Triangular-decagonal duoprismatic prism

From Polytope Wiki
Jump to navigation Jump to search
Triangular-decagonal duoprismatic prism
Rank5
TypeUniform
Notation
Bowers style acronymTradip
Coxeter diagramx x3o x10o
Elements
Tera10 triangular-square duoprisms, 2 triangular-decagonal duoprisms, 3 square-decagonal duoprisms
Cells10+20 triangular prisms, 30 cubes, 3+6 decagonal prisms
Faces20 triangles, 30+30+60 squares, 6 decagons]
Edges30+60+60
Vertices60
Vertex figureDigonal disphenoidal pyramid, edge lengths 1 (disphenoid base 1), (5+5)/2 (disphenoid base 2), 2 (remaining edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTisdip–trip–tisdip: 144°
 Tradedip–trip–tisdip: 90°
 Squadedip–cube–tisdip: 90°
 Tradedip–dip–squadedip: 90°
 Squadedip–dip–squadedip: 60°
HeightsTradedip atop tradedip: 1
 Dip atop squadedip:
Central density1
Number of external pieces15
Level of complexity30
Related polytopes
ArmyTradip
RegimentTradip
DualTriangular-decagonal duotegmatic tegum
ConjugateTriangular-decagrammic duoprismatic prism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryA2×I2(10)×A1, order 240
ConvexYes
NatureTame

The triangular-decagonal duoprismatic prism or tradip, also known as the triangular-decagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 triangular-decagonal duoprisms, 3 square-decagonal duoprisms, and 10 triangular-square duoprisms. Each vertex joins 2 triangular-square duoprisms, 2 square-decagonal duoprisms, and 1 triangular-decagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

Vertex coordinates[edit | edit source]

The vertices of a triangular-decagonal duoprismatic prism of edge length 1 are given by:

Representations[edit | edit source]

A triangular-decagonal duoprismatic prism has the following Coxeter diagrams:

  • x x3o x10o (full symmetry)
  • xx3oo xx10oo&#x (triangular-decagonal duoprism atop triangular-decagonal duoprism)
  • ox xx xx10oo&#x (decagonal prism atop square-decagonal duoprism)