It takes both tetrahedra and octahedra to fill space indefinitely

Fig. 9-6. (a) Tetrahedra do not fit together.
(b) Tetrahedra rearranged vertex to vertex.
(c) A second row of tetrahedra is placed above the first, such that all tetrahedra meet vertex to vertex; the arrangement automatically creates octahedral cavities.
(d) Alternating tetrahedra and octahedra can fill space indefinitely.

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