Tetrahedron atop truncated tetrahedron
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Tetrahedron atop truncated tetrahedron | |
---|---|
Rank | 4 |
Type | Segmentotope |
Notation | |
Bowers style acronym | Tetatut |
Coxeter diagram | xx3ox3oo&#x |
Elements | |
Cells | 1+4 tetrahedra, 4 triangular cupolas, 1 truncated tetrahedron |
Faces | 4+4+12 triangles, 6 squares, 4 hexagons |
Edges | 6+6+12+12 |
Vertices | 4+12 |
Vertex figures | 4 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 angles | Tet–3–tricu: 120° |
Tricu–4–tricu: 90° | |
Tet–3–tut: 60° | |
Tut-6-tricu: 60° | |
Height | |
Central density | 1 |
Related polytopes | |
Army | Tetatut |
Regiment | Tetatut |
Dual | Tetrahedral-triakis tetrahedral tegmoid |
Conjugate | None |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | A3×I, order 24 |
Convex | Yes |
Nature | Tame |
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]
- Klitzing, Richard. "tetatut".