Square-octagrammic duoprism

Square-octagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sistodip
Coxeter diagram	x4o x8/3o ()
Elements
Cells	8 cubes, 4 octagrammic prisms
Faces	8+32 squares, 4 octagrams
Edges	32+32
Vertices	32
Vertex figure	Digonal disphenoid, edge lengths √2–√2 (base 1) and √2 (base 2 and sides)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{3-\sqrt2}2} ≈ 0.89045$
Hypervolume	$2(\sqrt2-1) ≈ 0.82843$
Dichoral angles	Stop–8/3–stop: 90°
	Cube–4–stop: 90°
	Cube–4–cube: 45°
Height	1
Central density	3
Number of external pieces	20
Level of complexity	12
Related polytopes
Army	Semi-uniform sodip
Regiment	Sistodip
Dual	Square-octagrammic duotegum
Conjugate	Square-octagonal duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B2×I2(8), order 128
Convex	No
Nature	Tame

The square-octagrammic duoprism, also known as sistodip or the 4-8/3 duoprism, is a uniform duoprism that consists of 8 cubes and 4 octagrammic prisms, with 2 of each at each vertex.

The square-octagrammic duoprism can be vertex-inscribed into the great tesseractitesseractihexadecachoron.

Vertex coordinates

The coordinates of a square-octagrammic duoprism, centered at the origin and with unit edge length, are given by:

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

Representations

A square-octagrammic duoprism has the following Coxeter diagrams:

• x4o x8/3o (full symmetry)
• x x x8/3o () (I₂(8)×A₁×A₁ symmetry, octagrammic prismatic prism)

External links

• Bowers, Jonathan. "Category A: Duoprisms".

• Klitzing, Richard. "sistodip".