Heptagrammic pyramid

Heptagrammic pyramid
Rank	3
Type	Segmentotope
Space	Spherical
Notation
Bowers style acronym	Shappy
Coxeter diagram	ox7/2oo&#x
Elements
Faces	7 triangles, 1 heptagram
Edges	7+7
Vertices	1+7
Vertex figures	1 heptagram, edge length 1
	7 isosceles triangles, edge lengths 1, 1, 2cos(2π/7)
Measures (edge length 1)
Circumradius	$\frac{1}{\sqrt{4-\frac{1}{\sin^2\frac{2\pi}{7}}}} ≈ 0.65039$
Volume	$\frac{7\sqrt{4-\frac{1}{\cos^2\frac{2\pi}{7}}}}{24\tan\frac{2\pi}{7}} ≈ 0.35763$
Height	$\frac{\sqrt{4-\frac{1}{\sin^2\frac{2\pi}{7}}}}{2} ≈ 0.76877$
Related polytopes
Army	Non-RF heppy
Regiment	Shappy
Dual	Heptagrammic pyramid
Conjugates	Heptagonal pyramid, great heptagrammic pyramid
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	I2(7)×I, order 14
Convex	No
Nature	Tame

The heptagrammic pyramid or shappy is a pyramid with a heptagrammic base and 7 triangles as sides. A version with equilateral triangles exists and is orbiform.

External links

• Klitzing, Richard. "shappy".