Decagonal-dodecagonal duoprism

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Decagonal-dodecagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymDatwadip
Info
Coxeter diagramx10o x12o
SymmetryI2(10)×I2(12), order 480
ArmyDatwadip
RegimentDatwadip
Elements
Vertex figureDigonal disphenoid, edge lengths (5+5)/2 (base 1), (2+6)/2 (base 2), and 2 (sides)
Cells12 decagonal prisms, 10 dodecagonal prisms
Faces120 squares, 12 decagons, 10 dodecagons
Edges120+120
Vertices120
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTwip–12–twip: 144°
 Dip–10–dip: 150°
 Twip–4–dip: 90°
Central density1
Euler characteristic0
Number of pieces22
Level of complexity6
Related polytopes
DualDecagonal-dodecagonal duotegum
ConjugatesDecagonal-dodecagrammic duoprism, Decagrammic-dodecagonal duoprism, Decagrammic-dodecagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame

The decagonal-dodecagonal duoprism or datwadip, also known as the 10-12 duoprism, is a uniform duoprism that consists of 10 dodecagonal prisms and 12 decagonal prisms, with two of each joining at each vertex.

This polychoron can be alternated into a pentagonal-hexagonal duoantiprism, although it cannot be made uniform. The dodecagons can also be alternated into long ditrigons to create a pentagonal-hexagonal prismantiprismoid, which is also nonuniform.

Vertex coordinates[edit | edit source]

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

Representations[edit | edit source]

A decagonal-dodecagonal duoprism has the following Coxeter diagrams:

  • x10o x12o (full symmetry)
  • x5x x12o (decagons as dipentagons)
  • x6x x10o (dodecagons as dihexagons)
  • x5x x6x (both of these applied)

External links[edit | edit source]