Cell-penetrating peptides (CPPs), such as the HIV TAT peptide, are able to translocate across cellular membranes efficiently. A number of mechanisms, from direct entry to various endocytotic mechanisms (both receptor independent and receptor dependent), have been observed but how these specific amino acid sequences accomplish these effects is unknown. We show how CPP sequences can multiplex interactions with the membrane, the actin cytoskeleton, and cell-surface receptors to facilitate different translocation pathways under different conditions. Using "nunchuck" CPPs, we demonstrate that CPPs permeabilize membranes by generating topologically active saddle-splay ("negative Gaussian") membrane curvature through multidentate hydrogen bonding of lipid head groups. This requirement for negative Gaussian curvature constrains but underdetermines the amino acid content of CPPs. We observe that in most CPP sequences decreasing arginine content is offset by a simultaneous increase in lysine and hydrophobic content. Moreover, by densely organizing cationic residues while satisfying the above constraint, TAT peptide is able to combine cytoskeletal remodeling activity with membrane translocation activity. We show that the TAT peptide can induce structural changes reminiscent of macropinocytosis in actin-encapsulated giant vesicles without receptors.