Here, we report the synthesis and structure of three high-silica molecular sieves, SSZ-35, SSZ-36, and SSZ-39, that are prepared from a library of 37 different cyclic and polycyclic quaternized amine molecules that are used as structure-directing agents (SDAs). The size and shape of the quaternized amine molecules are purposely designed in order to obtain novel zeolite structures, and the synthesis of these molecules is presented. The selectivity for the three molecular sieve phases is found to depend on both the SDA and the degree of heteroatom lattice substitution of Al3+ or B3+ in the silicate framework. Molecular modeling is utilized to probe the effects of the nonbonded SDA/zeolite-framework interaction energy on the selectivity for the observed molecular sieve phase. The Rietveld refinement of the powder X-ray data confirms the structure of the SSZ-39 zeolite to be isomorphous with the aluminophosphate molecular sieve, SAPO-LS (AEI). The structure of SSZ-36 is found to possess a range of fault probabilities between the two-dimensional channel system, end-member polymorphs, ITQ-3 and RUB-13 (International Zeolite Association Codes ITE and RTH, respectively). The SSZ-35 structure is reported to contain a one-dimensional pore system possessing stacked cages circumscribed by alternating rings of 10 and 18 tetrahedral atoms (10- and 18-membered rings).