Octagrammic prism

Octagrammic prism
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Stop
Coxeter diagram	x x8/3o ()
Elements
Faces	8 squares, 2 octagrams
Edges	8+16
Vertices	16
Vertex figure	Isosceles 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 angles	4–8/3: 90°
	4–4: 45°
Height	1
Central density	3
Number of external pieces	18
Level of complexity	6
Related polytopes
Army	Semi-uniform Op, edge lengths $\sqrt2-1$ (base) 1 (sides)
Regiment	Stop
Dual	Octagrammic tegum
Conjugate	Octagonal prism
Convex core	Octagonal prism
Abstract & topological properties
Flag count	96
Euler characteristic	2
Orientable	Yes
Genus	0
Properties
Symmetry	I2(8)×A1, order 32
Convex	No
Nature	Tame

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)

External links

• Klitzing, Richard. "stop".

• Wikipedia Contributors. "Octagrammic prism".
• McCooey, David. "Octagrammic Prism"