniform compound with hecatonicosachoric symmetry exist based on duoprisms using icosagons and their star forms.