Hexakis tesseract

Hexakis tesseract
(OFF file)
Rank	4
Type	Uniform dual
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	$\arccos \left(-{\frac {4}{5}}\right)\approx 143.13010^{\circ }$
Central density	1
Related polytopes
Dual	Truncated hexadecachoron
Abstract & topological properties
Flag count	1536
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 ${\frac {3{\sqrt {2}}}{4}}\approx 1.06066$ times the length of those of the tesseract. Varying the hexadecachoron's edge length to be anywhere between ${\frac {\sqrt {2}}{2}}\approx 0.70711$ and ${\sqrt {2}}\approx 1.41421$ times that of the tesseract gives a fully symmetric variant of this polychoron.