Great heptagrammic pyramid

Great heptagrammic pyramid
Rank3
TypeSegmentotope
SpaceSpherical
Notation
Bowers style acronymGishpy
Coxeter diagramox7/3oo&#x
Elements
Faces7 triangles, 1 great heptagram
Edges7+7
Vertices1+7
Vertex figures1 great heptagram, edge length 1
7 isosceles triangles, edge lengths 1, 1, 2cos(3π/7)
Measures (edge length 1)
Circumradius${\displaystyle \frac{1}{\sqrt{4-\frac{1}{\sin^2\frac{3\pi}{7}}}} ≈ 0.58243}$
Volume${\displaystyle \frac{7\sqrt{4-\frac{1}{\sin^2\frac{3\pi}{7}}}}{24\tan\frac{3\pi}{7}} ≈ 0.11430}$
Height${\displaystyle \frac{\sqrt{4-\frac{1}{\sin^2\frac{3\pi}{7}}}}{2} ≈ 0.85847}$
Related polytopes
ArmyNon-RF heppy
RegimentGishpy
DualGreat heptagrammic pyramid
ConjugatesHeptagonal pyramid, heptagrammic pyramid
Abstract & topological properties
OrientableYes
Properties
SymmetryI2(7)×I, order 14
ConvexNo
NatureTame

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