# Octagrammic duoprism

The octagrammic duoprism or stodip, also known as the octagrammic-octagrammic duoprism, the 8/3 duoprism or the 8/3-8/3 duoprism, is a noble uniform duoprism that consists of 16 octagrammic prisms, with 4 meeting at each vertex.

Octagrammic duoprism
Rank4
TypeUniform
Notation
Bowers style acronymStodip
Coxeter diagramx8/3o x8/3o ()
Elements
Cells16 octagrammic prisms
Faces64 squares, 16 octagrams
Edges128
Vertices64
Vertex figureTetragonal disphenoid, edge lengths 2–2 (bases) and 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {2-{\sqrt {2}}}}\approx 0.76537}$
Inradius${\displaystyle {\frac {{\sqrt {2}}-1}{2}}\approx 0.20711}$
Hypervolume${\displaystyle 4(3-2{\sqrt {2}})\approx 0.68629}$
Dichoral anglesStop–4–stop: 90°
Stop–8/3–stop: 45°
Central density9
Number of external pieces32
Level of complexity12
Related polytopes
ArmyOdip, edge length ${\displaystyle {\sqrt {2}}-1}$
RegimentStodip
DualOctagrammic duotegum
ConjugateOctagonal duoprism
Abstract & topological properties
Flag count1536
Euler characteristic0
OrientableYes
Properties
SymmetryI2(8)≀S2, order 512
ConvexNo
NatureTame

The octagrammic duoprism can be vertex-inscribed into a sphenoverted tesseractitesseractihexadecachoron or great distetracontoctachoron.

## Vertex coordinates

The vertices of an octagrammic duoprism, centered at the origin and with unit edge length, are given by:

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

## Representations

An octagrammic duoprism has the following Coxeter diagrams:

• x8/3o x8/3o (           ) (full symmetry)
• x4/3x x8/3o (           ) (B2×I2(8) symmetry, some octagrams as ditetragrams)
• x4/3x x4/3x (           ) (B2≀S2 symmetry, all octagrams as ditetragrams)