a tetrahedral interstice
The smaller of the two gaps in a close-packed anion stack is the tetrahedral interstice. Here a cation is hugged by just four anions arranged at the corners of a tetrahedron, a little three-sided pyramid, with the cation at its centre. Because there are only four neighbours, the coordination number is 4, and the pocket is tighter than an octahedral hole, so it suits smaller cations.
The geometry says a tetrahedral hole just fits a cation whose radius is 0.225 times the anion radius, so radius ratios below about 0.414 favour four-fold coordination. These holes are twice as plentiful as octahedral ones: every anion in the close-packed array is associated with two tetrahedral holes, one pointing up and one pointing down. In a face-centred-cubic cell that means eight tetrahedral holes, at the quarter positions inside the cube, versus four octahedral holes.
Fill half of the tetrahedral holes in an FCC anion array and you get zinc blende (cubic SiC, GaAs); do the same in an HCP array and you get wurtzite (AlN, ZnO, GaN). Fill all of them and you get the fluorite or antifluorite structure; fill just one-eighth and you help build spinel. Honest caveat: tetrahedral coordination is often a sign of covalent, directional bonding (the sp3 bonds of carbon and silicon), not merely a small radius ratio, so many tetrahedral ceramics are better understood through bonding than through sphere-packing alone.
In cubic silicon carbide (beta-SiC) each silicon atom sits in a tetrahedral pocket of four carbons and each carbon in a tetrahedral pocket of four silicons, the same 4:4 tetrahedral framework as diamond, but with two kinds of atom.
Four anions around a cation: coordination number 4.
There are twice as many tetrahedral holes as octahedral holes, but they are smaller. A cation too big for a tetrahedral pocket will push its four neighbours apart or simply refuse to sit there and take an octahedral site instead.