Decagonal-truncated dodecahedral duoprism

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Decagonal-truncated dodecahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymDatid
Coxeter diagramx10o x5x3o ()
Elements
Tera20 triangular-decagonal duoprisms, 12 decagonal duoprisms
Cells200 triangular prisms, 30+60+120 decagonal prisms, 10 truncated dodecahedra
Faces200 triangles, 300+600 squares, 60+120 decagons
Edges300+600+600
Vertices600
Vertex figureDigonal disphenoidal pyramid, edge lengths 1, (5+5)/2, (5+5)/2 (base triangle), (5+5)/2 (top), 2 (side edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTiddip–tid–tiddip: 144°
 Tradedip–dip–dedip:
 Dedip–dip–dedip:
 Tradedip–trip–tiddip: 90°
 Dedip–dip–tiddip: 90°
Central density1
Number of external pieces42
Level of complexity30
Related polytopes
ArmyDatid
RegimentDatid
DualDecagonal-triakis icosahedral duotegum
ConjugateDecagrammic-quasitruncated great stellated dodecahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryH3×I2(10), order 2400
ConvexYes
NatureTame

The decagonal-truncated dodecahedral duoprism or datid is a convex uniform duoprism that consists of 10 truncated dodecahedral prisms, 12 decagonal duoprisms, and 20 triangular-decagonal duoprisms. Each vertex joins 2 truncated dodecahedral prisms, 1 triangular-decagonal duoprism, and 2 decagonal duoprisms.

Vertex coordinates[edit | edit source]

The vertices of a decagonal-truncated dodecahedral duoprism of edge length 1 are given by all even permutations of the last three coordinates of:

Representations[edit | edit source]

A decagonal-truncated dodecahedral duoprism has the following Coxeter diagrams:

  • x10o x5x3o (full symmetry)
  • x5x x5x3o (decagons as dipentagons)