Compound of two heptagrams

Compound of two heptagrams
(OFF file)
Rank	2
Type	Regular
Notation
Bowers style acronym	Gosted
Schläfli symbol	{14/4}
Elements
Components	2 heptagrams
Edges	14
Vertices	14
Vertex figure	Dyad, length 2cos(2π/7)
Measures (edge length 1)
Circumradius	${\frac {1}{2\sin \left({\frac {2\pi }{7}}\right)}}\approx 0.63952$
Inradius	${\frac {1}{2\tan \left({\frac {2\pi }{7}}\right)}}\approx 0.39874$
Area	${\frac {7}{2\tan {\frac {2\pi }{7}}}}\approx 2.79116$
Angle	${\frac {3\pi }{7}}\approx 77.14286^{\circ }$
Central density	4
Number of external pieces	28
Level of complexity	2
Related polytopes
Army	Ted, edge length ${\frac {\sin {\frac {\pi }{14}}}{2\sin {\frac {\pi }{7}}\cos {\frac {\pi }{7}}}}$
Dual	Compound of two heptagrams
Conjugates	Compound of two heptagons, compound of two great heptagrams
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 great stellated tetradecagon or gosted is a polygon compound composed of two heptagrams. As such it has 14 edges and 14 vertices.

It is the third stellation of the tetradecagon.

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

Vertex coordinates

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

• $\left(\pm 1,\,0\right),$
• $\left(\pm \cos {\frac {\pi }{7}},\,\pm \sin {\frac {\pi }{7}}\right),$
• $\left(\pm \cos {\frac {2\pi }{7}},\,\pm \sin {\frac {2\pi }{7}}\right),$
• $\left(\pm \cos {\frac {3\pi }{7}},\,\pm \sin {\frac {3\pi }{7}}\right).$

External links

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