Stellated tetradecagon

Stellated tetradecagon
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Stad
Schläfli symbol	{14/2}
Elements
Components	2 heptagons
Edges	14
Vertices	14
Vertex figure	Dyad, length 2cos(π/7)
Measures (edge length 1)
Circumradius	$\frac{1}{2\sin\frac\pi7} \approx 1.15238$
Inradius	$\frac{1}{2\tan\frac\pi7} \approx 1.03826$
Area	$\frac{7}{2\tan\frac\pi7} \approx 7.26782$
Angle	$\frac{5\pi}{7} \approx 128.57143^\circ$
Central density	2
Number of external pieces	28
Level of complexity	2
Related polytopes
Army	Ted, edge length $\frac{1}{2\cos\frac{\pi}{14}}$
Dual	Stellated tetradecagon
Conjugates	Great stellated tetradecagon, spinostellated tetradecagon
Convex core	Tetradecagon
Abstract & topological properties
Flag count	28
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	I2(14), order 28
Convex	No
Nature	Tame

The stellated tetradecagon or stad is a polygon compound composed of two heptagons. As such it has 14 edges and 14 vertices.

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

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

Vertex coordinates

Coordinates for a stellated tetradecagon of edge length 2sin(π/7), centered at the origin, are:

• $\left(\pm1,\,0\right),$
• $\left(\pm\cos\frac{\pi}{7},\,\pm\sin\frac{\pi}{7}\right),$
• $\left(\pm\cos\frac{2\pi}{7},\,\pm\sin\frac{2\pi}{7}\right),$
• $\left(\pm\cos\frac{3\pi}{7},\,\pm\sin\frac{3\pi}{7}\right).$

External links

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