Tetrahedral-hexadecachoric duoprism
Tetrahedral-hexadecachoric duoprism | |
---|---|
Rank | 7 |
Type | Uniform |
Notation | |
Bowers style acronym | Tethex |
Coxeter diagram | x3o3o o4o3o3x () |
Elements | |
Exa | 16 tetrahedral duoprisms, 4 triangular-hexadecachoric duoprisms |
Peta | 32+64 triangular-tetrahedral duoprisms, 6 hexadecachoric prisms |
Tera | 24+96 tetrahedral prisms, 128 triangular duoprisms, 4 hexadecachora |
Cells | 8+64 tetrahedra, 96+192 triangular prisms |
Faces | 32+128 triangles, 144 squares |
Edges | 48+96 |
Vertices | 32 |
Vertex figure | Octahedral tettene, edge lengths 1 (base octahedron and top triangle) and √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diexal angles | Tetdip–tratet–tetdip: 120° |
Trahex–tratet–tetdip: 90° | |
Trahex–hexip–trahex: | |
Heights | Hex atop trahex: |
Tetdip atop tet-dual tetdip: | |
Central density | 1 |
Number of external pieces | 20 |
Level of complexity | 35 |
Related polytopes | |
Army | Tethex |
Regiment | Tethex |
Dual | Tetrahedral-tesseractic duotegum |
Conjugate | None |
Abstract & topological properties | |
Flag count | 322560 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | B4×A3, order 9216 |
Convex | Yes |
Nature | Tame |
The tetrahedral-hexadecachoric duoprism or tethex is a convex uniform duoprism that consists of 4 triangular-hexadecachoric duoprisms and 16 tetrahedral duoprisms. Each vertex joins 3 triangular-hexadecachoric duoprisms and 8 tetrahedral duoprisms. It is a duoprism based on a tetrahedron and a hexadecachoron, and is thus also a convex segmentoexon, as a hexadecachoron atop triangular-hexadecachoric duoprism.
The tetrahedral-hexadecachoric duoprism can be vertex-inscribed into a demihepteract.
Vertex coordinates[edit | edit source]
The vertices of a tetrahedral-hexadecachoric duoprism of edge length 1 are given by all even sign changes of the first three coordinates, plus all permutations and sign changes of the last four coordinates, of:
Representations[edit | edit source]
A tetrahedral-hexadecachoric duoprism has the following Coxeter diagrams:
- x3o3o o4o3o3x (full symmetry)
- x3o3o x3o3o *e3o (D4×A3 symmetry)
External links[edit | edit source]
- Klitzing, Richard. "tethex".