Stellated dodecagon

The stellated dodecagon, or sedog, is a polygon compound composed of two hexagons. As such it has 12 edges and 12 vertices.

Stellated dodecagon
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Sedog
Schläfli symbol	{12/2}
Elements
Components	2 hexagons
Edges	12
Vertices	12
Vertex figure	Dyad, length √3
Measures (edge length 1)
Circumradius	1
Inradius	$\frac{\sqrt3}{2} ≈ 0.86603$
Area	$3\sqrt3 ≈ 5.19615$
Angle	120°
Central density	2
Number of external pieces	24
Level of complexity	2
Related polytopes
Army	Dog, edge length $\frac{\sqrt6-\sqrt2}{2}$
Dual	Stellated dodecagon
Conjugate	Stellated dodecagon
Convex core	Dodecagon
Abstract & topological properties
Flag count	24
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(12), order 24
Convex	No
Nature	Tame

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

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

Vertex coordinates

Coordinates for the vertices of a stellated dodecagon of edge length 1 centered at the origin are given by:

• $\left(±\frac12,\,±\frac{\sqrt3}{2}\right),$
• $\left(±1,\,0\right),$
• $\left(±\frac{\sqrt3}{2},\,±\frac12\right),$
• $\left(0,\,±1\right).$

Variations

The stellated dodecagon can be varied by changing the angle between the two component hexagons from the usual 30°. These 2-hexagon compounds generally have a dihexagon as their convex hull and remain uniform, but not regular, with hexagonal symmetry only.

External links

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