Amide bonds -NH-CO- preferentially exist in trans conformations, the cis conformation being thermodynamically unfavored with respect to the trans by about 2 kcal/mol. Yet, the main reason most proteins or peptides cannot be made from cis-peptide plaques only lies in that connecting them into open chains appears to be sterically impracticable. It is possible, however, to build all-cis cyclic peptides in which all cis-plaques are efficiently locked. The present work examines, through quantum calculations, the structural and energetic issues associated with these peculiar arrangements. Systematic exploration at DFT-B3LYP level of the potential-energy surfaces for all-cis cyclopolyglycines cG(n)(c) (n = 2-10,15), and to a lesser extent, for all-cis cyclopolyalanines and all-cis cyclopolyphenylalanines confirms that all these structures are true minima. Optimal ring size occurs around eight peptide units, resulting in planar cG(7)(c), cG(8)(c), and cG(g)(c). 7 8 91 In smaller systems, the ring strain is relieved through nonplanar cup-like distortions, particularly in cG(6)(c).. From 10 peptide units and beyond, the ring framework distorts into a saddle-edge shape. These molecules disclose some molecular flexibility, as combinatorial tilting of the plaques may give sets of minima close in energy. Indexes based on isodesmic reactions are used to estimate the energy for joining all-cis or alltrans plaques into cyclic peptides. One of them, the mean plaque-junction energy (MPJE) suggests that within sensible sizes from six peptide units and beyond, all-cis plaque association is almost equally favorable as all-trans one. The frame of radiating cis-amide bonds can be considered as defining a new kind of peptidic material, endowed with specific self-assembling properties.