Decagonal duoprism

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Decagonal duoprism
Decagonal duoprism.png
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymDedip
Info
Coxeter diagramx10o x10o
SymmetryI2(10)≀S2, order 800
ArmyDedip
RegimentDedip
Elements
Vertex figureTetragonal disphenoid, edge lengths (5+5)/2 (bases) and 2 (sides)
Cells20 decagonal prisms
Faces100 squares, 20 decagons
Edges200
Vertices100
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dichoral anglesDip–10–dip: 144º
 Dip–4–dip: 90°
Central density1
Euler characteristic0
Number of pieces20
Level of complexity3
Related polytopes
DualDecagonal duotegum
ConjugateDecagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame

The decagonal duoprism or dedip, also known as the decagonal-decagonal duoprism, the 10 duoprism or the 10-10 duoprism, is a noble uniform duoprism that consists of 20 decagonal prisms, with four at each vertex. It is also the 20-9 gyrochoron. It is the first in an infinite family of isogonal decagonal dihedral swirlchora and also the first in an infinite family of isochoric decagonal hosohedral swirlchora.

This polychoron can be alternated into a pentagonal duoantiprism, although it cannot be made uniform.

A unit decagonal duoprism can be vertex-inscribed into the small ditetrahedronary hexacosihecatonicosachoron.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a decagonal duoprism of edge length 1, centered at the origin, are given by:

Representations[edit | edit source]

A decagonal duoprism has the following Coxeter diagrams:

  • x10o x10o (full symmetry)
  • x5x x10o (one decagon as dipentagon)
  • x5x x5x (both decagons have pentagonal symmetry)

External links[edit | edit source]