# Triangular-decagonal duoprism

Triangular-decagonal duoprism Rank4
TypeUniform
Notation
Coxeter diagramx3o x10o (       )
Elements
Cells10 triangular prisms, 3 decagonal prisms
Faces10 triangles, 30 squares, 3 decagons
Edges30+30
Vertices30
Vertex figureDigonal disphenoid, edge lengths 1 (base 1), (5+5)/2 (base 2), and 2 (sides)
Measures (edge length 1)
Circumradius${\sqrt {\frac {11+3{\sqrt {5}}}{6}}}\approx 1.71795$ Hypervolume${\frac {5{\sqrt {15+6{\sqrt {5}}}}}{8}}\approx 3.33169$ Dichoral anglesTrip–3–trip: 144°
Trip–4–dip: 90°
Dip–10–dip: 60°
Height${\frac {\sqrt {3}}{2}}\approx 0.86603$ Central density1
Number of external pieces13
Level of complexity6
Related polytopes
DualTriangular-decagonal duotegum
ConjugateTriangular-decagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryA2×I2(10), order 120
ConvexYes
NatureTame

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

It is also a CRF segmentochoron, being decagon atop decagonal prism. It is designated K-4.94 on Richard Klitzing's list.

## Vertex coordinates

Coordinates for the vertices of a triangular–decagonal duoprism of edge length 1, centered at the origin, are given by:

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

A triangular-decagonal duoprism has the following Coxeter diagrams:

• x3o x10o (full symetry)
• x3o x5x (A2×H2 symmetry, decagon as dipentagon)
• ox xx10oo&#x (I2(10)×A1 axial, decagon atop decagon prism)
• ox xx5xx&#x (H2×A1 axial)