Small hexadecagram

Small hexadecagram
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Shed
Coxeter diagram	x16/3o
Schläfli symbol	{16/3}
Elements
Edges	16
Vertices	16
Vertex figure	Dyad, length √2+√2-√2
Measures (edge length 1)
Circumradius	$\sqrt{2-\sqrt2+\sqrt{\frac{10-7\sqrt2}{2}}} ≈ 0.89998$
Inradius	$\frac{-1+\sqrt2+\sqrt{4-2\sqrt2}}{2} ≈ 0.74830$
Area	$4(-1+\sqrt2+\sqrt{4-2\sqrt2}) ≈ 5.98642$
Angle	112.5°
Central density	3
Number of external pieces	32
Level of complexity	2
Related polytopes
Army	Hed, edge length $1-\sqrt2+\sqrt{2-\sqrt2}$
Dual	Small hexadecagram
Conjugates	Hexadecagon, Hexadecagram, Great hexadecagram
Convex core	Hexadecagon
Abstract & topological properties
Flag count	32
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(16), order 32
Convex	No
Nature	Tame

The small hexadecagram, or shed, is a non-convex polygon with 16 sides. It's created by taking the second stellation of a hexadecagon. A regular small hexadecagram has equal sides and equal angles.

It is one of three regular 16-sided star polygons, the other two being the hexadecagram and the great hexadecagram.

It is the uniform truncation of the octagram.

Vertex coordinates

The vertices of a regular small hexadecagram of edge length 1 are given by all permutations of:

• $\left(±\frac12,\,±\frac{-1+\sqrt2+\sqrt{4-2\sqrt2}}{2}\right),$
• $\left(±\frac{1+\sqrt{2-\sqrt2}}{2},\,±\frac{-1+\sqrt2+\sqrt{2-\sqrt2}}{2}\right).$

External links

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

• Wikipedia Contributors. "Hexadecagram".