Triangular-dodecagonal duoprism

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Triangular-dodecagonal duoprism
Rank4
TypeUniform
Notation
Bowers style acronymTitwadip
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
Hypervolume
Dichoral anglesTrip–3–trip: 150°
 Trip–4–twip: 90°
 Twip–12–twip: 60°
Height
Central density1
Number of external pieces15
Level of complexity6
Related polytopes
ArmyTitwadip
RegimentTitwadip
DualTriangular-dodecagonal duotegum
ConjugateTriangular-dodecagrammic duoprism
Abstract & topological properties
Flag count864
Euler characteristic0
OrientableYes
Properties
SymmetryA2×I2(12), order 144
Flag orbits6
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[edit | edit source]

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

  • ,
  • ,
  • ,
  • ,
  • ,
  • .

Representations[edit | edit source]

A triangular-dodecagonal duoprism has the following Coxeter diagrams:

  • x3o x12o () (full symetry)
  • x3o x6x () (A2×G2 symmetry, dodecagon as dihexagon)
  • ox xx12oo&#x (I2(12)×A1 axial, dodecagon atop dodecagon prism)
  • ox xx6xx&#x (G2×A1 axial)

External links[edit | edit source]