Tetrahedron atop truncated tetrahedron

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Tetrahedron atop truncated tetrahedron
Rank4
TypeSegmentotope
Notation
Bowers style acronymTetatut
Coxeter diagramxx3ox3oo&#x
Elements
Cells1+4 tetrahedra, 4 triangular cupolas, 1 truncated tetrahedron
Faces4+4+12 triangles, 6 squares, 4 hexagons
Edges6+6+12+12
Vertices4+12
Vertex figures4 triangular prisms, edge lengths 1 (base) and 2 (sides)
 12 skewed triangular pyramids, edge lengths 1 (base) and 2, 3, 3 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTet–3–tricu: 120°
 Tricu–4–tricu: 90°
 Tet–3–tut: 60°
 Tut-6-tricu: 60°
Height
Central density1
Related polytopes
ArmyTetatut
RegimentTetatut
DualTetrahedral-triakis tetrahedral tegmoid
ConjugateNone
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryA3×I, order 24
ConvexYes
NatureTame

Tetrahedron atop truncated tetrahedron, or tetatut, is a CRF segmentochoron (designated K-4.56 on Richard Klitzing's list). As the name suggests, it consists of a tetrahedron and a truncated tetrahedron as bases, connected by 4 further tetrahedra and 4 triangular cupolas.

It can be obtained as a segment of the rectified tesseract, which can be formed by attaching these segmentochora to both bases of the truncated tetrahedral cupoliprism.

Vertex coordinates[edit | edit source]

The vertices of a tetrahedron atop truncated tetrahedronsegmentochoron of edge length 1 are given by:

  • and all even sign changes of first three coordinates
  • and all permutatoins and even sign changes of first three coordinates

External links[edit | edit source]