Heptagonal pyramid

The heptagonal pyramid, or heppy, is a pyramid with a heptagonal base and 7 triangles as sides. The version with equilateral triangles as sides is hyperbolic, and is the vertex-first cap of the order-7 triangular tiling. Other variants with isosceles triangles as sides exist, that can be placed in 3D Euclidean space.

Heptagonal pyramid
Rank	3
Type	CRF
Space	Hyperbolic
Notation
Bowers style acronym	Heppy
Coxeter diagram	ox7oo&#x
Elements
Faces	7 triangles, 1 heptagon
Edges	7+7
Vertices	1+7
Vertex figures	1 heptagon, edge length 1
	7 isosceles triangles, edge lengths 1, 1, 2cos(π/7)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{1-\cos^2\frac{\pi}{7}}{3-4\cos^2\frac{\pi}{7}}} ≈ 0.87306 i$
Volume	$\frac{7\sqrt{4\sin^2\frac{\pi}{7}-1}}{24\sin\frac{\pi}{7}\tan\frac{\pi}{7}} ≈ 0.69371 i$
Height	$\frac{\sqrt{4\sin^2\frac{\pi}{7}-1}}{2\sin\frac{\pi}{7}} ≈ 0.57270 i$
Related polytopes
Army	Heppy
Regiment	Heppy
Dual	Heptagonal pyramid
Abstract & topological properties
Flag count	56
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	I2(7)×I, order 14
Convex	Yes
Net count	64