# Triangular-decagrammic duoprism

Triangular-decagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx3o x10/3o ()
Elements
Cells10 triangular prisms, 3 decagrammic prisms
Faces10 triangles, 30 squares, 3 decagrams
Edges30+30
Vertices30
Vertex figureDigonal disphenoid, edge lengths 1 (base 1), 5–5/2 (base 2), 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {11-3{\sqrt {5}}}{6}}}\approx 0.84575}$
Hypervolume${\displaystyle {\frac {5{\sqrt {15-6{\sqrt {5}}}}}{8}}\approx 0.78651}$
Dichoral anglesTrip–4–stiddip: 90°
Trip–3–trip: 72°
Stiddip–10/3–stiddip: 60°
Height${\displaystyle {\frac {\sqrt {3}}{2}}\approx 0.86603}$
Central density3
Number of external pieces13
Level of complexity12
Related polytopes
DualTriangular-decagrammic duotegum
ConjugateTriangular-decagonal duoprism
Abstract & topological properties
Flag count720
Euler characteristic0
OrientableYes
Properties
SymmetryA2×I2(10), order 120
ConvexNo
NatureTame

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

## Vertex coordinates

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

• ${\displaystyle \left(0,\,{\frac {\sqrt {3}}{3}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5-2{\sqrt {5}}}}{2}}\right)}$,
• ${\displaystyle \left(0,\,{\frac {\sqrt {3}}{3}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\right)}$,
• ${\displaystyle \left(0,\,{\frac {\sqrt {3}}{3}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5-2{\sqrt {5}}}}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,0\right)}$.

## Representations

A triangular-decagrammic duoprism duoprism has the following Coxeter diagrams: