Small-pore zeolites with large cavities are attractive because they are well suited for applications in the field of gas separation, methanol-to-olefin (MTO) conversion, and selective catalytic reduction of NO emissions from diesel engines (SCR deNOx). Three such novel materials, SSZ-98, SSZ-105, and SSZ-112, are reported in this study. SSZ-98 is a high-silica ERI zeolite that was discovered by trial-and-error experimentation using 1,4-dimethyl-1,4-diazoniabicyclo[2.2.2]octane as the organic structure-directing agent (OSDA) and K+ as the inorganic cation. A molecular modeling study then revealed 7 novel thermodynamically more favorable OSDAs that were experimentally shown to produce SSZ-98, using kinetically favorable synthesis conditions that were established during its earlier discovery. The high-silica content that was promoted by using high-silica Y zeolites as reagents, along with the flexibility in tuning crystal size and morphology, offers considerable advantages for the application of this material. SSZ-105 is the first zeolite reported to show the intergrowth structure between ERI and LEV. Such an intergrowth was predicted by a careful structural analysis of the end members and then synthesized by a series of controlled experiments using N,N-dimethylpiperidinium as the OSDA. With the guidance of DIFFaX faulting analysis, it was found that when more of the LEV stacking is incorporated in the intergrowth structure, the product SiO2/Al2O3 ratio (SAR) becomes higher and the crystal size becomes larger. By investigating the synthesis boundary conditions of the phase selectivity for ERI, LEV, and ERI/LEV intergrowth, SSZ-105 covering a full range of intergrowth ratios between ERI and LEV could be synthesized. SSZ-112 is the first aluminosilicate zeolite with the AFT structure. With the assistance of molecular modeling, both 1-methyl-1-propylpiperidinium and 1-butyl-1-methylpyrrolidinium were identified as appropriate OSDAs to produce the CHA/AFX intergrowth structure. When another OSDA, hexamethonium, was combined with either of the two OSDAs in the synthesis, SSZ-112 with the AFT structure was surprisingly obtained. The development of these zeolites showed that the synthesis of small-pore zeolites with large cavities, including those with intergrowth structural features, could be rationalized if molecular modeling and structural analysis are used in combination with synthetic chemistry.