Hexadecagon

Hexadecagon
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Hed
Coxeter diagram	x16o
Schläfli symbol	{16}
Elements
Edges	16
Vertices	16
Vertex figure	Dyad, length √2+√2+√2
Measures (edge length 1)
Circumradius	$\sqrt{2+\sqrt2+\sqrt{\frac{10+7\sqrt2}{2}}} ≈ 2.56292$
Inradius	$\frac{1+\sqrt{2}+\sqrt{4+2\sqrt{2}}}{2} ≈ 2.51367$
Area	$4(1+\sqrt{2}+\sqrt{4+2\sqrt{2}}) ≈ 20.10936$
Angle	157.5°
Central density	1
Number of pieces	16
Level of complexity	1
Related polytopes
Army	Hed
Dual	Hexadecagon
Conjugates	Small hexadecagram, Hexadecagram, Great hexadecagram
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	I2(16), order 26
Convex	Yes
Nature	Tame

The hexadecagon is a polygon with 16 sides. A regular hexadecagon has equal sides and equal angles.

It is the uniform truncation of the octagon.

Hexadecagons and their stellations appear as faces in 8 scaliform polychora.

Vertex coordinates

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

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

Stellations

• Stellated hexadecagon (compound of 2 octagons)
• Small hexadecagram
• Tetrasquare (compound of 4 squares)
• Hexadecagram
• Dioctagram (compound of 2 octagrams)
• Great hexadecagram

External links

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

• Wikipedia Contributors. "Hexadecagon".