A survey of high-pressure silicates reveals 12 distinct high-density structural topologies with octahedral Si. Seven of these structure types - stishovite, perovskite, ilmenite, hollandite, calcium ferrite, pyrochlore and K2NiF4 type - contain only six-coordinated silicon. Other high-pressure silicates, including those with the garnet, pyroxene, wadeite, anhydrous phase B and phase B structures, contain both tetrahedral and octahedral Si. Five systematic trends among these dozen structures suggest the existence of other, as yet unobserved, possible mantle Si phases. The criteria are: (1) structures like rutile, hollandite and calcium ferrite formed from edge-sharing chains of silicon octahedra; (2) germanates synthesized at room pressure with octahedral Ge; (3) isomorphs of room-pressure oxides with 3+ or 4+ transition-metal cations; (4) high-pressure magnesium silicates related to room-pressure aluminates by the substitution 2Al –> Mg + Si; and (5) the homologous structures in system Mg-Si-O-H that includes phase B and anhydrous phase B. Each of these criteria can be used to predict other potential octahedral Si phases. Of special interest are predicted structure types that fulfill more than one criterion: diaspore-type (MgSi)O2(OH)2, aerugite-type Mg10Si3O16, sphene-type CaSi2O5, benitoite-type BaSi4O9, gibbsite-type MgSi(OH)6 and pseudobrookite-type Fe2SiO5.