# Triangular-dodecagonal duoprism

Triangular-dodecagonal duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx3o x12o (       )
Elements
Cells12 triangular prisms, 3 dodecagonal prisms
Faces12 triangles, 36 squares, 3 dodecagons
Edges36+36
Vertices36
Vertex figureDigonal disphenoid, edge lengths 1 (base 1), (2+6)/2 (base 2), and 2 (sides)
Measures (edge length 1)
Circumradius${\sqrt {\frac {7+3{\sqrt {3}}}{3}}}\approx 2.01628$ Hypervolume${\frac {3(3+2{\sqrt {3}})}{4}}\approx 4.84808$ Dichoral anglesTrip–3–trip: 150°
Trip–4–twip: 90°
Twip–12–twip: 60°
Height${\frac {\sqrt {3}}{2}}\approx 0.86603$ Central density1
Number of external pieces15
Level of complexity6
Related polytopes
DualTriangular-dodecagonal duotegum
ConjugateTriangular-dodecagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryA2×I2(12), order 144
ConvexYes
NatureTame

The triangular-dodecagonal duoprism or titwadip, also known as the 3-12 duoprism, is a uniform duoprism that consists of 3 dodecagonal prisms and 12 triangular prisms, with two of each joining at each vertex. It can also be seen as a convex segmentochoron, being a dodecagon atop a dodecagonal prism.

This polychoron can be subsymmetrically faceted into a 12-4 step prism, although it cannot be made uniform.

## Vertex coordinates

The vertices of a triangular-dodecagonal duoprism of edge length 1, centered at the origin, are given by:

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