Double pyramid
A pyramid of edge of size 2 contains six pyramids of edge size one... and holes. Four regular tetrahedra of side one fit in there.
This shows that the volume of the great pyramid, which is worth eight small pyramids, is equivalent to the volume of six pyramids and four tetrahedra. So two tetrahedra are worth one pyramid, which is also a half octahedron.
Encuentre estas igualdades de volumen analíticamente (¡buena suerte!).