Hexakis tesseract

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 anything less than $$\sqrt2 ≈ 1.41421$$ times that of the tesseract (including having the two be the same edge length) gives a fully symmetric variant of this polychoron.