Hexakis tesseract

Hexakis tesseract
Rank	4
Type	Uniform dual
Space	Spherical
Notation
Coxeter diagram	o4o3m3m
Elements
Cells	48 square pyramids
Faces	96 isosceles triangles, 24 squares
Edges	32+64
Vertices	8+16
Vertex figure	8 cubes, 16 triakis tetrahedra
Measures (edge length 1)
Dichoral angle	$\arccos\left(-\frac45\right) ≈ 143.13010°$
Central density	1
Related polytopes
Dual	Truncated hexadecachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	Yes
Nature	Tame

The hexakis tesseract, also known as the square-pyramidal tetracontoctachoron, is a convex isochoric polychoron with 48 square pyramids as cells. It can be obtained as the dual of the truncated hexadecachoron.

It can also be obtained as the convex hull of a tesseract and a hexadecachoron, where the edges of the hexadecachoron are $\frac{3\sqrt2}{4} ≈ 1.06066$ times the length of those of the tesseract. Varying the hexadecachoron's edge length to be anywhere between $\frac{\sqrt2}2 ≈ 0.70711$ and $\sqrt2 ≈ 1.41421$ times that of the tesseract gives a fully symmetric variant of this polychoron.