Colloidal particles equipped with two, three, or four negatively charged patches, which endow the particles with 2-fold, 3-fold, or tetrahedral symmetries, form 1D chains, 2D layers, and 3D packings when polarized by an AC electric field. Two-patch particles, with two patches on opposite sides of the particle (2-fold symmetry) pack into the cmm plane group and 3D packings with I4mm space group symmetry, in contrast to uncharged spherical or ellipsoidal colloids that typically crystallize into a face-centered ABC layer packing. Three-patch particles (3-fold symmetry) form chains having a 21 screw axis symmetry, but these chains pair in a manner such that each individual chain has one-fold symmetry but the pair has 21 screw axis symmetry, in an arrangement that aligns the patches that would favor Coulombic interactions along the chain. Surprisingly, some chain pairs form unanticipated double-helix regions that result from mutual twisting of the chains about each other, illustrating a kind of polymorphism that may be associated with nucleation from short chain pairs. Larger 2D domains of the three-patch particles crystallize in the p6m plane group with alignment (with respect to the field) and packing densities that suggest random disorder in the domains, whereas four-patch particles form 2D domains in which close-packed rows are aligned with the field.