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Originally Posted by danieltalis
No, the octahedron on it's own is not a spacefiller. Coupled with a tetrahedron there is a spacefilling situation.
There are only five known polyhedra with regular faces that are spacefillers and the cube is the only Platonic solid.
A spacefiller packs space entirely when stacked against itself.
Why is this important?
Because metaphysically, polyhedral shapes are potent. They are the energy building blocks of space. The more primal the better and the tetrahedron, the octahedron and the cube are the most primal.
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Thank you danieltalis for correcting me, and providing that interesting information.