# Heptagonal pyramid

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Heptagonal pyramid
Rank3
TypeCRF
SpaceHyperbolic
Notation
Bowers style acronymHeppy
Coxeter diagramox7oo&#x
Elements
Faces7 triangles, 1 heptagon
Edges7+7
Vertices1+7
Vertex figures1 heptagon, edge length 1
7 isosceles triangles, edge lengths 1, 1, 2cos(π/7)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{1-\cos^2\frac{\pi}{7}}{3-4\cos^2\frac{\pi}{7}}} ≈ 0.87306 i}$
Volume${\displaystyle \frac{7\sqrt{4\sin^2\frac{\pi}{7}-1}}{24\sin\frac{\pi}{7}\tan\frac{\pi}{7}} ≈ 0.69371 i}$
Height${\displaystyle \frac{\sqrt{4\sin^2\frac{\pi}{7}-1}}{2\sin\frac{\pi}{7}} ≈ 0.57270 i}$
Related polytopes
ArmyHeppy
RegimentHeppy
DualHeptagonal pyramid
Abstract & topological properties
Flag count56
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryI2(7)×I, order 14
ConvexYes
Net count64

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.