Dodecagonal-truncated octahedral duoprism

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Dodecagonal-truncated octahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymTwatoe
Coxeter diagramx12o o4x3x ()
Elements
Tera6 square-dodecagonal duoprisms, 12 truncated octahedral prisms, 8 hexagonal-dodecagonal duoprisms
Cells72 cubes, 96 hexagonal prisms, 12+24 dodecagonal prisms, 12 truncated octahedra
Faces72+144+288 squares, 96 hexagons, 24 dodecagons
Edges144+288+288
Vertices288
Vertex figureDigonal disphenoidal pyramid, edge lengths 2, 3, 3 (base triangle), 2+3 (top), 2 (side edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTope–toe–tope: 150°
 Sitwadip–twip–hitwadip:
 Hitwadip–twip–hitwadip:
 Sitwadip–cube–tope: 90°
 Hitwadip–hip–tope: 90°
Central density1
Number of external pieces26
Level of complexity30
Related polytopes
ArmyTwatoe
RegimentTwatoe
DualDodecagonal-tetrakis hexahedral duotegum
ConjugateDodecagrammic-truncated octahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB3×I2(12), order 1152
ConvexYes
NatureTame

The dodecagonal-truncated octahedral duoprism or twatoe is a convex uniform duoprism that consists of 12 truncated octahedral prisms, 8 hexagonal-dodecagonal duoprisms, and 6 square-dodecagonal duoprisms. Each vertex joins 2 truncated octahedral prisms, 1 square-dodecagonal duoprism, and 2 hexagonal-dodecagonal duoprisms.

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

Vertex coordinates[edit | edit source]

The vertices of a dodecagonal-truncated octahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:

Representations[edit | edit source]

A dodecagonal-truncated octahedral duoprism has the following Coxeter diagrams:

  • x12o o4x3x () (full symmetry)
  • x12o x3x3x ()
  • x6x o4x3x () (dodecagons as dihexagons)
  • x6x x3x3x ()