# Square-octagrammic duoprism

Square-octagrammic duoprism Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSistodip
Coxeter diagramx4o x8/3o (         )
Elements
Cells8 cubes, 4 octagrammic prisms
Faces8+32 squares, 4 octagrams
Edges32+32
Vertices32
Vertex figureDigonal 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 anglesStop–8/3–stop: 90°
Cube–4–stop: 90°
Cube–4–cube: 45°
Height1
Central density3
Number of external pieces20
Level of complexity12
Related polytopes
ArmySemi-uniform sodip
RegimentSistodip
DualSquare-octagrammic duotegum
ConjugateSquare-octagonal duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB2×I2(8), order 128
ConvexNo
NatureTame

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)