Stellated hexadecagon

Stellated hexadecagon
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Shad
Schläfli symbol	{16/2}
Elements
Components	2 octagons
Edges	16
Vertices	16
Vertex figure	Dyad, length √2+√2
Measures (edge length 1)
Circumradius	$\sqrt{\frac{2+\sqrt2}{2}} \approx 1.30656$
Inradius	$\frac{1+\sqrt2}{2} \approx 1.20711$
Area	$4(1+\sqrt2) \approx 9.65685$
Angle	135°
Central density	2
Number of external pieces	32
Level of complexity	2
Related polytopes
Army	Hed, edge length $\sqrt{\frac{4+2\sqrt2-\sqrt{20+14\sqrt2}}{2}}$
Dual	Stellated hexadecagon
Conjugate	Dioctagram
Convex core	Hexadecagon
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	I2(16), order 32
Convex	No
Nature	Tame

The stellated hexadecagon or shad is a polygon compound composed of two octagons. As such it has 16 edges and 16 vertices.

As the name suggests, it is the first stellation of the hexadecagon.

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

Vertex coordinates

Coordinates for a stellated hexadecagon 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".