From a practical viewpoint, the various motifs found on “modern” cut glass, that is, cut glass produced since the seventeenth century (the Romans were doing this even earlier!), can be grouped into three main types of cutting. Each type is produced by a stone cutting wheel that grinds the surface of the glass into either (a) a flat surface, (b) a depressed surface, or (c) a grooved surface. These three surfaces are produced by cutting wheels with edges (faces) that have three corresponding profiles: (a) a flat, or nearly flat, edge that results in facets (flutes, panels), (b) a convex edge that results in bullseyes (olives, etc.), or (c) a V-shaped, or mitered, edge that results in grooves that are V-shape in cross-section, miter cuts (splits, etc.).
The profiles of these three basic types can be modified considerably depending upon the cutting that is required. Michael Manginella, in a lecture to the American Cut Glass Association in 2005, displayed a poster that illustrates seven different profiles: flat (sharp strap), convex (punty, olive), offset convex, concave, miter, offset miter, and gang wheel (The Hobstar, Vol. 28, No. 2, p. 4819 (Oct 2005). Even this number is insufficient for some tasks, however. For example, to replicate the miter cutting that forms the basic design of Hawkes’ Pueblo pattern, it is necessary for the cutter to modify his wheel’s profile to such an extent that that he produces one that is unique. Nevertheless, the vast majority of cutting can be carried out by using wheels with the three basic profiles: flat, convex, and miter.
Some useful references:
Basic cutting types: Elville 1953; Elville 1960, pp. 172-90; Elville 1967, pp. 65-71. Also see specific entries in Newman 1977.
Detailed early history of engraving and cutting: Charleston, R. J., 1964: Wheel-engraving and -cutting: some early equipment. 1. Engraving, Journal of Glass Studies, Vol. 6, pp. 83-100. Charleston, R. J., 1965: Wheel engraving and -cutting: some early equipment. 2. Water-power and cutting, Journal of Glass Studies, Vol. 7, pp. 41-54