Hexadecagon

Hexadecagon
(OFF file)
Rank	2
Type	Regular
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	${\sqrt {2+{\sqrt {2}}+{\sqrt {\frac {10+7{\sqrt {2}}}{2}}}}}\approx 2.56292$
Inradius	${\frac {1+{\sqrt {2}}+{\sqrt {4+2{\sqrt {2}}}}}{2}}\approx 2.51367$
Area	$4(1+{\sqrt {2}}+{\sqrt {4+2{\sqrt {2}}}})\approx 20.10936$
Angle	157.5°
Central density	1
Number of external pieces	16
Level of complexity	1
Related polytopes
Army	Hed
Dual	Hexadecagon
Conjugates	Small hexadecagram, Hexadecagram, Great hexadecagram
Abstract & topological properties
Flag count	32
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(16), order 32
Flag orbits	1
Convex	Yes
Nature	Tame

The hexadecagon, or hed, 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 non-prismatic scaliform polychora.

Vertex coordinates

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

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

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".