Tetrakis hexadecachoron

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Tetrakis hexadecachoron
Rank4
TypeUniform dual
Notation
Coxeter diagramm4m3o3o ()
Elements
Cells64 triangular pyramids
Faces32 triangles, 96 isosceles triangles
Edges24+64
Vertices8+16
Vertex figure16 tetrahedra, 8 triakis octahedra
Measures (edge length 1)
Dichoral angle
Central density1
Related polytopes
DualTruncated tesseract
Abstract & topological properties
Flag count1536
Euler characteristic0
OrientableYes
Properties
SymmetryB4, order 384
ConvexYes
NatureTame

The tetrakis hexadecachoron, also known as the triangular-pyramidal hexacontatetrachoron, is a convex isochoric polychoron with 64 triangular pyramids as cells. It can be obtained as the dual of the truncated tesseract.

As the tetrakis square duotegum, it is the square member of an infinite family of isochoric tetrakis duotegums.

It can also be obtained as the convex hull of a tesseract and a hexadecachoron, where the edges of the hexadecachoron are times the length of those of the tesseract. Varying the hexadecachoron's edge length to be anything more than times that of the tesseract gives a fully symmetric variant of this polychoron.