Octagrammic prism

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Octagrammic prism
Prism 8-3.png
Rank3
TypeUniform
SpaceSpherical
Bowers style acronymStop
Info
Coxeter diagramx x8/3o
SymmetryI2(8)×A1, order 32
ArmySemi-uniform Op
RegimentStop
Elements
Vertex figureIsosceles triangle, edge lengths 2–2, 2, 2
Faces8 squares, 2 octagrams
Edges8+16
Vertices16
Measures (edge length 1)
Circumradius(5–22)/2 ≈ 0.73681
Volume2(2–1) ≈ 0.82843
Dihedral angles4–8/3: 90°
 4–4: 45°
Height1
Central density3
Euler characteristic2
Related polytopes
DualOctagrammic bipyramid
ConjugateOctagonal prism
Properties
ConvexNo
OrientableYes
NatureTame

The octagrammic prism, or stop, is a prismatic uniform polyhedron. It consists of 2 octagrams and 8 squares. Each vertex joins one octagram and two squares. As the name suggests, it is a prism based on an octagram.

Similar to how an octagonal prism can be vertex-inscribed into the small rhombicuboctahedron, an octagrammic prism can be vertex inscribed into the quasirhombicuboctahedron.

Vertex coordinates[edit | edit source]

An octagrammic prism of edge length 1 has vertex coordinates given by:

  • (±1/2, ±(2–1)/2, ±1/2),
  • (±(2–1)/2, ±1/2, ±1/2).

Representations[edit | edit source]

An octagrammic prism has the following Coxeter diagrams:

  • x x8/3o (full symmetry)
  • x x4/3x (base has BC2 symmetry)

External links[edit | edit source]