Octakis icositetrachoron

The octakis icositetrachoron, also known as the triangular-pyramidal hecatonicenneacontadichoron, is a convex isochoric polychoron with 192 triangular pyramids as cells. It can be obtained as the dual of the truncated icositetrachoron.

It can also be obtained as the convex hull of two dually oriented icositetrachora, where one has edges exactly $$\frac{5\sqrt2}{6} ≈ 1.17851$$ times the length of those of the other. Any convex hull of two dual icositetrachora where one is more than $$\frac{3\sqrt2}{4} = 1.06066$$ times the edge length of the other gives a fully symmetric variant of this polychoron.

Variations
The octakis icositetrachoron has variants that remain isochoric under BC4 symmetry (called the great sphenoidal hecatonenneacontadichoron) and D4 symmetry (called the tetrahedral hecatonenneacontadichoron).