Truncated tetrahedral prism

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Truncated tetrahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymTuttip
Coxeter diagramx x3x3o ()
Elements
Cells4 triangular prisms, 4 hexagonal prisms, 2 truncated tetrahedra
Faces8 triangles, 6+12 squares, 8 hexagons
Edges12+12+24
Vertices24
Vertex figureSphenoid, edge lengths 1, 3, 3 (base), 2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTrip–4–hip:
 Tut–6–hip: 90°
 Tut–3–trip: 90°
 Hip–4–hip:
Height1
Central density1
Number of external pieces10
Level of complexity12
Related polytopes
ArmyTuttip
RegimentTuttip
DualTriakis tetrahedral tegum
ConjugateNone
Abstract & topological properties
Flag count576
Euler characteristic0
OrientableYes
Properties
SymmetryA3×A1, order 48
ConvexYes
NatureTame

The truncated tetrahedral prism or tuttip is a prismatic uniform polychoron that consists of 2 truncated tetrahedra, 4 hexagonal prisms, and 4 triangular prisms. Each vertex joins 1 truncated tetrahedron, 1 triangular prism, and 2 hexagonal prisms. As the name suggests, it is a prism based on the truncated tetrahedron. As such it is also a convex segmentochoron (designated K-4.57 on Richard Klitzing's list).

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a truncated tetrahedral prism of edge length 1 are given by all permutations and even sign changes of the first three coordinates of:

Representations[edit | edit source]

A truncated tetrahedral prism has the following Coxeter diagrams:

  • x x3x3o (full symmetry)
  • xx3xx3oo&#x (bases considered separately)
  • x2s4o3x () (bases as snub)
  • xxx xux3oox&#xt (A2×A1 symmetry, triangular prism-first)
  • x(xu)(xu)x-3-x(xo)(oo)o-&#xr (A2 axial)
  • xxxx xuxo oxux&#xt (A1×A1×A1 axial, square-first)

External links[edit | edit source]