Dioctagram

Dioctagram
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Diog
Schläfli symbol	{16/6}
Elements
Components	2 octagrams
Edges	16
Vertices	16
Vertex figure	Dyad, length √2-√2
Measures (edge length 1)
Circumradius	$\sqrt{\frac{2-\sqrt2}{2}} \approx 0.54120$
Inradius	$\frac{\sqrt2-1}{2} \approx 0.20711$
Area	$4(\sqrt2-1) \approx 1.65685$
Angle	45°
Central density	6
Number of external pieces	32
Level of complexity	2
Related polytopes
Army	Hed, edge length $\sqrt{\frac{4-2\sqrt2-\sqrt{4-2\sqrt2}}{2}}$
Dual	Dioctagram
Conjugate	Stellated hexadecagon
Convex core	Hexadecagon
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	I2(16), order 32
Convex	No
Nature	Tame

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:

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

External links

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