Great heptagrammic antiprismatic prism

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Great heptagrammic antiprismatic prism
Rank4
TypeUniform
Notation
Bowers style acronymGishappip
Coxeter diagramx2s2s14/3o ()
Elements
Cells14 triangular prisms, 2 great heptagrammic prisms, 2 great heptagrammic antiprisms
Faces28 triangles, 14+14 squares, 4 great heptagrams
Edges14+28+28
Vertices28
Vertex figureIsosceles trapezoidal pyramid, edge lengths 1, 1, 1, 2cos(3π/7) (base), 2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTrip–4–giship:
 Gishap–7/3–giship: 90°
 Gishap–3–trip: 90°
 Trip–4–trip:
HeightsGishap atop gishap: 1
 Giship atop gyro giship:
Number of external pieces74
Related polytopes
ArmySemi-uniform heappip
RegimentGishappip
DualGreat heptagrammic antitegmatic tegum
ConjugateHeptagonal antiprismatic prism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(I2(14)×A1)+×A1, order 56
ConvexNo
NatureTame

The great heptagrammic antiprismatic prism or gishappip is a prismatic uniform polychoron that consists of 2 great heptagrammic antiprisms, 2 great heptagrammic prisms, and 14 triangular prisms. Each vertex joins 1 great heptagrammic antiprism, 1 great heptagrammic prism, and 3 triangular prisms. As the name suggests, it is a prism based on the great heptagrammic antiprism. Being a prism based on an orbiform polytope, it is also a segmentochoron.

Vertex coordinates[edit | edit source]

The vertices of a great heptagrammic antiprismatic prism, centered at the origin and with edge length 2sin(3π/7), are given by the following points, as well as the central inversions of their first three coordinates:

where

Representations[edit | edit source]

A great heptagrammic antiprismatic prism has the following Coxeter diagrams:

  • x2s2s14/3o (full symmetry)
  • x2s2s7/3s ()
  • xx xo7/3ox&#x (great heptagrammic prism atop gyrated great heptagrammic prism)

External links[edit | edit source]