# Decagonal-decagrammic duoprism

Decagonal-decagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx10o x10/3o ()
Elements
Cells10 decagonal prisms, 10 decagrammic prisms
Faces100 squares, 10 decagons, 10 decagrams
Edges100+100
Vertices100
Vertex figureDigonal disphenoid, edge lengths (5+5)/2 (base 1), (5–5)/2 (base 2), 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {3}}\approx 1.73205}$
Hypervolume${\displaystyle {\frac {25{\sqrt {5}}}{4}}\approx 13.97542}$
Dichoral anglesStiddip–10/3–stiddip: 144°
Dip–4–stiddip: 90°
Dip–10–dip: 72°
Central density3
Number of external pieces30
Level of complexity12
Related polytopes
ArmySemi-uniform dedip
DualDecagonal-decagrammic duotegum
ConjugateDecagonal-decagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(10)×I2(10), order 400
ConvexNo
NatureTame

The decagonal-decagrammic duoprism or distadedip, also known as the 10-10/3 duoprism, is a uniform duoprism that consists of 10 decagonal prisms and 10 decagrammic prisms, with 2 of each at each vertex.

This polychoron can be alternated into the great duoantiprism, which can be made uniform.

## Vertex coordinates

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

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

## Representations

A decagonal-decagrammic duoprism has the following Coxeter diagrams: