# Heptagrammic pyramid

Heptagrammic pyramid
Rank3
TypeSegmentotope
Notation
Bowers style acronymShappy
Coxeter diagramox7/2oo&#x
Elements
Faces7 triangles, 1 heptagram
Edges7+7
Vertices1+7
Vertex figures1 heptagram, edge length 1
7 isosceles triangles, edge lengths 1, 1, 2cos(2π/7)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {1}{\sqrt {4-{\frac {1}{\sin ^{2}{\frac {2\pi }{7}}}}}}}\approx 0.65039}$
Volume${\displaystyle {\frac {7{\sqrt {4-{\frac {1}{\cos ^{2}{\frac {2\pi }{7}}}}}}}{24\tan {\frac {2\pi }{7}}}}\approx 0.35763}$
Height${\displaystyle {\frac {\sqrt {4-{\frac {1}{\sin ^{2}{\frac {2\pi }{7}}}}}}{2}}\approx 0.76877}$
Related polytopes
ArmyNon-RF heppy
RegimentShappy
DualHeptagrammic pyramid
ConjugatesHeptagonal pyramid, great heptagrammic pyramid
Abstract & topological properties
OrientableYes
Properties
SymmetryI2(7)×I, order 14
ConvexNo
NatureTame

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.