We describe the synthesis of trihydroxylated cyclohexane β-amino acids from (-)-shikimic acid, in their cis and trans configuration, and the incorporation of the trans isomer into a trans-2-aminocyclohexanecarboxylic acid peptide chain. Subsequently, the hydroxyl groups were partially or totally deprotected. The structural study of the new peptides by FTIR, CD, solution NMR and DFT calculations revealed that they all fold into a 14-helix secondary structure, similarly to the homooligomer of trans-2-aminocyclohexanecarboxylic acid. This means that the high degree of substitution of the cyclohexane ring of the new residue is compatible with the adoption of a stable helical secondary structure and opens opportunities for the design of more elaborate peptidic foldamers with oriented polar substituents at selected positions of the cycloalkane residues.