a tectosilicate

Take the sharing all the way: let every tetrahedron share all four of its corners, and the sheets close up into a rigid, three-dimensional scaffold reaching in every direction. That is a tectosilicate, or framework silicate (from the Greek tekton, builder). There are no isolated islands, no free ends, no easy cleavage plane; the structure is one continuous, interlocked cage of tetrahedra. Quartz and the feldspars are the two great framework families, and together they make up more than half the Earth's crust.

When every oxygen bridges two silicons, each oxygen is shared equally, so the formula collapses to the simplest silicate stoichiometry of all: SiO2, a Si:O ratio of exactly 1:2. Pure silica frameworks such as quartz are electrically neutral all by themselves and need no extra cations. But the framework can also be doped: swap some Si4+ for Al3+ and each swap leaves the cage one negative charge short, a deficit made up by parking a large cation, K+, Na+, or Ca2+, in the roomy channels of the framework. That is exactly how the feldspars (KAlSi3O8, NaAlSi3O8, CaAl2Si2O8) and the porous zeolites are built.

Framework silicates are the most polymerised, most refractory, and often the most rigid silicates. Their open cages give quartz its distinctive alpha-beta transformation on heating and give feldspar its role as a flux that melts to a stiff glass in porcelain. The channels in the aluminosilicate frameworks are also why zeolites can act as molecular sieves and ion exchangers. So framework does not mean dense and featureless; the same all-corners-shared rule builds both the hardest quartz and the most cavernous, sponge-like zeolites.