A series of novel non-ionic amphiphiles with dendritic oligoglycerol head groups of different generations ([G1]-[G3]) and lipophilic/fluorophilic tail segments, comprising single or double tail alkyl chains, C8F17-perfluoro rod segments as well as flexible spacer groups of different lengths were designed and synthesized. We expected that the differences in the size of the dendritic head groups in combination with perfluorinated segments would have an impact on the supramolecular structures formed in aqueous solution if compared with the hydrogenated analogues. Investigating the self-assembly behavior mainly by cryogenic transmission electron microscopy (cryo-TEM) and cryo-electron tomography (cryo-ET) we found as a new result the formation of perforated bilayer vesicles (stomatosomes) and bicontinuous network structures. Surprisingly, we have observed stomatosome formation by self-assembly of single component fluorinated dendritic amphiphiles. These assembly structures turned out to be extremely robust against harsh conditions, although there are strong indications that they represent non-equilibrium structures, which eventually transform into a bicontinuous cubic network structure of double diamond symmetry. In general, the molecular asymmetry of amphiphiles tuned by chemical design induced the expected trend from spherical micelles through worm-like micelles to perforated bilayers and three-dimensional network structures.