# Dioctagram

Dioctagram Rank2
TypeRegular
SpaceSpherical
Notation
Bowers style acronymDiog
Schläfli symbol{16/6}
Elements
Components2 octagrams
Edges16
Vertices16
Measures (edge length 1)
Circumradius$\sqrt{\frac{2-\sqrt2}{2}} \approx 0.54120$ Inradius$\frac{\sqrt2-1}{2} \approx 0.20711$ Area$4(\sqrt2-1) \approx 1.65685$ Angle45°
Central density6
Number of external pieces32
Level of complexity2
Related polytopes
ArmyHed, edge length $\sqrt{\frac{4-2\sqrt2-\sqrt{4-2\sqrt2}}{2}}$ DualDioctagram
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryI2(16), order 32
ConvexNo
NatureTame

The dioctagram or diog is a polygon compound composed of two octagrams. As such it has 16 edges and 16 vertices.

It is the fifth stellation of the hexadecagon.

Its quotient prismatic equivalent is the octagrammic antiprism, which is three-dimensional.

## Vertex coordinates

Coordinates for a dioctagram of edge length 2+2, centered at the origin, are all permutations of:

• $\left(\pm1,\,0\right),$ • $\left(\pm\frac{2+\sqrt2}{2},\,\pm\frac{2-\sqrt2}{2}\right),$ • $\left(\pm\frac{\sqrt2}{2},\,\pm\frac{\sqrt2}{2}\right).$ 