# Triangular-decagonal duoprism

(Redirected from 10-3 duoprism)
Triangular-decagonal duoprism Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx3o x10o
SymmetryA2×I2(10), order 120
Elements
Vertex figureDigonal disphenoid, edge lengths 1 (base 1), (5+5)/2 (base 2), and 2 (sides)
Cells10 triangular prisms, 3 decagonal prisms
Faces10 triangles, 30 squares, 3 decagons
Edges30+30
Vertices30
Measures (edge length 1)
Circumradius$\sqrt{\frac{11+3\sqrt5}{6}} ≈ 1.71795$ Hypervolume$\frac{5\sqrt{15+6\sqrt5}}{8} ≈ 3.33169$ Dichoral anglesTrip–3–trip: 144°
Trip–4–dip: 90°
Dip–10–dip: 60°
Height$\frac{\sqrt3}{2} ≈ 0.86603$ Central density1
Euler characteristic0
Number of pieces13
Level of complexity6
Related polytopes
DualTriangular-decagonal duotegum
ConjugateTriangular-decagrammic duoprism
Properties
ConvexYes
OrientableYes
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:

• $\left(0,\,\frac{\sqrt3}{3},\,0,\,±\frac{1+\sqrt5}{2}\right),$ • $\left(0,\,\frac{\sqrt3}{3},\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4}\right),$ • $\left(0,\,\frac{\sqrt3}{3},\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12\right),$ • $\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,±\frac{1+\sqrt5}{2}\right),$ • $\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4}\right),$ • $\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12\right),$ ## 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)