Tetrahedral-hexadecachoric duoprism

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Tetrahedral-hexadecachoric duoprism
Rank7
TypeUniform
Notation
Bowers style acronymTethex
Coxeter diagramx3o3o o4o3o3x ()
Elements
Exa16 tetrahedral duoprisms, 4 triangular-hexadecachoric duoprisms
Peta32+64 triangular-tetrahedral duoprisms, 6 hexadecachoric prisms
Tera24+96 tetrahedral prisms, 128 triangular duoprisms, 4 hexadecachora
Cells8+64 tetrahedra, 96+192 triangular prisms
Faces32+128 triangles, 144 squares
Edges48+96
Vertices32
Vertex figureOctahedral tettene, edge lengths 1 (base octahedron and top triangle) and 2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Diexal anglesTetdip–tratet–tetdip: 120°
 Trahex–tratet–tetdip: 90°
 Trahex–hexip–trahex:
HeightsHex atop trahex:
 Tetdip atop tet-dual tetdip:
Central density1
Number of external pieces20
Level of complexity35
Related polytopes
ArmyTethex
RegimentTethex
DualTetrahedral-tesseractic duotegum
ConjugateNone
Abstract & topological properties
Flag count322560
Euler characteristic2
OrientableYes
Properties
SymmetryB4×A3, order 9216
ConvexYes
NatureTame

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]