The octahedron has 6 vertices. The octahedron fractal grows in powers of 6. Six octahedra
can be put together to form another octahedron with volume removed. Six stage-1 octahedron
fractals can be put together to form a stage-2 octahedron fractal that still has the exterior
shape of an octahedron. This process can go on and on.
I keep emphasizing that the Platonic solids (the dodecahedron, cube, icosahedron, octahedron,
and tetrahedron) are the only polyhedra with this special property that allows them to be
connected to form another such structure with volume removed. No other polyhedra have this