Octagonal-dodecagonal duoprismatic prism

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Octagonal-dodecagonal duoprismatic prism
Rank5
TypeUniform
Notation
Bowers style acronymOtwip
Coxeter diagramx x8o x12o
Elements
Tera12 square-octagonal duoprisms, 8 square-dodecagonal duoprisms, 2 octagonal-dodecagonal duoprisms
Cells96 cubes, 8+16 dodecagonal prisms, 12+24 octagonal prisms
Faces96+96+192 squares, 24 octagons, 16 dodecagons
Edges96+192+192
Vertices192
Vertex figureDigonal disphenoidal pyramid, edge lengths 2+2 (disphenoid base 1), 2+3 (disphenoid base 2), 2 (remaining edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesSodip–op–sodip: 150°
 Sitwadip–twip–sitwadip: 135°
 Sitwadip–cube–sodip: 90°
 Otwadip–op–sodip: 90°
 Sitwadip–twip–otwadip: 90°
Height1
Central density1
Number of external pieces22
Level of complexity30
Related polytopes
ArmyOtwip
RegimentOtwip
DualOctagonal-dodecagonal duotegmatic tegum
ConjugatesOctagonal-dodecagrammic duoprismatic prism, Octagrammic-dodecagonal duoprismatic prism, Octagrammic-dodecagrammic duoprismatic prism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryI2(8)×I2(12)×A1, order 768
ConvexYes
NatureTame

The octagonal-dodecagonal duoprismatic prism or otwip, also known as the octagonal-dodecagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 octagonal-dodecagonal duoprisms, 8 square-dodecagonal duoprisms, and 12 square-octagonal duoprisms. Each vertex joins 2 square-octagonal duoprisms, 2 square-dodecagonal duoprisms, and 1 octagonal-dodecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

This polyteron can be alternated into a square-hexagonal duoantiprismatic antiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a hexagonal-square prismatic prismantiprismoid or the dodecagons into long ditrigons to create a square-hexagonal prismatic prismantiprismoid, which are also both nonuniform.

Vertex coordinates[edit | edit source]

The vertices of an octagonal-dodecagonal duoprismatic prism of edge length 1 are given by all permutations of the first two coordinates of:

Representations[edit | edit source]

An octagonal-dodecagonal duoprismatic prism has the following Coxeter diagrams:

  • x x8o x12o (full symmetry)
  • x x4x x12o (octagons as ditetragons)
  • x x8o x6x (dodecagons as dihexagons)
  • x x4x x6x
  • xx8oo xx12oo&#x (octagonal-enneagonal duoprism atop octagonal-enneagonal duoprism)
  • xx4xx xx12oo&#x
  • xx8oo xx6xx&#x
  • xx4xx xx6xx&#x