# Great heptagrammic prism

Great heptagrammic prism Rank3
TypeUniform
SpaceSpherical
Bowers style acronymGiship
Coxeter diagramx x7/3o (       )
Elements
Vertex figureIsosceles triangle, edge lengths 2, 2, 2cos(3π/7)
Faces7 squares, 2 great heptagrams
Edges7+14
Vertices14
Measures (edge length 1)
Circumradius$\frac{\sqrt{1+\frac{1}{\sin^2\frac{3\pi}{7}}}}{2} ≈ 0.71626$ Volume$\frac{7}{4\tan\frac{3\pi}{7}} ≈ 0.39943$ Dihedral angles4–7/3: 90°
4–4: $\frac\pi7 ≈ 25.71429°$ Height1
Central density3
Euler characteristic2
Number of pieces16
Level of complexity6
Related polytopes
ArmySemi-uniform Hep
RegimentGiship
DualGreat heptagrammic tegum
ConjugatesHeptagonal prism, Heptagrammic prism
Convex coreHeptagonal prism
Topological properties
OrientableYes
Properties
SymmetryI2(7)×A1, order 28
ConvexNo
NatureTame

The great heptagrammic prism, or giship, is a prismatic uniform polyhedron. It consists of 2 great heptagrams and 7 squares. Each vertex joins one great heptagram and two squares. As the name suggests, it is a prism based on a great heptagram.

## Vertex coordinates

The coordinates of a great heptagrammic prism, centered at the origin and with edge length 2sin(3π/7), are given by:

• (1, 0, ±sin(3π/7)),
• (cos(2π/7), ±sin(2π/7), ±sin(3π/7)),
• (cos(4π/7), ±sin(4π/7), ±sin(3π/7)),
• (cos(6π/7), ±sin(6π/7), ±sin(3π/7)).