Decagonal-dodecahedral duoprism

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Decagonal-dodecahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymDadoe
Coxeter diagramx10o x5o3o ()
Elements
Tera12 pentagonal-decagonal duoprisms, 10 dodecahedral prisms
Cells120 pentagonal prisms, 30 decagonal prisms, 10 dodecahedra
Faces300 squares, 120 pentagons, 20 decagons
Edges200+300
Vertices200
Vertex figureTriangular scalene, edge lengths (1+5)/2 (base triangle), (5+5)/2 (top), 2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesDope–doe–dope: 144°
 Padedip–dip–padedip:
 Padedip–pip–dope: 90°
Central density1
Number of external pieces22
Level of complexity10
Related polytopes
ArmyDadoe
RegimentDadoe
DualDecagonal-icosahedral duotegum
ConjugateDecagrammic-great stellated dodecahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryH3×I2(10), order 2400
ConvexYes
NatureTame

The decagonal-dodecahedral duoprism or dadoe is a convex uniform duoprism that consists of 10 dodecahedral prisms and 12 pentagonal-decagonal duoprisms. Each vertex joins 2 dodecahedral prisms and 3 pentagonal-decagonal duoprisms.

Vertex coordinates[edit | edit source]

The vertices of a decagonal-dodecahedral duoprism of edge length 1 are given by:

as well as all even permutations of the last three coordinates of:

Representations[edit | edit source]

A decagonal-dodecahedral duoprism has the following Coxeter diagrams:

  • x10o x5o3o ()(full symmetry)
  • x5x x5o3o () (decagons as dipentagons)