Great heptagrammic prism

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Great heptagrammic prism
Heptagrammic prism 7-3.png
Rank3
TypeUniform
SpaceSpherical
Bowers style acronymGiship
Info
Coxeter diagramx x7/3o
SymmetryI2(7)×A1, order 28
ArmySemi-uniform Hep
RegimentGiship
Elements
Vertex figureIsosceles triangle, edge lengths 2, 2, 2cos(3π/7)
Faces7 squares, 2 great heptagrams
Edges7+14
Vertices14
Measures (edge length 1)
Circumradius1+1/sin2(3π/7)/2 ≈ 0.71626
Volume7/(4tan(3π/7)) ≈ 0.39943
Dihedral angles4–7/3: 90°
 4–4: π/7 ≈ 25.71429°
Height1
Central density3
Euler characteristic2
Related polytopes
DualGreat heptagrammic bipyramid
ConjugatesHeptagonal prism, Heptagrammic prism
Convex coreHeptagonal prism
Properties
ConvexNo
OrientableYes
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[edit | edit source]

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)).

External links[edit | edit source]