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Short peptides have emerged as versatile building blocks for supramolecular structures and hydrogels. In particular, the presence of aromatic amino acid residues and/or aromatic end groups is generally considered to be a prerequisite for initiating aggregation of short peptides into nanotubes or cross β-sheet type fibrils. However, the cationic GAG tripeptide surprisingly violates these rules. Specifically, in water/ethanol mixtures, GAG peptides aggregate into very long crystalline fibrils at temperatures below 35 °C where they eventually form a spanning network structure and, thus, a hydrogel. Two gel phases are formed in this network, and they differ substantially in chirality and thickness of the underlying fibrils, their rheological parameters, and the kinetics of oligomerization, fibrilization, and gel formation. The spectroscopic data strongly suggests that the observed fibrils do not exhibit canonical cross β-sheet structures and are indicative of a yet unknown secondary conformation. To complement our unusual experimental observations in this perspective article, we performed large-scale DFT calculations to probe the geometry and spectroscopic properties of these GAG oligomers. Most importantly, our experimental and computational results yield rather unconventional structures that are not reminiscent of classical cross-β-sheet structures, and we give two extremely likely candidates for oligomer structures that are consistent with experimental amide I′ profiles in IR and vibrational circular dichroism (VCD) spectra of the two gel phases.