Heptagrammic antiprismatic prism

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Heptagrammic antiprismatic prism
Rank4
TypeUniform
Notation
Bowers style acronymShappip
Coxeter diagramx2s2s14/2o ()
Elements
Cells14 triangular prisms, 2 heptagrammic prisms, 2 heptagrammic antiprisms
Faces28 triangles, 14+14 squares, 4 heptagrams
Edges14+28+28
Vertices28
Vertex figureIsosceles trapezoidal pyramid, edge lengths 1, 1, 1, 2cos(2π/7) (base), 2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTrip–4–trip:
 Trip–4–ship:
 Shap–7/2–ship: 90°
 Shap–3–trip: 90°
HeightsShap atop shap: 1
 Ship atop ship:
Number of external pieces46
Related polytopes
ArmySemi-uniform squahedip
RegimentShappip
DualHeptagrammic antitegmatic tegum
ConjugateGreat heptagrammic retroprismatic prism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(7)×A1×A1, order 56
ConvexNo
NatureTame

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

Vertex coordinates[edit | edit source]

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

where

Representations[edit | edit source]

A heptagrammic antiprismatic prism has the following Coxeter diagrams:

  • x2s2s14/2o (full symmetry)
  • x2s2s7/2s
  • xx xo7/2ox&#x (heptagrammic prism atop heptagrammic prism)

External links[edit | edit source]