a-sheet has been proposed as the main constituent of the prefibrillar intermediate during amyloid formation. Here the helical parameters of the a-sheet strand are calculated from average main-chain dihedral angles reported from molecular dynamics simulations. It is an almost linear polypeptide that forms a right-handed helix of about 100 Å diameter, with 100 residues and a rise of 30 Å per turn. The strands are curved but untwisted, which implies that neighboring strands need not coil to make interstrand hydrogen bonds. This suggests that compared to ß-sheets in native folded proteins, a-sheets can be larger and stack more easily to create extensive 3D blocks. It is shown that a-sheet is related to a category of structures termed “mirror” structures. Mirror structures have repetitive pairs of main-chain dihedral angles at residues i and i+1 that satisfy the condition ?i+1 = -?i, ?i+1 = -?i. They are uniquely identified by the two orientations of their peptide planes, specified by ?i and ?i. Their side chains point alternately in opposite directions. Interestingly, their conformations are insensitive to ?i and ?i in that the pseudo dihedral angle formed by four consecutive Ca atoms is always close to 180°. There are two types: “ß-mirror” and “a-mirror” structure; ß-mirror structures relate to ß-sheet by small peptide plane rotations, of less than 90°, while a-mirror structures are close to a-sheet and relate to ß-sheet by ~180° peptide plane flips. Most mirror structures, and in particular the a-mirror, form wide helices with diameters 50–70 Å. Their gentle curvature, and therefore that of the a-sheet, arises from the orientation of successive peptide units causing the difference in the bond angles at the C and N atoms of the peptide unit to gradually change the direction of the chain. Proteins 2008. © 2007 Wiley-Liss, Inc.