# Octagrammic prism

Octagrammic prism Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymStop
Coxeter diagramx x8/3o (       )
Elements
Faces8 squares, 2 octagrams
Edges8+16
Vertices16
Vertex figureIsosceles triangle, edge lengths 2–2, 2, 2
Measures (edge length 1)
Circumradius$\frac{\sqrt{5-2\sqrt2}}2 ≈ 0.73681$ Volume$2(\sqrt2-1) ≈ 0.82843$ Dihedral angles4–8/3: 90°
4–4: 45°
Height1
Central density3
Number of external pieces18
Level of complexity6
Related polytopes
ArmySemi-uniform Op, edge lengths $\sqrt2-1$ (base) 1 (sides)
RegimentStop
DualOctagrammic tegum
ConjugateOctagonal prism
Convex coreOctagonal prism
Abstract & topological properties
Flag count96
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryI2(8)×A1, order 32
ConvexNo
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

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

• $\left(±\frac12,\,±\frac{\sqrt2-1}{2},\,±\frac12\right),$ • $\left(±\frac{\sqrt2-1}{2},\,±\frac12,\,±\frac12\right).$ ## Representations

An octagrammic prism has the following Coxeter diagrams:

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