# Octagram

Octagram Rank2
TypeRegular
SpaceSpherical
Bowers style acronymOg
Info
Coxeter diagramx8/3o
Schläfli symbol{8/3}
SymmetryI2(8), order 16
ArmyOc
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
Euler characteristic0
Number of pieces16
Level of complexity2
Related polytopes
DualOctagram
ConjugateOctagon
Convex coreOctagon
Properties
ConvexNo
OrientableYes
NatureTame

The octagram, or og, 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 (BC2 symmetry)