Decagrammic duoprism

Decagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx10/3o x10/3o ()
Elements
Cells20 decagrammic prisms
Faces100 squares, 20 decagrams
Edges200
Vertices100
Vertex figureTetragonal disphenoid, edge lengths (5–5)/2 (bases) and 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {{\sqrt {10}}-{\sqrt {2}}}{2}}\approx 0.87403}$
Inradius${\displaystyle {\frac {\sqrt {5-2{\sqrt {5}}}}{2}}\approx 0.36327}$
Hypervolume${\displaystyle 25{\frac {5-2{\sqrt {5}}}{4}}\approx 3.29915}$
Dichoral anglesStiddip–4–stiddip: 90°
Stiddip–10/3–stiddip: 72°
Central density9
Number of external pieces40
Level of complexity12
Related polytopes
ArmyDedip
DualDecagrammic duotegum
ConjugateDecagonal duoprism
Abstract & topological properties
Flag count2400
Euler characteristic0
OrientableYes
Properties
SymmetryI2(10)≀S2, order 800
ConvexNo
NatureTame

The decagrammic duoprism or stadidip, also known as the decagrammic-decagrammic duoprism, the 10/3 duoprism or the 10/3-10/3 duoprism, is a noble uniform duoprism that consists of 20 decagrammic prisms, with 4 meeting at each vertex.

A unit decagrammic duoprism can be vertex-inscribed into a grand ditetrahedronary hexacosidishecatonicosachoron.

Vertex coordinates

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

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5-2{\sqrt {5}}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5-2{\sqrt {5}}}}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5-2{\sqrt {5}}}}{2}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5-2{\sqrt {5}}}}{2}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5-2{\sqrt {5}}}}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\right)}$,
• ${\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5-2{\sqrt {5}}}}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{2}},\,0,\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\right)}$,
• ${\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{2}},\,0,\,\pm {\frac {{\sqrt {5}}-1}{2}},\,0\right)}$.

Representations

A decagrammic duoprism duoprism has the following Coxeter diagrams: