# Square-octagrammic duoprism

Square-octagrammic duoprism
Rank4
TypeUniform
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${\displaystyle {\sqrt {\frac {3-{\sqrt {2}}}{2}}}\approx 0.89045}$
Hypervolume${\displaystyle 2({\sqrt {2}}-1)\approx 0.82843}$
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, edge lengths 1 (square), ${\displaystyle {\sqrt {2}}-1}$ (octagon)
RegimentSistodip
DualSquare-octagrammic duotegum
ConjugateSquare-octagonal duoprism
Abstract & topological properties
Flag count768
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:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}}\right)}$.

## Representations

A square-octagrammic duoprism has the following Coxeter diagrams: