Heptagonal pyramid

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${\displaystyle {\sqrt {\frac {1-\cos ^{2}{\frac {\pi }{7}}}{3-4\cos ^{2}{\frac {\pi }{7}}}}}\approx 0.87306i}$
Volume${\displaystyle {\frac {7{\sqrt {4\sin ^{2}{\frac {\pi }{7}}-1}}}{24\sin {\frac {\pi }{7}}\tan {\frac {\pi }{7}}}}\approx 0.69371i}$
Height${\displaystyle {\frac {\sqrt {4\sin ^{2}{\frac {\pi }{7}}-1}}{2\sin {\frac {\pi }{7}}}}\approx 0.57270i}$
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.