Tetrakis hexadecachoron

Tetrakis hexadecachoron
(OFF file)
Rank	4
Type	Uniform dual
Space	Spherical
Notation
Coxeter diagram	m4m3o3o ()
Elements
Cells	64 triangular pyramids
Faces	32 triangles, 96 isosceles triangles
Edges	24+64
Vertices	8+16
Vertex figure	16 tetrahedra, 8 triakis octahedra
Measures (edge length 1)
Dichoral angle	$\arccos\left(-\frac{2+3\sqrt2}7\right) \approx 153.10105^\circ$
Central density	1
Related polytopes
Dual	Truncated tesseract
Abstract & topological properties
Flag count	1536
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	Yes
Nature	Tame

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 $1+\sqrt2 \approx 2.41421$ times the length of those of the tesseract. Varying the hexadecachoron's edge length to be anything more than $\frac{3\sqrt2}{2} \approx 2.12132$ times that of the tesseract gives a fully symmetric variant of this polychoron.