Octagonal-dodecagonal duoprism

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Octagonal-dodecagonal duoprism
Rank4
TypeUniform
Notation
Bowers style acronymOtwadip
Coxeter diagramx8o x12o ()
Elements
Cells12 octagonal prisms, 8 dodecagonal prisms
Faces96 squares, 12 octagons, 8 dodecagons
Edges96+96
Vertices96
Vertex figureDigonal disphenoid, edge lengths 2+2 (base 1), (2+6)/2 (base 2), and 2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesOp–8–op: 150°
 Twip–12–twip: 135°
 Op–4–twip: 90°
Central density1
Number of external pieces20
Level of complexity6
Related polytopes
ArmyOtwadip
RegimentOtwadip
DualOctagonal-dodecagonal duotegum
ConjugatesOctagonal-dodecagrammic duoprism,
Octagrammic-dodecagonal duoprism,
Octagrammic-dodecagrammic duoprism
Abstract & topological properties
Flag count2304
Euler characteristic0
OrientableYes
Properties
SymmetryI2(8)×I2(12), order 384
Flag orbits6
ConvexYes
NatureTame

The octagonal-dodecagonal duoprism or otwadip, also known as the 8-12 duoprism, is a uniform duoprism that consists of 8 dodecagonal prisms and 12 octagonal prisms, with two of each joining at each vertex.

This polychoron can be alternated into a square-hexagonal duoantiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a hexagonal-square prismantiprismoid or the dodecagons into long ditrigons to create a square-hexagonal prismantiprismoid, or it can be subsymmetrically faceted into a digonal-triangular tetraswirlprism, which are nonuniform.

Vertex coordinates[edit | edit source]

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

  • ,
  • ,
  • ,
  • ,
  • ,
  • .

Representations[edit | edit source]

An octagonal-dodecagonal duoprism has the fllowing Coxeter diagrams:

  • x8o x12o () (full symmetry)
  • x4x x12o () (B2×I2(12) symmetry, octagons as ditetragons)
  • x6x x8o () (G2×I2(8) symmetry, dodecagons as dihexagons)
  • x4x x6x () (B2×G2 symmetry, both of these applied)

External links[edit | edit source]