Dodecagonal-truncated tetrahedral duoprism

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Dodecagonal-truncated tetrahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymTwatut
Coxeter diagramx12o x3x3o ()
Elements
Tera4 triangular-dodecagonal duoprisms, 12 truncated tetrahedral prisms, 4 hexagonal-dodecagonal duoprisms
Cells48 triangular prisms, 48 hexagonal prisms, 12 truncated tetrahedra, 6+12 dodecagonal prisms
Faces48 triangles, 72+144 squares, 48 hexagons, 12 dodecagons
Edges72+144+144
Vertices144
Vertex figureDigonal disphenoidal pyramid, edge lengths 1, 3, 3 (base triangle), 2+3 (top), 2 (side edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTuttip–tut–tuttip: 150°
 Titwadip-twip-hitwadip:
 Titwadip–trip–tuttip: 90°
 Hitwadip-hip-tuttip: 90°
 Hitwadip–twip–hitwadip:
Central density1
Number of external pieces20
Level of complexity30
Related polytopes
ArmyTwatut
RegimentTwatut
DualDodecagonal-triakis tetrahedral duotegum
ConjugateDodecagrammic-truncated tetrahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryA3×I2(12), order 576
ConvexYes
NatureTame

The dodecagonal-truncated tetrahedral duoprism or twatut is a convex uniform duoprism that consists of 12 truncated tetrahedral prisms, 4 hexagonal-dodecagonal duoprisms, and 4 triangular-dodecagonal duoprisms. Each vertex joins 2 truncated tetrahedral prisms, 1 triangular-dodecagonal duoprism, and 2 hexagonal-dodecagonal duoprisms.

Vertex coordinates[edit | edit source]

The vertices of a dodecagonal-truncated tetrahedral duoprism of edge length 1 are given by all permutations and even sign changes of the last three coordinates of:

Representations[edit | edit source]

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

  • x12o x3x3o (full symmetry)
  • x6x x3x3o () (A3×G2 symmetry, dodecagons as dihexagons)

External links[edit | edit source]

Klitzing, Richard. "n-tut-dip".