# Octagram

Octagram Rank2
TypeRegular
SpaceSpherical
Notation
Bowers style acronymOg
Coxeter diagramx8/3o (     )
Schläfli symbol{8/3}
Elements
Edges8
Vertices8
Measures (edge length 1)
Circumradius$\sqrt{\frac{2-\sqrt2}{2}} ≈ 0.54120$ Inradius$\frac{\sqrt2-1}{2} ≈ 0.20711$ Area$2(\sqrt2-1) ≈ 0.82843$ Angle45°
Central density3
Number of pieces16
Level of complexity2
Related polytopes
ArmyOc
DualOctagram
ConjugateOctagon
Convex coreOctagon
Abstract properties
Flag count16
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryI2(8), order 16
ConvexNo
NatureTame

The octagram is a non-convex polygon with 8 sides. It's created by stellating the octagon. A regular octagram has equal sides and equal angles.

This is the second stellation of the octagon, and the only one that is not a compound. The only other polygons with a single non-compound stellation are the pentagon, the decagon, and the dodecagon.

The octagram is the uniform quasitruncation of the square, and as such is the only regular star polygon to regularly appear in non-prismatic uniform polytopes in 5 dimensions and higher.

## Vertex coordinates

Coordinates for an octagram of unit edge length, centered at the origin, are all permutations of

• $\left(±\frac{\sqrt2-1}{2},\,±\frac12\right).$ ## Representations

An octagram has the following Coxeter diagrams:

• x8/3o (full symmetry)
• x4/3x (     ) (B2 symmetry)