A helicoid is a non-developable surface swept out by a line (the generator) which rotates with constant sense about another, non-parallel line (the heliaxis) whilst moving parallel to that line in a constant direction. Torsion may produce helicoids, though this is not a necessity. Previous references to helicoids and helices in structural geology are reviewed, and the basic properties of helicoids are compared with those of cylindrical and conical surfaces. A map and stereogram technique is developed for the recognition of nested (initially parallel, equally rotated, coaxial) macroscopic helicoids. The typically sigmoidal outcropping traces of nested helicoids show dip-direction reversals along trend. On stereograms, linear loci, each representing the poles from a single helicoid trace, diverge from a common pole. A nested set of macroscopic helocoidal cleavage surfaces from the Hill End Trough, southeastern Australia, are modelled and interpreted to have formed in two stages of torsion associated with accommodation of an adjacent granitoid intrusion. The volume affected by torsion is bound by curviplanar scissor faults. Helicoids may be found associated with: rotational porphyroblasts, deformed cylindrical bodies or strip-like surfaces (e.g. intrafolial fold axial planes), cylindrical diapirs with helical flow patterns, cylindrical scissor-faults, ductile shear zones, zones of constrictional strain, and en échelon segmented dykes and fracture planes.
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