# Triangular-hexagonal duoprism

Triangular-hexagonal duoprism
Rank4
TypeUniform
Notation
Bowers style acronymThiddip
Coxeter diagramx3o x6o ()
Elements
Cells6 triangular prisms, 3 hexagonal prisms
Faces6 triangles, 18 squares, 3 hexagons
Edges18+18
Vertices18
Vertex figureDigonal disphenoid, edge lengths 1 (base 1), 3 (base 2), and 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {2{\sqrt {3}}}{3}}\approx 1.15470}$
Hypervolume${\displaystyle {\frac {9}{8}}=1.125}$
Dichoral anglesTrip–3–trip: 120°
Trip–4–hip: 90°
Hip–6–hip: 60°
Height${\displaystyle {\frac {\sqrt {3}}{2}}\approx 0.86603}$
Central density1
Number of external pieces9
Level of complexity6
Related polytopes
ArmyThiddip
RegimentThiddip
DualTriangular-hexagonal duotegum
ConjugateNone
Abstract & topological properties
Flag count432
Euler characteristic0
OrientableYes
Properties
SymmetryA2×G2, order 72
Flag orbits6
ConvexYes
NatureTame

The triangular-hexagonal duoprism or thiddip, also known as the 3-6 duoprism, is a uniform duoprism that consists of 3 hexagonal prisms and 6 triangular prisms, with two of each meeting at each vertex.

The convex hull of two orthogonal triangular-hexagonal duoprisms is either the triangular duoexpandoprism or the triangular duotruncatoprism.

It is also a CRF segmentochoron, being a hexagon atop hexagonal prism. It is designated K-4.47 on Richard Klitzing's list.

## Vertex coordinates

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

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

## Representations

A triangular-hexagonal duoprism has the following Coxeter diagrams:

• x3o x6o () (full symmetry)
• x3x x3o () (A2×A2 symmetry, hexagon as ditrigon)
• s3s2x3x ()
• ox xx6oo&#x (G2×A1 axial, hexagon atop hexagonal prism)
• ox xx3xx&#x (A2×A1 axial, as above with ditrigon symmetry)
• xux xxx3ooo&#x (A2×A1 axial, triangular prism-first)