foliation

noun

1. (countable, uncountable)The process of forming into a leaf or leaves.
2. (countable, uncountable)The process of forming into pages; pagination.
3. (countable, uncountable)The numbering of the folios of a manuscript or a book.
4. (countable, uncountable)The manner in which the young leaves are disposed within the bud.
5. (countable, uncountable)The act of beating a metal into a thin plate, leaf, foil, or lamina.
6. (countable, uncountable)The act of coating with an amalgam of tin foil and quicksilver, as in making looking-glasses.
7. (countable, uncountable)The enrichment of an opening by means of foils, arranged in trefoils, quatrefoils, etc.; also, one of the ornaments.

   “The house was a big elaborate limestone affair, evidently new. Winter sunshine sparkled on lace-hung casement, on glass marquise, and the burnished bronze foliations of grille and door.”

8. (countable, uncountable)The property, possessed by some crystalline rocks, of being divided into plates or layers, due to the cleavage structure of one of the constituents, as mica or hornblende. It may sometimes include slaty structure or cleavage, though the latter is usually independent of any mineral constituent, and transverse to the bedding, it having been produced by pressure.

   “Formation of alteration minerals in the host rock during deformation within the shear zone is indicated by the parallel foliation within the secondary micaceous minerals and the unmineralized host schist.”

   “The dominant strike orientation of both bedding and foliation of Vermont bedrock is north or northeasterly.”

   “They show that curved inclusion trails may form even with no coupling, as the porphyroblast overgrows foliation that is deflected around it.”

   “In sedimentary rocks, the magnetic foliation results from a combination of depositional processes and diagenetic compaction.”

9. (countable, uncountable)A set of submanifolds of a given manifold, each of which is of lower dimension than it, but which, taken together, are coextensive with it.

   “Historically, the formalism which first arose for the material we discuss is that of measured foliations in surfaces.”

   “We will show that every closed 3-manifold has a foliation of codimension one. In 1952, G. Reeb published his construction of a foliation of the 3-sphere. About twelve years later, W. Lickorish [123] exhibited foliations of codimension one on every closed, orientable 3-manifold.”

   “The simplest example of a foliation is provided by a single submersion F : M → N, M and N being manifolds.”